-- Table structure for table `labelling1`
--

CREATE TABLE `labelling1` (
  `id` int(11) NOT NULL,
  `examYear` varchar(200) NOT NULL,
  `questions` longtext NOT NULL,
  `options` longtext NOT NULL,
  `answer` longtext NOT NULL,
  `explaination` longtext NOT NULL,
  `imageDir` varchar(500) NOT NULL,
  `topic` varchar(500) NOT NULL,
  `package_id` varchar(200) NOT NULL,
  `subject_id` varchar(200) NOT NULL
) ENGINE=InnoDB DEFAULT CHARSET=utf8mb4;

--
-- Dumping data for table `labelling1`
--

INSERT INTO `labelling1` (`id`, `examYear`, `questions`, `options`, `answer`, `explaination`, `imageDir`, `topic`, `package_id`, `subject_id`) VALUES
(1, '0', 'The period of a simple pendulum of length 80.0cm was found to have doubled when the length of the pendulum was increased by X. Calculate X.', '26.7cm~40.0cm~160.0cm~240.0cm', '240.0cm', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(2, '1', 'A body of mass 5kg movimg with a velocity of 30ms-1 due east is suddenly hit by another body and changes its velocity to 50ms-1 in the same direction. Calculate the magnitude of the impulse received.', '100Ns~150Ns~250Ns~400Ns', '100Ns', 'I = Ft = m(v - u)\n\n= 5(50 - 30) = 100', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(3, '2', 'Electric energy is measured in', 'ampere~coulomb~kilowatt-hour~kilowatt', 'kilowatt-hour', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(4, '3', 'A stone of mass 0.5kg is dropped from a height of 12m. Calculate its maximum kinetic energy. [g = 10ms-1]', '3.0J~6.0J~30.0j~60.0J', '60.0J', 'K.E = P.E = mgh\n\n= 0.5 x 10 x 12 = 60J', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(5, '4', 'A machine of efficiency 80% is used to lift a box. If the effort applied by the machine is twice the weight of the box. Calculate the velocity ratio of the machine', '0.5~0.63~0.8~1.6', '0.63', 'Y = \\(\\frac{M.A}{V.R} \\times \\frac{100}{1}\\)\n\n= \\(\\frac{\\frac{1}{2}}{V.R} \\times \\frac{100}{1}\\)\n\nV.R = 0.625', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(6, '5', 'A faulty thermometer registers 102.5oC t 100oC. If the thermometer has no zero hour, what will it register at 55oC?', '54.6oC~55.0oC~56.0oC~56.4oC', '56.4oC', 'x = \\(\\frac{102.5 \\times 55}{100}\\)\n\n= 56.375oC', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(7, '6', 'A rod of initial lenght 2m at a temperature of 25oC is heated to 80oC. Calculate the increase in length of the rod if its linear expansivity is 4.0 x 10-3K-1', '0.26m~0.44m~0.53m~0.84m', '0.44m', '\\(l_2 - l_1 = \\alpha l_1 (\\theta_2 - \\theta_1) = 4.0 \\times 10^{-3} \\times 2(80 - 25)\\)\n\n= 0.44m', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(8, '7', 'as a bicycle Tyre was being pumped up, it was noticed that contrary to Boyle\'s law the volume increased as the pressure increased. The best explanation of this is that Boyle\'s law is only true for', 'ideal gases~a fixed mass of gas~a mixture of gases~a gas at variable temperature', 'ideal gases', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(9, '8', 'It takes 4 minutes to boil a quantity of water using an electrical heating coil. How long will it take to boil the same quantity of water using the same coil if the current is doubled? [Neglect any external heat losses]', '8 minutes~4 minutes~2 minutes~1 minute', '2 minutes', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(10, '9', 'When table salt is added to ice, the melting point of the ice', 'is raised~is lowered~remains unchanged~is first raised, then lowered', 'is lowered', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(11, '10', 'Which of the following is used to measure relative humidity?', 'hydrometer~barometer~hypsometer~hygrometer', 'hygrometer', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(12, '11', 'Which of the following factors affect the rate of evaporation of a liquid? i. Exposed surface area ii Temperature of the surroundings iii. Thermal capacity of the liquid iv. Relative humidity of the surroundings', 'ii and iii only~ii, iii and iv only~i, iii and iv only~i, ii amd iv only', 'i, ii amd iv only', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(13, '12', 'The maximum displacement of a vibrating tunning fork is its', 'amplitude~frequency~period~wavelength', 'amplitude', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(14, '13', 'A boat is rocked by waves of speed 30ms-1 whose successive crest are 10m apart. Calculate the rate at which the boat recieves the waves', '30s-1~10s-1~3s-1~1s-1', '3s-1', 'F = \\(\\frac{v}{\\lambda} = \\frac{30}{10} = 3s^{-1}\\)', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(15, '14', 'Which of the following waves is not transverse', 'light waves~sound waves~sea waves~radio waves', 'sound waves', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(16, '15', 'Light travelling through a small pinhole usually does not make a shadow with a distinct sharp edge because of', 'diffraction~inteference~reflection~refraction', 'diffraction', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(17, '16', 'The angle of incidence of a ray of light on a plane mirror is 55o. Determine the angle between the reflected ray and the mirror', '35o~45o~55o~110o', '35o', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(18, '17', 'A concave mirror forms a magnified and errect image only when the object is placed', 'at the centre of curvature~at the focus~between the focus and the pole of the mirror~beyound the radius of curvature', 'between the focus and the pole of the mirror', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(19, '18', 'A thin lens is placed 50cm from an illustrated object. The image produced has linear magnification of \\(\\frac{1}{4}\\). Calculate the power of the lens in dioptres', '2.5D~5.0D~10.0D~25.0D', '10.0D', '\\(\\frac{1}{v} = \\frac{1}{u}\\)\n\nm = \\(\\frac{v}{u} = \\frac{1}{4} = \\frac{v}{50}\\)\n\nv = 12.5\n\nBut \\(\\frac{1}{v} + \\frac{i}{u} = \\frac{1}{f}\\)\n\n= \\(\\frac{1}{50} + \\frac{1}{12.5} = f\\)\n\nf = 10m\n\nP = \\(\\frac{100}{10} = 10D\\)', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(20, '19', 'Which of the following characteristics of light determines its colour?', 'velocity~wavelength~amplitude~intensity', 'wavelength', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(21, '20', 'Which of the following is not a part of the electro-magnetic spectrum?', 'x-rays~microwaves~infrared radiation~alpha rays', 'alpha rays', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(22, '21', 'Sound interference is necessary to produce the phenomenon of', 'beats~doppler effect~acoustic resonance~echo', 'beats', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(23, '22', 'A satellite in circular motion around the earth does not have', 'a gravitational force acting on it~a uniform velocity~an acceleration~a centripetal force acting on it', 'a uniform velocity', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(24, '23', 'When a conductor mounted on an insulating stand is charged and left for sometime, the conductor eventually loses all its charges. This is because the', 'electric charges evaporate from the surface of the conductor~charges are connected to earth~charges on the conductor are neutralized by opposite charges from the surrounding air~charges ionize the surrounding air', 'charges on the conductor are neutralized by opposite charges from the surrounding air', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(25, '24', 'An isolated metal sphere of radius R, carrying an electric charge Q, is situated in the medium of relative permitivity, Er. A test charge is placed at a point p, distance r from the surface of the sphere. Let Eo represent the permitivity of free space. The electric potential at p is given by the expression', '\\(\\frac{Q}{4 \\pi E_o E_r}\\)~\\(\\frac{Q}{4 \\pi E_o E_r (R +r)}\\)~\\(\\frac{Q}{4 \\pi E_o E_r(R - r)}\\)~\\(\\frac{Q}{4 \\pi E_o E_rR}\\)', '\\(\\frac{Q}{4 \\pi E_o E_rR}\\)', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(26, '25', 'An isolated metal sphere of radius R, carrying an electric charge Q, is situated in the medium of relative permitivity, Er. A test charge is placed at a point p, distance r from the surface of the sphere. Let Eo represent the permitivity of free space. The magnitude of the electric field intensity at P is given by the expression', '\\(\\frac{Q}{4 \\pi E_o E_r r^2}\\)~\\(\\frac{Q}{4 \\pi E_o E_r(R + r)^2}\\)~\\(\\frac{Q}{4 \\pi E_o E_r(R - r)^2}\\)~\\(\\frac{Q}{4 \\pi E_o E_rR^2}\\)', '\\(\\frac{Q}{4 \\pi E_o E_rR^2}\\)', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(27, '26', 'A resistor of resistance R is connected to a battery of negligible internal resistance. If a siilar resistor is connected in series with it the', 'effective resistance of the circuit is halved~total power dissipated is doubled~total current in the circuit is halved~terminal voltage is halved', 'total power dissipated is doubled', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(28, '27', 'A cell of e.m.f. 1.5V is connected in series with a resistor of resistance 3.0\\(\\Omega\\). A voltmeter connected across the cell registers 0.9V. Calculate the internal resistance of the cell', '2.0\\(\\Omega\\).~3.0\\(\\Omega\\).~5.0\\(\\Omega\\).~6.0\\(\\Omega\\).', '2.0\\(\\Omega\\).', '\\(\\frac{V}{R} = \\frac{E}{R + r}\\)\n\n\\(\\frac{0.9}{3} = \\frac{1.5}{3 + r}\\)\n\nr = 2\\(\\Omega\\).', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(29, '28', 'A wire of resistivity 4.40 x 10-5\\(\\Omega\\) cm has a cross sectional area of 7.50 x 10-4 cm2. Calculate the length of the wire that will be required to make a 4.0\\(\\Omega\\) resistor', '82.50 cm~68.18cm~15.90cm~11.95cm', '68.18cm', 'L = \\(\\frac{R.A}{e} = \\frac{4 \\times 7.50 \\times 106{-4}}{4.40 \\times 10^{-5}} = 68.18cm\\)', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(30, '29', 'A battery of e.m.f. 12.0V and internal resistance0.5\\(\\Omega\\) is connected to 1.5\\(\\Omega\\) and 4.0\\(\\Omega\\) series resistor. Calculate the terminal voltage of the battery.', '13.0V~11.0V~3.0V~1.0V', '11.0V', '\\(\\frac{V}{R} = \\frac{E}{R + r} = \\frac{V}{5.5} = \\frac{12}{6}\\)\n\nv = 11.0V', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(31, '30', 'If the direction of the curent in a straight wire is reversed, the magnetic field', 'remains the same~becomes parallel to the wire~ceases to exist~is oppositely directed', 'is oppositely directed', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(32, '31', 'An inductor of inductance 1.0H is connected in series with a capacitor of capacitance 2.0\\(\\mu F\\) in an a.c. circuit. to resonate', '112.5Hz~225.0Hz~323.5Hz~707.1Hz', '112.5Hz', 'fo = \\(\\frac{1}{2 \\pi \\sqrt{LC}} = \\frac{1}{2 \\times 3.14 \\sqrt{1 \\times 2 \\times 10^{-6}}}\\)\n\n= 112.5Hz', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(33, '32', 'An ammeter connected to an a.c circuit records 5.5. The peak current in the circuit is', '7.8A~7.1A~3.8A~3.5A', '7.8A', '\\(I_o = I_{rms} \\times \\sqrt{2} = 5.5 \\times 1.41 = 7.8A\\)', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(34, '33', 'Two isotopes of uranium are designed as \\(^{238}U\\) and \\(^{235}U\\). The numbers 238 and 235 represent their', 'atomic numbers~nucleon numbers~proton numbers~neutron numbers', 'nucleon numbers', 'neutrons + protons = the nucleus or mass numbers.\n\nU-238 has mass number(proton 92 + neutron 146=238)\nU-235 has mass number (proton 92 + neutron 143 =235)', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(35, '34', 'The main difference between between x-rays and \\(\\gamma-rays\\) lies in their', 'ionizing ability~absorption rate~mode of production~mode of propagation', 'mode of propagation', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(36, '35', 'An electron of mass 9.1 x 10-31 kg moves with a speed of 107ms-1. Calculate the wavelength of the associates wave[h = 6.6 x 10-34Js]', '9.0 x 10-24m~4.55 x 10-17m~7.25 x 10-11m~6.20 x 10-8m', '7.25 x 10-11m', '\\(\\lambda = \\frac{hc}{\\frac{1}{2}mv^2}\\)\n\n= \\(\\frac{6.6 x 10^{-34} \\times 3 \\times 10^8}{0.5 \\times 9.1 \\times 10^{-3} (10^7)^2}\\)\n\n= 7.25 x 10-11m', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(37, '36', 'Which of the following properties of a long steel bar would alter if the bar were melted, recast into a cube and allowed to cool to its original temperature?', 'sensity~volume~specific heat capacity~electrical resistance', 'volume', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(38, '37', 'Which of the following instruments is best for measuring the diameter of a thin constantan wire?', 'callipers~metre rule~micometer screw guage~vernier callipers', 'micometer screw guage', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(39, '38', 'What is the density of a fuel of relative density 0.72? [Density of water = 1000kg m-3]', '72 kgm-3~720 kgm-3~7200 kgm-3~72000 kgm-3', '720 kgm-3', 'P = 0.72 x 1000 = 720', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(40, '39', 'The types of motion which a cylindrical drum rolling down an inclined plane undergoes are', 'circular and translational~rotational and translational~rotational and circular~rectilinear and circular', 'rotational and translational', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(41, '40', 'Which of the following statements about static friction is correct? It', 'is independent of the nature of the surface in contact~depends on the area of surface in contact~depends on the relative motion between the surface in contact~depends on the weight of the moving body', 'depends on the relative motion between the surface in contact', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(42, '41', 'Which of the following statements about moving particle is correct?', 'if the resultant force acting on the particle is zero, then it is in dynamic equillibrium~If the resultant force acting on the acting on the particle is greater than zero, then it is moving with a uniform velocity~the rate of change of its momentum with time tales place in a direction opposite to that of its motion~the particle falling freely covers equal distances in equal time interval', 'the particle falling freely covers equal distances in equal time interval', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(43, '42', 'Two cars X and Y travelling in opposite directions along the same high way at uniform velocities 110 kmh-1 and 90kmh-1 respectively pass each other at a certain point. The velocity of X relative to Y at the time they pass each other is', '200 kmh-1~100 kmh-1~40 kmh-1~20 kmh-1', '200 kmh-1', 'R = 110 + 90 = 200', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(44, '43', 'The average speed of an object is determined by dividing the sum of its initial and final speeds by two only when the acceleration is', 'changing~uniform~increasing~decreasing', 'uniform', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(45, '44', 'a body is projected horizonatlly from the top of a cliff 45m above the ground. if the body lands at a distance 30m from the foot of the cliff, calculate the speed of projection. [g = 10ms-2]', '10ms-1~15ms-1~20ms-1~30ms-1', '30ms-1', 'V2 = U2 + 2gh \n\n= 02 + 2 x 10 x 45 = 30', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(46, '45', 'Which of the following statements best describes a rigid body? A body which', 'is not equally deformed~when deformed regains it shape~is brittle~when deformed remains deformed', 'is not equally deformed', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(47, '46', 'simple harmonic oscillator has a period of 0.02s and amplitude of 0.25m. Calculate the speed in ms-1 at the centre of the oscillation', '125\\(\\pi\\)~25.00\\(\\pi\\)~100.00 \\(\\pi\\)~400.00\\(\\pi\\)', '25.00\\(\\pi\\)', 'V = WX = \\(\\frac{2\\pi \\times 0.25}{0.02} = 25\\pi\\)', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(48, '47', 'A vertical string, suspended from a fixed point and having a small mass attached to the free end is set into oscillations. Which of the following statements about the system are correct? i. The potential energy of the mass is a minimum at the middle of the swing ii. Its kinetic energy is a maximum at the middle of the swing iii. The sum of the potential and kinetic energies is constant throughout the swing', 'i,ii and iii~i and ii only~ii and iii only~i and iii only', 'ii and iii only', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(49, '48', 'A moving body of mass 25.0kg undergoes a uniform retardation of 20.0ms-2. Calculate the magnitude of the retardating force', '1.25N~8.00N~45.00N~500.00N', '500.00N', 'F = MG \n\n= 25 x 20 = 500N', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(50, '49', 'Which of the following sources of energy is', 'i, ii and iii~i and ii only~i and iii only~ii and iii only', 'ii and iii only', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(51, '50', 'a machine is said to be a third class lever when the', 'load is between the fulcrum and effort~fulcrum is between the effort and the load~effort is between the fulcrum and load~fulcrum is directly below the load', 'effort is between the fulcrum and load', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(52, '51', 'a thermometer records 680 mmHg at steam point and 440 mmHg at ice point. The temperature it records at 380 mmHg is', '-25oC~-20oC~20oC~25oC', '-25oC', '\\(\\frac{440 - 380}{680 - 380} = \\frac{0 - x}{100 - x}\\) \n\n= -25oC', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(53, '52', 'The advantages of the thermoelectric thermometer include the following characteristics except that it', 'can measure rapidly changing temperatures~can measure high and low temperature~can measure high and low temperature almost at a point~is fairly sensitive', 'is fairly sensitive', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(54, '53', 'In a thermos flask, heat loss by radiation is minimizes by the', 'silvered surfaces~vacuum within the doubled walls~plastic stopper~cork support', 'silvered surfaces', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(55, '54', 'The pressure P, volume V, and absolute temperature T of a given mass of an ideal gas change simultaneously. Which of the followng equations is correct about the gas?', 'PV = \\(\\frac{constant}{T}\\)~\\(\\frac{P}{T} = Constant\\)~\\(\\frac{P}{V} = \\frac{constant}{T}\\)~\\(\\frac{I}{T} = \\frac{constant}{PV}\\)', '\\(\\frac{I}{T} = \\frac{constant}{PV}\\)', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(56, '55', 'Specific heat capacity 36.4 Jkg-1 K-1 of a body means that when 36.4J of heat energy is supplied to a body of', 'mass 100kg the temperature rises by 1k~mass 1kg, the temperature by 1000K~mass 1kg, the temperature rises by 1K~mass 100kg, the temperature rises by 1000k', 'mass 1kg, the temperature rises by 1K', 'The specific heat capacity of a body is the heat energy required to raise a body of mass 1kg through a temperature of 1K.', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(57, '56', 'The diagram above shoes three forces F1, F2 and F3, which of the following ewuations is correct?', 'F3 = F1 + F2~F2 = F1 + F3~F1 = F2 - F3~F1 = F2 + F3', 'F1 = F2 + F3', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(58, '57', 'An electric drill rated 400W is used to drill a hole in copper of mass 400g in 20s. Calculate the rise in temperature if all the heat produced is absorbed by the copper. [specific heat capacity of copper = 400Jkg-1K-1]', '100oC~75oC~50oC~45oC', '50oC', '\\(\\theta = \\frac{Pt}{MC} = \\frac{400 \\times 20}{0.4 \\times 400} = 50^o\\)', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(59, '58', 'A solid of mass 0.5kg initially at 50oC melts at 60oC. Calculate the quantity of heat required to melt it completely. [specific heat capacity of the solid =2.0KJ kg-1K-1][Specific latent heat of fusion of solid =1.0 KJ kg-1]', '1500J~10000J~10500J~15000J', '10500J', 'Q = ML + C\\(\\theta\\) \n\n= 0.5 x 1000 + 0.5 x 2000 x 10 \n\n= 10500', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(60, '59', 'Dew point is not affected by', 'temperature~wind~the amount of water vapour in the atmosphere~atmospheric pressure', 'atmospheric pressure', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(61, '60', 'A certain wave has a speed of 20ms-1. If the frequency of the wave is 0.25Hz, calculate the distance between successive crests of the wave', '5.0m~40.0m~50.0m~80.0m', '80.0m', '\\(\\lambda = \\frac{v}{f} = \\frac{20}{0.25} = 80\\)', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(62, '61', 'The ability of a wave to spread around corners is called', 'polarisation~dispersion~diffraction~reflection', 'diffraction', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(63, '62', 'The following devices use plane mirrors in their operations, except', 'periscope~sextant~kaleidoscope~binoculars', 'binoculars', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(64, '63', 'When an object is placed at the principal focus of a concave mirror, the location of the image formed is', 'between principal focus and pole~between principal focus and centre of curvature~at infinity~at centre of curvature', 'at infinity', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(65, '64', 'From the diagram, the correct equation for the refractive index n of the medium is', 'n = tan i~n = \\(\\frac{sin i}{sin 90^o}\\)~n = \\(\\frac{sin i}{cos (90^o - i)}\\)~n = sin 90oC', 'n = \\(\\frac{sin i}{sin 90^o}\\)', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(66, '65', 'A ray of light travels from air to water. The refeactive index of water is given by the expression', '\\(\\frac{\\text{velocity in water}}{\\text{velocity in air}}\\)~\\(\\frac{\\text{sine of angle of refraction}}{\\text{sine of angle of incidence}}\\)~\\(\\frac{\\text{apparent depth}}{\\text{real depth }}\\)~\\(\\frac{\\text{wavelength in air}}{\\text{wavelength in water}}\\)', '\\(\\frac{\\text{wavelength in air}}{\\text{wavelength in water}}\\)', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(67, '66', 'A lens that is thinner at the middle and thicher at the edges is', 'diverging~converging~plano-convex~converging meniscus', 'diverging', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(68, '67', 'Which of the following electromagnetic wave has the longest wavelength?', 'radio-waves~gamma rays~infrared waves~ultraviolet rays', 'radio-waves', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(69, '68', 'The amplitude of a sound wave determines its', 'frequency~quality~loudness~pitch', 'loudness', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(70, '69', 'As the air column of length L in an air pipe decreases, the frequency of the sationary wave emitted', 'decreases~increases~varies as L2~varies as \\(\\sqrt{L}\\)', 'decreases', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(71, '70', 'A positively charged glass rod is placed near the cap of a positively charged electroscope. The divergence of the leaf is observed to', 'decrease~increase~remain the same~increase and collapse immediately', 'increase', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(72, '71', 'Capacitors are used in the following devices, except', 'water pumping machines~ceiling fans~electric irons~television sets', 'electric irons', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(73, '72', 'Use the diagram above to calculate the current, I.', '0.60A~0.97A~1.03A~5.00A', '0.97A', '\\(\\frac{1}{R} = \\frac{1}{R_1} + \\frac{1}{R_2}\\)\n\n= \\(\\frac{1}{6} + \\frac{1}{4}\\)\n\nR = \\(\\frac{12}{5} = 2.5\\Omega\\)\n\nR = 2.4 + 10 = 12.4\n\nV = IR\n\nI = \\(\\frac{v}{R} = \\frac{12}{12.4} = 0.97\\)', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(74, '73', 'Determine the potential difference. V across the parallel resistors', '2.0V~2.3V~3.0V~0.7V', '2.3V', 'V = IR \n\n= 0.97 x 2.4 = 2.3V', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(75, '74', 'A galvanometer of internal resistance 50\\(\\Omega\\) and full scale deflection of 20 mA is converted into a voltmeter by connecting a resistor of resistance 1950\\(\\Omega\\) in series to it. Calculate the maximum voltage that can be read by the voltmeter', '20V~30V~38V~40V', '40V', 'V = IR1 + IR2 \n\n= 0.02 x 50 + 0.02 x 1950 = 40V', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(76, '75', 'In the wiring of houses, the fuse is connected to the wire coloured', 'blue~brown~yellow~yellow and green', 'brown', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(77, '76', 'Which of the following factors does not affect the electric resistance of wire?', 'length~mass~temperature~cross-sectional area', 'mass', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(78, '77', 'Which of the following factors will increase the sensitivity of moving coil meter?', 'strong spring~low numbers of turns~small area of coil~soft iron core', 'soft iron core', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(79, '78', 'In order to prevent bar magnets from losing their strength, they are stored wih keepers such that the two bars are placed with', 'like poles facing each other and the keepers placed between them~like poles facing each other and the keepers placed between them~unlike poles facing each other and the keepers placed at their ends~unlike poles facing each other and the keepers placed between them', 'unlike poles facing each other and the keepers placed at their ends', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(80, '79', 'The energy, E stored in an inductor of inductance L when current I passes through it is given by the equation', 'E = \\(\\frac{1}{2} LI^2\\)~E = LI2~E \\(\\frac{1}{2}LI\\)~E = \\(\\frac{1}{2} L^2I\\)', 'E = LI2', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(81, '80', 'The resonant frequency of an a.c circuit is 1000 kHz. If each of the capacitance and inductance in the circuit is reduced by 50%, and no other changes are made, the resonant frequency will become', '250kHz~750kHz~1000kHz~2000kHz', '2000kHz', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(82, '81', 'Eddy currents can be reduced by', 'using coil of high resistance~winding the coil on a soft iron core~creating holes in the metal plates~using coil of low resistance', 'creating holes in the metal plates', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(83, '82', 'an electron moves with a speed of 2.0 x 106ms-1 in a straight line. Calculate the wave length of the electron wave. [mass of an electron = 9.1 x 10-31 kg][Planck\'s constant = 6.6 x 10-34Js]', '3.63 x 10-19m~6.51 x 10-9m~4.24 x 10-8m~7.25 x 10-8m', '4.24 x 10-8m', '\\(\\lambda = \\frac{hc}{\\frac{1}{2}mv^2} = \\frac{6.6 \\times 10^{-38} \\times 3 \\times 10^8}{\\frac{1}{2} \\times 9.1 \\times 10^{-31} (2 \\times 10^6)^2}\\)\n\n= 4.24 x 10-8m', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(84, '83', 'Oxidation of the filament in a light bulb is prevented by the introduction of', 'hydrogen~oxygen~argon~mercury vapour', 'argon', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(85, '84', 'In a cathode ray tube, the function of the x-plates is to', 'deflect the electron beam horizontally~deflect the electron beam vertically~reflect the electron beam~generate sinusoid waves', 'deflect the electron beam horizontally', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(86, '85', 'A nuclide represented as \\(^{70}_{32}X\\) has a neutron-proton ratio of', '0.5~0.8~1.2~1.5', '1.2', '\\(\\frac{38}{32} = 1.2\\)', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(87, '86', 'Neutrons are used to induce artificial radioactivity because they', 'are energetic~have no charge~have no mass~are ionizing', 'have no charge', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(88, '87', 'Which of the following statements is not correct?', '~molecules of ice, water and water vapour do not differ in the structure of their molecules~molecules of water vapour attract each other with forces far less than the forces of attraction between water molecules~water is less compressible than water vapour', '', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(89, '88', 'The density P of a spherical ball of diameter d and mass m is given by', 'P = \\(\\frac{3m}{4 \\pi d^3}\\)~p = 4\\(\\pi md^3\\)~p = \\(\\frac{6m}{\\pi d^3}\\)~p = \\(\\frac{3m}{2 \\pi d^3}\\)', 'p = \\(\\frac{6m}{\\pi d^3}\\)', 'p = \\(\\frac{M}{V} = \\frac{M}{\\frac{4}{3} \\pi (\\frac{d}{\\pi})^3}\\)\n\n= \\(\\frac{6m}{\\pi d^3}\\)', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(90, '89', 'A metal rod of density 7000 kgm-3 and cross-sectional area of 0.001257m2 has a mass of 1.76kg. Calculate its length.', '0.20m~0.25m~0.40m~0.50m', '0.20m', 'P = \\(\\frac{M}{AL}\\)\n\nL = \\(\\frac{M}{CA}\\)\n\n= \\(\\frac{1.76}{7000 \\times 0.001257}\\)\n\n= 0.2m', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(91, '90', 'The pressure in a liquid', 'is the same at all points in the liquid~decreases with depth~is the same in all directions at a given point~is equal to the atmospheric pressure', 'is the same in all directions at a given point', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(92, '91', 'The property of a fluid that is used to determine its suitability as a lubricant is its', 'capillarity~viscocity~surface tension~relative density', 'viscocity', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(93, '92', 'The area under a velocity-time graph represents', 'final velocity attained~distance covered~acceleration~workdone', 'distance covered', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(94, '93', 'In the absence of gravitational force, the weight of the body is', 'its mass~zero~its density~its volume', 'zero', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(95, '94', 'Which of the following propeties is not considered in choosing mercury as a thermomemetric liquid?', 'density~expansivity~conductivity~opacity', 'density', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(96, '95', 'A stone of mass 300g is released from rest from the top of a bulding of height 100m. Determine the kinetic energy gained by the stone when it is a quarter way down from the point of release.[g = 10 ms-2]', '750.0J~225.0J~75.0J~22.5J', '75.0J', 'K.E = P.E = mgh \n\n= 0.3 x 10 x 100 - 0.3 x 10 x 75 \n\n= 75J', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(97, '96', 'A body of mass 120g placed at the 10cm mark on a uniform metre rule makes the rule settle horizontally on a fulcrum places at 35cm mark. Calculate the mass of the rule', '60g~80g~120g~200g', '200g', 'm = \\(\\frac{25 \\times 120}{15}\\)\n\n= 200g', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(98, '97', 'Two simple pendulum A and B of equal lengths and of masses 5g and 20g respectively are located in the same environment. The periods TA and TB of their respective oscillations are related by the equations', 'TA = 4TB~TA = \\(\\frac{1}{4} T_B\\)~TA = TB~TA = 5TB', 'TA = TB', 'The period of a simple pendulum is dependent on the frequency. It is also dependent on the length of the pendulum but not the mass. Since the two pendulums have equal length, then their periods are equal as well.', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(99, '98', 'An object of mass 5.0 kg moves with a velocity of 10ms-1. Calculate its momentum.', '50.0 kgms-1~15.0 kgms-1~2.0 kgms-1~0.5 kgms-1', '50.0 kgms-1', 'Momentum = MV \n\n= 5 x 10 = 50', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(100, '99', 'A coin is pushed from the edge of a laboratory bench with a horizontal velocity of 15.0 ms-1. If the height of the bench from the floor is 1.5m, calculate the distance from the foot of the bench to the point of impact with the floor [g = 10ms-2]', '0.75m~2.25m~8.22m~15.00m', '8.22m', 'S = U\\(\\sqrt{\\frac{2h}{g}}\\)\n\n= 15\\(\\sqrt{\\frac{2 \\times 1.5}{10}}\\)\n\n= 8.22m', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(101, '100', 'Which of the following statements correctly defines a simple machine? A device', 'that can produce electric current~which can only carry people from one place to another~with which work can be done easily~which changes the state of rest or of uniform motion of an object', 'with which work can be done easily', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(102, '101', 'The radius of a wheel is 30.0 cm and that of its axle is 6.0cm. Calculate the effort required to lift a load of 120.0N using this machine. Assuming 100% efficiency', '600.0N~40.0N~24.0N~20.0N', '24.0N', 'V.R = \\(\\frac{R}{r} = \\frac{30}{6} = 5\\)\n\n\\(\\gamma = \\frac{M.A}{V.R} \\times \\frac{100}{1} \\)\n\nM.A = \\(\\frac{100 \\times 5}{100} = 5\\)\n\nEffort = \\(\\frac{L}{M.A} = \\frac{120}{5}\\)\n\n= 24N', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(103, '102', 'A hypsometer is used for determining', 'steam point~relative humidity~ice point~relative density', 'steam point', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(104, '103', 'Which of the following equations shows how how the linear expansivity (\\(\\alpha\\)) and the cubic expansivity (\\(\\gamma\\)) of a material are related?', '\\(\\gamma = \\alpha\\)~\\(\\gamma = 1 - \\alpha\\)~\\(\\gamma = 2 \\alpha\\)~\\(\\gamma = 3 \\alpha\\)', '\\(\\gamma = 3 \\alpha\\)', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(105, '104', 'Which of the following statements about anomalous expansion of water are correct? i. There is contraction between 0oC and 4oC. ii. There is expansion between 0oC and 100oC. iii. The volume is minimum at 4oC. iv. The volume is maximum at 4oC', 'i and ii only~ii and iii only~i and iii only~ii and iv only', 'i and iii only', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(106, '105', 'Which of the following assumptions is not valid for an ideal gas ?', 'molecules of a particular gas are identical~molecules moves freely throughout the volume of the container~force of attraction between molecules is negligible~molecules move at constant speed between collisions', 'force of attraction between molecules is negligible', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(107, '106', 'A body is pulled over a distance of 500m by a force of 20N. If the power developed is o.4 kW, calculate the time interval during which the force is applied', '0.2s~2.5s~25.0s~250.0s', '25.0s', 't = \\(\\frac{fs}{p} = \\frac{20 \\times 500}{0.4 \\times 1000} = 25s\\)', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(108, '107', 'A metal of mass 200g at a temperature of 100oC is placed in 100g of water at 25oC in a container of negligible heat capacity. If the final steady temperature is 30oC, calculate the specific heat capacity of the metal. [specific heat capacity of the water is 4200 Jkg-1 K-1]', '150 Jkg-1K-1~300 Jkg-1K-1~320 Jkg-1K-1~1960 Jkg-1K-1', '150 Jkg-1K-1', 'MC\\(\\theta\\)metal = MC\\(\\theta _{water}\\) \n\n0.2 x C x 70 = 0.1 x 4200 x 5\n\nC = 150', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(109, '108', 'Ether produces a cooling effect when it is poured on the hand because it has', 'low conductivity~high conductivity~high latent heat of vaporization~low latent heat of vaporization', 'high latent heat of vaporization', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(110, '109', 'Which of the following statements about the image formed by a plane mirror is not correct?', 'it is laterally inverted~it has unit magnifiation~it is formed by actual intersection of rays~its distance from the mirror is equal to that of the object from the mirror', 'it is formed by actual intersection of rays', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(111, '110', 'The image formed by a convex mirror is always', 'real, erect and diminished~real, inverted and diminished~virtual, inverted and diminished~virtual, erect and diminshed', 'virtual, erect and diminshed', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(112, '111', 'A ray undergoes a minimum deviation at 40o when it is incident on equilateral triangular glass prism. Calculate the refractive index of the prism', '1.48~1.5~1.53~1.67', '1.53', 'n = \\(\\frac{\\sin \\frac{1}{2} (dm + A)}{\\sin \\frac{1}{2} A}\\)\n\n= \\(\\frac{\\sin \\frac{1}{2} (40 + 60)}{\\sin \\frac{1}{2} \\times 60}\\)\n\n= 1.532', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(113, '112', 'Total internal reflection occurs in an optical prism when light rays', 'travel from the prism into an optically denser medium~are incident in the prism at an angle greater than the critical angle~are incident normally in the prism~travel from the prism to the air', 'are incident in the prism at an angle greater than the critical angle', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(114, '113', 'The speed of light in a certain medium is V while its speed in a vacuum is C. The absolute refractive index of the medium is', 'C + V~\\(\\frac{C}{V}\\)~\\(\\frac{V}{C}\\)~C - V', '\\(\\frac{C}{V}\\)', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY');
INSERT INTO `labelling1` (`id`, `examYear`, `questions`, `options`, `answer`, `explaination`, `imageDir`, `topic`, `package_id`, `subject_id`) VALUES
(115, '114', 'An object is placed 20.0cm in front of a converging lens of focal length 15.0cm. Calculate its image distance', '1.3cm~8.6cm~35.0cm~60.0cm', '60.0cm', '\\(\\frac{1}{v} = \\frac{1}{f} - \\frac{1}{U}\\)\n\n\\(\\frac{1}{15} - \\frac{1}{20} = 60cm\\)', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(116, '115', 'Presbyopia is a defect of the eye resulting from', 'weak ciliary muscles~short eyeball~loss of sphericity of the lens~long eyeball', 'weak ciliary muscles', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(117, '116', 'The focal length of the eye-piece of an astronomical telescope is f1, while the focal length of the object is f2. Fro normal adjustment, the angular magnification is given by', '\\(\\frac{f_2}{f_1}\\)~1 - \\(\\frac{f_2}{f_1}\\)~\\(\\frac{f_2}{f_1}\\) - 1~\\(\\frac{f_1}{f_2}\\)', '\\(\\frac{f_2}{f_1}\\)', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(118, '117', 'two sound waves have frequencies of 12Hz and 10Hz. Calculate their beats period', '0.5s~1.0s~1.2s~2.0s', '0.5s', '\\(f_1 - f_2 = \\frac{1}{T}\\)\n\n12 - 10 = \\(\\frac{1}{2}\\)\n\n= 0.5', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(119, '118', 'The main difference between echo and reverberation is that', 'reverberation is reflected sound while echo is refracted sound~the time interval between incident sound and reflecte sound is shorter for reverbration~the amplitude of an echo is greater~reverberation is from acoustic speakers while echo comes from clifts', 'the time interval between incident sound and reflecte sound is shorter for reverbration', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(120, '119', 'Which of the following statements about the electromagnetic waves is correct?', 'radio waves have longer frequencies than x-rays~x-rays have the longest wavelength~some of the waves travel at 3.0 x 108ms-1~white light occupies a region beyond ultraviolet rays', 'some of the waves travel at 3.0 x 108ms-1', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(121, '120', 'The correct relationship between \"G\" and \"g\" in a gravitational field is given by the equation (Where the symbols have their usual meanings)', 'g = \\(\\frac{GM}{R}\\)~g = \\(\\frac{GM}{R^2}\\)~g = \\(\\frac{GM^2}{R}\\)~g = \\(\\frac{GM^2}{R^2}\\)', 'g = \\(\\frac{GM}{R^2}\\)', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(122, '121', 'The capacitance of a parallel-plate capacitor', 'decreases when the seperation between the plate decreases~increases when the optential difference between the plates is increased~is greater without a dielectric material between the plates than with a dielectric~is greater with a dielectric between the plates than without a dielectric.', 'is greater with a dielectric between the plates than without a dielectric.', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(123, '122', 'When the pointed end of an uncharged optical pin is brought near the cap cf a positively charged electroscope, it is observed that the gold', 'collapse slowly~vibrate~are not affected~diverge rapidly', 'collapse slowly', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(124, '123', 'Which of the following substances does not conduct electricity?', 'graphite~glass~sulphuric acid~table salt solution', 'glass', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(125, '124', 'The unit of capacitance is', 'farad~coulomb~henry~ohms', 'farad', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(126, '125', 'An ammeter with a full scale deflection of 10mA has an internal resistance 0.5\\(\\Omega\\). calculate the resistance of the shunt required to adapt it to read up to 3A', '0.0167\\(\\Omega\\)~0.0130\\(\\Omega\\)~0.0250\\(\\Omega\\)~0.1000\\(\\Omega\\)', '0.0167\\(\\Omega\\)', '\\(R_2 = \\frac{I_1R_1}{I_2} = \\frac{0.01 \\times 5}{2.99}\\)\n\n= 0.0167', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(127, '126', 'The resistivity, \\(\\mathit{P}\\), of a material of length l, cross-sectional area A, resistance R, is given by the equation', '\\(\\mathit{P} = \\frac{RA}{l}\\)~\\(\\mathit{P} = \\frac{l}{RA}\\)~\\(\\mathit{P} = \\frac{Rl}{A}\\)~\\(\\mathit{P} = \\frac{R}{Al}\\)', '\\(\\mathit{P} = \\frac{RA}{l}\\)', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(128, '127', 'A wire of length 30cm is moved with a speed of 2ms-1 at right angles to a magnetic field of flux density 0.4T. calculate the emf induced in the wire', '0.15V~0.24V~2.70V~24.00V', '0.24V', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(129, '128', 'Which of the following practices will lead to losses in electrical power transmission?', 'using transmission cables of large diameter~transmitting at high voltage and low current~transmitting at relatively low voltage and high current~using a set-up transformer at the production end', 'transmitting at relatively low voltage and high current', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(130, '129', 'For photoelectric emission, the threshold frequency is the', 'maximum frequency of incident radiation that will eject elecrons~minimum fraquency of incident radiation required to eject elecrons~frequency which results in the emission of the greater number of electrons~fraquency whch impacts greatest kinetic energy to emitte electrons', 'minimum fraquency of incident radiation required to eject elecrons', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(131, '130', 'Which of the following properties is not applicable to X-rays? They', 'travel in straight lines~travel with the speed of light~are deflected by magnetic field~affect photographic films', 'are deflected by magnetic field', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(132, '131', 'Uranium-234 disintegrated to form Thorium-230 by emitting', 'alpha particles~gamma rays~beta negative rays~beta positive rays', 'alpha particles', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(133, '132', 'The change in mass of fuel during a nuclear reaction is 2.0 x 10-27 kg. Calculate the amount of energy released. (Speed of light = 2.0 x 108ms-1)', '1.8 x 10-10J~9.0 x 10-11J~6.0 x 10-19J~1.2 x 10-45J', '1.8 x 10-10J', 'Q = \\(\\Delta MC^2\\) \n\n= 2 x 10-27(3 x 10)2\n\n= 1.8 x 10-10J', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(134, '133', 'Nuclear fusion is not used as a source of enegy because', 'very high temperature is needed for the reaction~the fuel for the reaction is not easy to obtain~less energy is released~the reaction is too slow', 'very high temperature is needed for the reaction', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(135, '134', 'Using the circuit diagram above. Calculate the total charge in the circuit', '80\\(\\mu C\\)~35\\(\\mu C\\)~20\\(\\mu C\\)~16\\(\\mu C\\)', '16\\(\\mu C\\)', 'C - \\(C_1 + C_2 = 2 + 6 = \\mu F\\)\n\n\\(\\frac{1}{C} = \\frac{1}{C_1} + \\frac{1}{C_1} + \\frac{1}{C_2} = \\frac{1}{8} + \\frac{1}{2}\\)\n\nC = \\(\\frac{8}{5 \\mu F}\\)\n\nQ = CV \n\n= \\(\\frac{8}{5} \\times 10 = 16\\mu C\\)', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(136, '135', 'Using the circuit diagram above. Calculate the potential difference across the capacitors in parallel', '10.0V~8.0V~6.7V~2.0V', '2.0V', 'V = \\(\\frac{Q}{V} = \\frac{16}{8} = 2\\Gamma\\)', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(137, '136', 'The derived unit of pressure can be expressed as', 'kgms-2~kg m-1s-2~kg m-2s-2~kg m-1s2', 'kg m-1s-2', 'Pressure = \\(\\frac{Force}{Area}\\)\nForce = mass x acceleration\n\\(\\therefore\\) Pressure = \\(\\frac{mass \\times acceleration}{Area}\\)\n= \\(\\frac{kg \\times m \\times s^{-2}}{m^2}\\)\n= kg m\\(^{-1}\\) s\\(^{-2}\\)', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(138, '137', 'The diagram above illustrates trapped air in a syringe placed in water that is gradually heated. It is observed that the piston rises as the temperature of the water rises. Which of the following statements explains this observation?', 'frequency of collision of trapped air molecules with walls of the syringe is more~molecules of trapped air expands more~speed of the trapped air molecules decreases~number of molecules of trapped air increases', 'molecules of trapped air expands more', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(139, '138', 'Which of the following devices is used to determine the relative density of an acid?', 'manometer~hydrometer~hypsometer~hygrometer', 'hydrometer', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(140, '139', 'A block of wood of density 0.6 gcm\\(^{-3}\\), weighing 3.06N in air, floats freely in a liquid of density 0.9 gcm\\(^{-3}\\). Calculate volume of the portion immersed (g = 10ms\\(^{-2}\\))', '510cm3~340cm3~254cm3~170cm3', '340cm3', 'V = \\(\\frac{M}{D}\\)\n\n= \\(\\frac{3.06}{10} \\times \\frac{1000}{0.9} = 340\\)', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(141, '140', 'A metal ball of weight W falls through a column of glycerine of viscosity V. If the ball experiences an upthrust U and terminal velocity', 'W ~W = U + V~W = U - V~W ', 'W = U + V', 'When terminal velocity is attained, The equation of motion becomes\nmg - V - U = 0\n\\(\\therefore\\) mg = W = U + V', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(142, '141', 'The movement of fluid up or down a narrow tube is', 'osmosis~brownian motion~capillarity~diffusion', 'capillarity', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(143, '142', 'Which of the following substances is the most volatile at room temperature?', 'water~diesel~petrol~kerosine', 'petrol', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(144, '143', 'A bird flies at 10ms\\(^{-1}\\) for 3s, 15ms\\(^{-1}\\) for 3s and 20 ms\\(^{-1}\\) for 4s. Calculate the bird\'s average speed', '4.5 ms-1~15.0 ms-1~15.5 ms-1~51.7 ms-1', '15.5 ms-1', 'Av. speed = \\(\\frac{3 \\times 15 + 3 \\times 10 + 4 \\times 20}{3 + 3 + 4}\\)\n\n= 15.5 ms\\(^{-1}\\)', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(145, '144', 'The time of flight for a projectile motion is given by the expression', '\\(\\frac{U sin \\theta}{g}\\)~\\(\\frac{U sin \\theta}{2g}\\)~\\(\\frac{2U sin \\theta}{g}\\)~\\(\\frac{U sin 2\\theta}{g}\\)', '\\(\\frac{2U sin \\theta}{g}\\)', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(146, '145', 'An object is dropped from the top of a tower. If it takes 4s for it to reach the ground, calculate the height of the tower.(g = 10 ms-2, ignore air resistance)', '20m~40m~80m~160m', '80m', 'H = \\(\\frac{1}{2} gt^2\\)\n\n\\(\\frac{1}{2} \\times 10 \\times 4^2 = 80\\)', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(147, '146', 'When a body is slightly tilted, it is found that its centre of gravity is slightly raised. What is the state of equilibrium of the body?', 'unstable~stable~neutral~cannot be determined', 'stable', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(148, '147', 'A simple pendulum makes 50 oscillations in one minute. Determine its period of oscillation', '0.02s~0.83s~1.20s~50.00s', '1.20s', 'T = \\(\\frac{t}{n} = \\frac{60}{50} = 1.2\\)', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(149, '148', 'The tendency for a stationary body to continue to remain at rest when a force is applied to it is known as', 'friction~impulse~inertia~momentum', 'inertia', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(150, '149', 'A resultant force of magnitude 15N acts on a body of mass 250g. Calculate the magnitude of the acceleration', '0.06 ms-2~3.75ms-2~16.67ms-2~60.00ms-2', '60.00ms-2', 'a = \\(\\frac{F}{M} = \\frac{15}{0.25} = 60\\)', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(151, '150', 'A girl stands on a scale in a lift. If the reading on the scale is less than her weight, then the lift is moving', 'upward at uniform speed~upward with uniform acceleration~downward with uniform speed~downward with uniform acceleration', 'downward with uniform acceleration', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(152, '151', 'The S.I unit of heat is', 'joule~kelvin~watt~ampere', 'joule', 'Heat is a form of energy (heat energy). The S.I unit of energy generally is Joules (J).', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(153, '152', 'A body is pulled through a distance of 500m by a force of 20N. If the power developed is 0.4kW, calculate the time for which the force acts', '250.0s~25.0s~2.5s~0.5s', '25.0s', 'Force x Distance = Power x Time\nTime = \\(\\frac{Force \\times Distance}{Power}\\)\n= \\(\\frac{20 \\times 500}{0.4 \\times 1000}\\)\n= 25.0s', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(154, '153', 'A metal sheet of area 100cm\\(^2\\) was heated through 70', '100.06 cm2~100.12cm2~100.24cm2~100.36cm2', '100.24cm2', 'Formula', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(155, '154', 'The thermopile is a device for detecting', 'radioactive radiations~radiant energy~x-rays~the presence of electrons', 'radiant energy', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(156, '155', 'In the formation of sea breeze. wind blows from', 'sky to land~sea to sky~land to sea~sea to land', 'sea to land', 'A sea breeze describes a wind that blows from the ocean (sea) inland towards land.', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(157, '156', 'A piece of copper of mass 20g at a temperature of 110', '0.37g~0.60g~2.40g~2.70g', '2.70g', 'Mice = \\(\\frac{MC}{\\theta}\\)\n\n= \\(\\frac{20 \\times 0.4 \\times 110}{330}', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(158, '157', 'Which of the following factors decreases the rate of evaporation of a liquid?', 'increase in pressure over the liquid~lowering the boiling point~decreasing in humidity~wind', 'increase in pressure over the liquid', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(159, '158', 'When two waves are superimposed on each other, the following occurrences are possible, except', 'nodal lins~anti nodal lines~stationary waves~dispersion', 'dispersion', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(160, '159', 'Which of the following properties of waves is exclusive to transverse waves?', 'reflection~interference~diffraction~polarization', 'polarization', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(161, '160', 'An object of height 2.5cm is places 20cm from a convex mirror of focal length 10cm. Calculate the height of its image.', '2.5 cm~3.0cm~5.0cm~25.0cm', '2.5 cm', '\\(\\frac{1}{v} = \\frac{1}{f} - \\frac{1}{u}\\)\n= \\(\\frac{1}{10} - \\frac{1}{2} = \\frac{1}{20}\\)\nv = 20\n\nbut h\\(_i\\)', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(162, '161', 'A ray of light passes from air to water to glass to air. Given that the refractive index for light passing from air to water is \\(\\frac{4}{3}\\) and air to glass is \\(\\frac{3}{2}\\), calculate the refractive index of glass relative to water', '0.5~0.67~0.75~1.13', '1.13', '\\(_{g} \\eta _{w} = \\frac{ _g', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(163, '162', 'An object is placed at a point X between the focal point F and the optical centre C of a diverging lens. If F is the focal point on the other side of the lens, the image of the object is formed between', 'F and X~X and C~C and F~F and 2F', 'X and C', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(164, '163', 'An object is placed 10cm from a converging lens of foal length 15cm. Calculate the magnification of the image formed', '3~1.5~0.6~0.3', '3', '\\(\\frac{1}{f} = \\frac{1}{v} + \\frac{1}{u}\\)\n\\(\\frac{1}{v} = \\frac{1}{f} - \\frac{1}{u}\\)\n\n\\(\\frac{1}{15} - \\frac{1}{10} = \\frac{2 -', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(165, '164', 'A telescope is said to be in normal adjustment when the', 'focal length of he objective is greater than that of the eyepiece~focal length of the eyepiece is greater than that of the objective~focal length of the eyepiece is equal to that of the objective~objective focal point coincides wih that of the eyepiece', 'objective focal point coincides wih that of the eyepiece', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(166, '165', 'The sound heard by a person after the reflection of the sound generated by him is called', 'reverberation~resonance~echo~audibility', 'echo', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(167, '166', 'Which of the following sets of coloured light is', 'i and ii only~ii and iii only~iv only~i, ii and iv only', 'iv only', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(168, '167', 'When two like charges are brought together, the potential energy of the system formed will', 'increase because work is done against the field~increase because work is done by the field~decrease because work is done by the field~decrease because work is done against the field', 'decrease because work is done against the field', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(169, '168', 'Two capacitors, each of capacitance 2\\(\\mu\\)F', '6.0 x 10-5C~1.2 x 10-4C~2.4 x 10-4C~4.8 x 10-4C', '2.4 x 10-4C', 'C = \\(C_1 + C_2 = 2 + 2 = 4 \\mu F\\)\n\nbut Q = CV\n\n= 4', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(170, '169', 'Which of the following properties is an advantage of lead-acid accumulator over an alkaline accumulator?', 'possesses low internal resistance~can be recharges~has shorter life span~possesses high e.m.f', 'possesses high e.m.f', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(171, '170', 'Six dry cells each of e.m.f. 2.0 and internal resistance of 1.0\\(\\Omega\\) are connected in parallel across a load of 3.0\\(\\Omega\\). Calculate the effective current in the circuit.', '0.63A~0.50A~0.31A~0.22A', '0.63A', 'I = \\(\\frac{f}{n} = \\frac{1}{6 - 2}\\)\n\nI = \\(\\frac{v}{R + r} = \\frac{2}{3} + \\frac{1}{6} = 0.63\\)A', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(172, '171', 'Two similar cells are used to light two similar lamps as illustrated in the diagrams above. In which of the circuit diagrams are the lamps brightest?', 'P~Q~R~S', 'P', 'The determinant of the brightness of a bulb is the power (watts) of the circuit.\nRecall that Power (P) = \\(\\frac{V^2}{R}\\).\nSince the resistance is to be used as a divisor, it means the smaller the resistance, the greater the power.', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(173, '172', 'A 120\\(\\Omega\\) resistor dissipates 8 kJ of heat in 20s. Calculate the current through the resistor', '5.8A~6.9A~30.0A~33.3A', '5.8A', 'Q = I2Rt\n\nI = \\(\\sqrt{\\frac{Q}{Rt}}\\)\n\n= \\(\\sqrt{\\frac{8000}{12 \\times 20}}\\)\n\n= 5.8', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(174, '173', 'The magnetic relay is a device used for', 'timing in sports~storing magnetic field~readin the magnitude of magnetic flux~controlling another circuit carrying larger current', 'controlling another circuit carrying larger current', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(175, '174', 'the core of a transformer is usually laminated in order to', 'reduce magnetic leakage~reduce eddy current~prevent vibration of the transformer~make magnetic reversal in the core much easier', 'reduce eddy current', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(176, '175', 'Which of the following modes is the most economical method of transmitting electrical power over long distances?', 'alternating current at low voltage and high current~alternating current at high voltage and high current~alternating current at high voltage and low current~direct current at low voltage and high current', 'alternating current at high voltage and low current', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(177, '176', 'An inductor is connected to a 24V, 50Hz mains supply. If the current through the inductor is 1.5A, calculate the inductance of the inductor (\\(\\pi = \\frac{22}{7}\\))', '8.0 x 102H~7.5 x 10oH~1.6 x 10oH~5.1 x 10-2H', '5.1 x 10-2H', '\\(X_L = \\frac{V}{I} = \\frac{24}{1.5} = 16\\Omega\\)\n\nL = \\(\\frac{XL}{2 \\pi f} = \\frac{16}{2 \\pi 50}\\)\n\n= 0.05H', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(178, '177', 'In a R-C circuit', 'Irms leads Vrms by 60o~Irms slags Vrms by 60o~Vrms lags Irms by 90o~Vrms leads Irms by 90o', 'Vrms lags Irms by 90o', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(179, '178', 'An atom in an excited state is one whose', 'potential energy is minimum~potential energy is maximum~electron are in the conduction band~electron have moved to higher energy level', 'electron have moved to higher energy level', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(180, '179', 'A metal with a work function of 3.0ev is irradiated with ultraviolet light of energy 4.0 ev. The kinetic energy of the ejected electron is', '1.0eV~3.0eV~4.0eV~7.0eV', '1.0eV', 'K.E = hf - Wo\n\n= 4 - 3 = 1eV', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(181, '180', 'Which of the following statements about X-rays is correct? X-rays', 'are produced when a metal surface is irradiated with ultraviolet light~are produced when a metal target is used to block fast miving electrons~have long wavelengths and are therefoer very penetrating~are not part of the electromagnetic spectrum', 'are produced when a metal target is used to block fast miving electrons', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(182, '181', 'Which of the following arrangements of radiations is in the order of decreasing penetrating power?', '\\(\\alpha, \\beta, \\gamma\\)~\\(\\alpha, \\gamma, \\beta\\)~\\(\\gamma, \\beta, \\alpha\\)~\\(\\beta, \\gamma, \\alpha\\)', '\\(\\gamma, \\beta, \\alpha\\)', 'Thanks for your contribution, corrections have been made.', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(183, '182', 'Which of the following radiations emitted in radioactive decay has momentum, a fairly high penetrating power and is deflected by a magnet?', 'alpha particles~beta particle~gamma radiation ~X-radiation', 'beta particle', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(184, '183', 'The rising of a liquid in an open and ended glass tube of narrow bore is', 'osmosis~adhesion~capillarity~surface tension', 'capillarity', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(185, '184', 'Which of the following units is equivalent to the watt?', 'kgms-2~kgm2s-3~kgm2s-2~kgm2s-1', 'kgm2s-3', '\\(Power = \\frac{\\text{Work done}}{time}\\)\n= \\(\\frac{Force \\times distance}{time}\\)\n= \\(\\frac{mass \\times acceleration \\times distance}{time}\\)\n= \\(\\frac{kg \\times m \\times m}{s^{2} \\times s}\\)\n= \\(kgm^{2} s^{-3}\\)', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(186, '185', 'Which of the following statements about pressure in a liquid is correct?', 'the pressure in a liquid increases with depth~the higher the density of a liquid, the lower the pressure it exerts~pressure in liquid act only in a direction perpendicular to the sides of the containing vessel~pressure is independent of the acceleration due to gravity', 'the pressure in a liquid increases with depth', 'At different depths, the pressure of a liquid differs.', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(187, '186', 'Solid friction, like viscosity is', 'independent of the surface area in contact~independent of the relative motion between layers~dependent on normal reaction~in opposition to motion', 'in opposition to motion', 'The force acting on a body due to the viscous resistance of the surrounding fluid is called the drag force and it acts in the direction opposite to the direction of motion. So also does friction.', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(188, '187', 'The slope of a linear distance-times graph represents', 'acceleration~displacement~speed~velocity', 'speed', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(189, '188', 'A body of mass 2kg is released from rest on a plane inclined at an angle of 60', '3.1ms-2~5.2ms-2~6.0ms-2~8.7ms-2', '8.7ms-2', 'a = g sin \\(\\theta\\)\n\n= 10 sin 60\n\n= 8.7 ms\\(^{-2}\\)', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(190, '189', 'The total area under a force-velocity graph represents', 'energy~momentum~power~pressure', 'power', 'Power = Force x Velocity.\nTherefore, the area under the force- velocity graph gives Power.', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(191, '190', 'A body of mass 20g projected vertically upwards in vacuum returns to the point of projection after 1.2s. [g = 10ms\\(^{-2}\\)]. Calculate the speed of projection', '1.2ms-1~6.0ms-1~12.0ms-1~0.6ms-1', '6.0ms-1', 'V = u - gt\n\nu = v + gt\n\n= 0 + 10 x 0.6\n\n= 6ms\\(^{-1}\\)', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(192, '191', 'A body of mass 20g projected vertically upwards in vacuum returns to the point of projection after 1.2s. [g = 10ms-2]. Determine the potential energy of the body at the maximum height of its motion', '0.36J~0.72J~360.00J~720.00J', '0.36J', 'P.E at max = K.E on projection \n\n= \\(\\frac{1}{2}\\)mv2 = \\(\\frac{1}{2} \\times 0.02 \\times 6^2 = 0.36J\\)', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(193, '192', 'The maximum displacement on either side of the equilibrium position of an object in simple harmonic motion represents', 'period~amplitude~wavelength~frequency', 'amplitude', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(194, '193', 'From Newton\'s first law of motion,', 'a body can only undergo translational motion~once a body remains at rest no force acts on it~the net force acting in uniform linear motion is zero~a body\'s inertia is its weight', 'the net force acting in uniform linear motion is zero', 'The key point of this law', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(195, '194', 'A body of mass 11kg is suspended from a ceiling fan by an aluminum wire of length 2m and diameter 2mm. Calculate the elastic energy stored in the wire [Young\'s modulus of aluminum is 7.0 x 1010Nm-2, g = 10ms-2, \\(\\pi\\) = 3.142]', '1.1 x 10-1J~5.5 x 10-2J~1.1 x 10-4J~5.5 x 10-8J', '5.5 x 10-2J', 'e = \\(\\frac{4FI}{Y \\pi d^2} = \\frac{4 \\times 11 \\times 10 \\times 2}{7 \\times 10^3 \\times 3.14(2 \\times 10^{-2})^2}\\)\n\n= 0.001m\n\nE = \\(\\frac{1}{2} Fe = \\frac{1}{2} \\times 110 \\times 0.001\\)\n\n= 5.5 x 10-2J', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(196, '195', 'The velocity ratio of an inclined plane', 'increases with increase in the angle of inclination~increases with decrease in the angle of inclination~decreases with decrease in the angle of inclination~is independent of the angle of inclination', 'increases with increase in the angle of inclination', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(197, '196', 'Which of the following types of thermometer is used for the calibration of other thermometers?', 'liqud-in-glass thermometer~constant volume gas thermometer~optical pyrometer~thermocouple', 'constant volume gas thermometer', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(198, '197', 'The magnitude of the expansion or contraction of a substance depends on the i. temperature change ii. nature of the substance iii. size of the substance. Which of the statements above are correct?', 'i and ii only~ii and iii only~i and iii only~i, ii and iii', 'i and ii only', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(199, '198', 'Highly polished silvery surfaces are', 'poor absorbers and poor emitters of radiation~poor absorbers and good emitters of radiation~good absorbers and poor emitters of radiation~good absorbers and good emitters of radiation', 'poor absorbers and good emitters of radiation', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(200, '199', 'The volume of a given mass of gas at 27oC and 800 mmHg is 76cm2. Calculate its volume at s.t.p', '100.0 cm3~72.8 cm3~60.0 cm3~36.4 cm3', '72.8 cm3', '\\(V_2 = \\frac{P_1V_1T_2}{P_2T_1} = \\frac{800 \\times 76 \\times 273}{760 \\times 300}\\)\n\n= 72.8cm3', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(201, '200', 'Ice of mass 10g at 5', '105J~3255J~3465J~16821J', '3465J', 'Q = ML + MC\\(\\theta\\)\n\n= 10 x 335 + 10 x 2.1 x 5\n\n= 3465J', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(202, '201', 'An electric heater has a resistance of 50\\(\\Omega\\). When it is immersed in water and connected to mains source, it draws a current of 4.0A. Calculate the heat gained by the water if the heater is switched on for 2 minutes, assuming no heat losses to the surroundings', '4200J~1600J~24000J~96000J', '96000J', 'Q = I2RT\n\n= 42 x 50 x 2 x 60\n\n= 96000J', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(203, '202', 'When salt is dissolved in water, the freezing point of the water', 'increases~decreases~remains the same~increases and later decrease', 'decreases', 'The salt in the water (same for any other impurities)', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(204, '203', 'The equation of a certain progressive transverse wave is y = 2 sin 2 \\(\\pi ( \\frac{t}{0.01} - \\frac{x}{30})\\), where x and y are in cm and t in seconds. Calculate the period of the wave.', '0.001s~0.010s~10.000s~100.000s', '0.010s', 'Compare', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(205, '204', 'At which position should an object be placed in front of a concave mirror in order to obtain an image which is of the same size as the object?', 'at the centre of curvature~at the principal focus~between the pole and principal focus~between the centre of curvature and principal focus', 'at the centre of curvature', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(206, '205', 'Images formed by a convex mirror are always', 'magnified~behind the mirror~real~inverted', 'behind the mirror', 'Convex mirrors always form virtual images, which appear behind the mirror.', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(207, '206', 'The refractive index of a material is 1.5. Calculate the critical angle at the glass-air interface', '19o~21o~39o~42o', '42o', 'Sin C = \\(\\frac{1}{\\eta} = \\frac{1}{1.5} = 0.6667\\)\n\nC = sin\\(^{-1}\\) 0.6667\n\n= 42', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(208, '207', 'A diverging lens of focal length 30cm produces an image 20cm from the lens. Determine the object distance', '10cm~12cm~50cm~60cm', '60cm', 'Lens formula', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(209, '208', 'Which of the following statements about the Galilean telescope is not correct?', 'the final image is inverted~it is shorter than terrestial telescope~the final image is erect~it has a small field of view', 'the final image is inverted', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(210, '209', 'Which of the following radiations has it\'s frequency lower than that of infrared radiation?', 'Utra-violet rays~gamma rays~x-rays~radio waves', 'radio waves', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(211, '210', 'A string under tension produces a note of frequency 14Hz. Determine the frequency when the tension is quadrupled.', '14Hz~18Hz~28Hz~56Hz', '28Hz', 'The formula for the frequency in a stringed instrument ', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(212, '211', 'Which of the following statements about waves in pipes is correct?', 'for open pipes, there is only one end correction to be accounted for~for closed pipes, there are two end corrections to be accounted for~only odd harmonics are possible in closed pipes~all harmonics are possible in closed pipes', 'only odd harmonics are possible in closed pipes', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(213, '212', 'When a person holds a negatively charges metal rod and stands bare-footed on the ground, how will the charges leak?', 'negative charges flows to the ground through the person\'s body~positive charges flow from the ground through his body to neutralize the negative charges~positive charges in the air neutralizes the negative charges the person is holding~negative charges will leak through the air', 'negative charges flows to the ground through the person\'s body', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(214, '213', 'A charge of 2.0 x 10\\(^{-5}\\) C experiences a force of 80N in a uniform electric field. Calculate the magnitude of the electric field intensity', '8.0 x 106 NC-1~4.0 x 106 NC-1~4.0 x 104 NC-1~2.0 x 104 NC-1', '4.0 x 106 NC-1', 'E = \\(\\frac{F}{Q} = \\frac{80}{2 \\times 10^{-5}}\\)\n\n= 4 x 10\\(^6\\) NC\\(^{-1}\\)', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(215, '214', 'A potential difference of 12V is applied across the ends of a 6\\(\\Omega\\) resistor for 10 minutes. Determine the quantity of heat generated', '720J~1200J~14400J~43200J', '14400J', 'Q = \\(\\frac{V^2 t}{R}\n= \\frac{12^2 \\times 10 \\times 60}{6}\\)\n\n= 14400J', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(216, '215', 'Which of the following instruments is used to determine the accurate value of the electromotive force of a cell?', 'voltmeter~meterbridge~voltameter~potentiometer', 'potentiometer', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(217, '216', 'The capacitance of parallel plates capacitors varies', 'inversely as the square of the distance between the plates~directly as the square of the distance between the plates~inversely as the distance between the plates~directly as the distance between the plate', 'inversely as the square of the distance between the plates', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(218, '217', 'Which of the following devices does not makes use of eddy current for its action? A', 'galvanometer~speedometer~induction furnace~speedometer', 'galvanometer', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(219, '218', 'A coil of inductance 0.12 H and resistance 4\\(\\Omega\\), is connected across a 240V, 50Hz supply. Calculate the current through it. [\\(\\pi\\) = 3.142]', '6.3A~33.3A~37.2A~40.0A', '6.3A', 'XL = \\(2\\pi f L\\)\n\n= = 2 x 3.142 x 50 x 0.12\n\n= 37.68\\(\\Omega\\)\n\nZ = \\(\\sqrt{R^2 + X_L^2} = \\sqrt{4^2 + 37.68^2}\\)\n\nI = \\(\\frac{V}{z} = \\frac{240}{37.89}\\)\n\n= 6.3A', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(220, '219', 'The work function of a metal is 2.56 x 10-19J. Calculate the frequency of a photon whose energy is required to eject from the metal an electron with kinetic energy of 3.0ev. [1 eV = 1.6 x 10-19J, h = 6.6 x 10-34Js]', '5.56 x 1019Hz~1.66 x 1019Hz~1.12 x 1015Hz~8.42 x 1014Hz', '1.12 x 1015Hz', 'F = \\(\\frac{K.E + Wo}{h}\\)\n\n= \\(\\frac{3.0 \\times 1.6 \\times 10^{-19} + 2.56 \\times 106{-19}}{6.6 \\times 106{-34}}\\)\n\n- 1.12 x 10-15HZ', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(221, '220', 'The minimum energy required to cause photoelectric emission when the surface of a metal is irradiated with electromagnetic radiation of suitable frequency is called', 'critical energy~ionization energy~work function~planck\'s constant', 'work function', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(222, '221', 'Which of the following particles are termed nucleons in a neutral atom?', 'protons and neutrons~neutrons and electrons~protons and electrons~protons, electrons and neutrons', 'protons and neutrons', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(223, '222', 'Which of the following statements about the use of radioisotopes is not correct? They are used to', 'induce mutations in plants and animals to obtain new and improved varieties~trace the paths of metabolic processes in plants and animals~estmate the age of rocks~locate broken bones', 'induce mutations in plants and animals to obtain new and improved varieties', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(224, '223', 'Which of the following phenomena supports the theory that waves have a particle nature?', 'electron diffraction~photoelectric effect~diffraction of light~x-ray interference', 'diffraction of light', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(225, '224', 'A block of wood of mass 5kg is pulled on a platform by a force of 40N as illustrated in the diagram above. If the frictional force, F experienced by the block is 12N, calculate the magnitude of the acceleration of the acceleration of the block', '2.4ms-2~5.6ms-2~8.0ms-2~2.4ms-2', '5.6ms-2', 'F + Ma = P\n\na = \\(\\frac{P - F}{m}\\)\n\n= \\(\\frac{40 - 12}{5} = 5.6ms^{-2}\\)', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(226, '225', 'Four co-planar forces of magnitudes 10N, 17N, 6N and 20N act at point O as shown in the above diagram. Determine the magnitude of the resultant force', '53.N~21.0N~7.0N~5.0N', '5.0N', 'Vertical resultant = 10 - 6 = 4N\n\nHorizontal resultant = 20 - 17 = 3N\n\nR = \\(\\sqrt{3^2 + 4^2}\\)\n\n= 5N', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(227, '226', 'The outlet of a bicycle pump is used to inflate a football as illustrated in the diagram above. Why does the pressure of the air inside the pump increases as the pump handle is slowly pushed downward at constant temperature?', 'momentum of the air molecules are increased~volume occupied by the molecules are increased~frequency of collision of the air molecules with the walls of the pump is increased~more air molecules are collidin with one another in the system', 'frequency of collision of the air molecules with the walls of the pump is increased', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(228, '227', 'The diagram above illustrates a waveform. Which of the point on the waveform are in phase?', 'P and R~R and T~P and T~Q and S', 'Q and S', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(229, '228', 'An electric circuit is connected as illustrated above. Determine the equivalent e.m.f and current flowing through the circuit respectively, neglecting the internal resistance of the cells', '2V, 1.0A~2V, 4.0A~6V, 0.3a~6V, 3.0a', '2V, 1.0A', 'cells in V = voltage of the cell \n\n= 2V\n\nI = \\(\\frac{v}{R} = \\frac{2}{3}\\)\n\n= 1A', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(230, '229', 'A ball falling through a viscous liquid is acted upon by', 'upthrust only~upthrust and the ball\'s weight~the ball\'s weight and viscous force~upthrust, the ball\'s weight and viscous force', 'upthrust, the ball\'s weight and viscous force', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(231, '230', 'An object of mass m moves with a uniform speed v round a circular path of radius r. If its angular speed is \\(\\omega\\), the magnitude of the centripetal force acting on it is', '\\(m \\omega^2 r\\)~\\(\\frac{mv^2}{r}\\)~\\(m \\omega r\\)~\\(\\frac{mv^2}{r^2}\\)', '\\(\\frac{mv^2}{r}\\)', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY');
INSERT INTO `labelling1` (`id`, `examYear`, `questions`, `options`, `answer`, `explaination`, `imageDir`, `topic`, `package_id`, `subject_id`) VALUES
(232, '231', 'When an elastic material is stretched by a force, the energy stored in it is', 'kinetic~potential~thermal~electrical', 'potential', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(233, '232', 'When the linear momentum of a body is constant, the net force acting on it', 'is zero~increases~decreases~remains constant', 'is zero', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(234, '233', 'If no net force acts on an object, the object maintains a state of rest or constant speed in a straight line. The above is a statement of Newton\'s', 'first law of motion~second law of motion~third law of motion~law of universal gravitation', 'first law of motion', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(235, '234', 'Which of the following pairs of physical quantities is made up of vectors?', 'speed and displacement~mass and force~dislacement and acceleration~momentum and length', 'dislacement and acceleration', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(236, '235', 'The knowledge of surface tension is applied in the following areas except in', 'manufacturing of rain coats~production of palm oil~floating of a needle on water~washing of plates with soapy water', 'production of palm oil', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(237, '236', 'A body is projected vertically upwards with a speed of 10 ms-1 from a point 2m above the ground. Calculate the total time taken for the body to reach the ground. [g = 10ms-2]', '1.00s~2.00s~2.18s~3.00s', '2.00s', 'T = \\(\\frac{2u}{g} = \\frac{2 \\times 10}{10} = 2s\\)', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(238, '237', 'A car starts from rest and covers a distance of 40m in 10s. Calculate the magnitude of its acceleration', '0.25ms-2~0.80ms-2~3.20ms-2~4.00ms-2', '0.80ms-2', 'S = ut + \\(\\frac{1}{2} at^2\\)\n\n40 = 0 x 10 + \\(\\frac{1}{2}\\) x a x 102\n\n50a = 40\n\na = \\(\\frac{40}{50}\\)\n\n= 0.8ms-2', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(239, '238', 'The diagram above illustrates a uniform metre rule which is balanced on a pivot by some masses. Calculate the value of M', '500.0g~400.0g~44.4g~25.0g', '25.0g', 'clockwise moment = Anti-clock wise moment \n\n= M x 40 = 100 x 10\n\nM = \\(\\frac{1000}{40}\\)\n\n= 25g', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(240, '239', 'The period of a simple pendulum X is 5s. What is the period of a simple pendulum Y which makes 50 vibrations in the same time it takes X to make 20 vibrations?', '12.5s~2.5s~2.0s~1.2s', '2.0s', 'It takes X 5s for 1 complete vibration.\n', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(241, '240', 'Alcohol of mass 21g and density 0.7g cm-3 is mixed with 10g of water. Determine the density of the mixture [density of water = 1.0gcm-3]', '0.775gcm-3~0.875gcm-3~0.780gcm-3~0.880gcm-3', '0.775gcm-3', '\\(V_A = \\frac{M}{D} = \\frac{21}{0.7} = 30cm^3\\)\n\n\\(V_w = \\frac{M}{D} = \\frac{10}{1} = 10cm^3\\)\n\nVmixture = 30 + 10 = 40cm3\n\nMmixture = 21 + 10 = 31g\n\nDmixture = \\(\\frac{m}{v} = \\frac{31}{40} = 0.775\\)', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(242, '241', 'A device that converts mechanical energy into electrical energy is', 'a dynamo~an electric motor~an induction coil~a transformer', 'a dynamo', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(243, '242', 'The S.I unit of power is', 'N~Pa~W~J', 'W', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(244, '243', 'A screw-jack has the distance between its successive threads as P and the length of its tommy bar as r. Its velocity ratio is given by the expression', '\\(\\frac{2 \\pi r^2}{P}\\)~\\(\\frac{2 \\pi r}{P}\\)~\\(\\frac{2 \\pi}{rp}\\)~\\(\\frac{P}{2 \\pi r}\\)', '\\(\\frac{2 \\pi r}{P}\\)', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(245, '244', 'Heat transfer by conduction is similar to wave motion because', 'there is increase in temperature~transfer of materials is involved~charged particles vibrates at right angles~no transfer of materials is involved', 'no transfer of materials is involved', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(246, '245', 'The temperature at which the water vapor in the air saturates the air and begins to condense is known as', 'dew point~critical point~boiling point~triple point', 'dew point', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(247, '246', 'The change of state from solid to liquid occurs', 'at constant temperature~when temperature is lower than the boiling point~when temperature is just near freezing point~when temperature is equal to the boiling point', 'at constant temperature', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(248, '247', 'Which of the following types of thermometers can be used to measure a range of temperature from -50', 'i only~ii only~iii only~i and ii only', 'iii only', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(249, '248', 'A body of mass M kg rests on a plane inclined at an angle \\(\\theta\\) to the horizontal. The component of the weight of the body parallel to the plane is', 'Mg sin \\(\\theta\\)~Mg cos \\(\\theta\\)~Mg tan \\(\\theta\\)~Mg sec \\(\\theta\\)', 'Mg sin \\(\\theta\\)', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(250, '249', 'A quantity of water at 20oC is mixed with another quantity of water at 70oC. The final steady temperature of the mixture is 40oC. Determine the ratio of the mass of the cold water to that of the hot water', '7~3~2~1', '3', 'Q = MC\\(\\theta\\)\n\nM = \\(\\frac{Q}{C\\theta}\\)\n\n\\(\\frac{Q}{20C}\\) ', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(251, '250', 'The mass of an empty density bottle is 30g. When filled with a liquid, the mass reduces to 38g. Calculate the apparent cubic expansivity of the liquid', '6.25 x 10K-1~6.25 x 10-3K-1~2.50 x 10-3K-1~2.50 x 10-4K-1', '6.25 x 10-3K-1', 'Apparent cubic expansivity = \\(\\frac{\\text{mass of hot liquid expelled}}{\\text{mass of hot liquid left x temp. rise}}\\)\n\n= \\(\\frac{2}{8 \\times 40} = 0.00625\\)', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(252, '251', 'A car', '0.23hp~0.40hp~4.00hp~4.40hp', '4.00hp', 'P = FV = \\(\\frac{100 \\times 30}{1000} = 3 kW\\)\n\n\\(\\frac{3}{0.75} = 4hp\\)', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(253, '252', 'The quality of a note depends on its', 'frequency~pitch~overtones~amplitude', 'overtones', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(254, '253', 'A transverse wave can be distinguished from a longitudinal wave by', 'diffraction~relection~refraction~polarization', 'polarization', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(255, '254', 'Refraction of lights differs from reflection in that, in refraction i. at least two media are involved ii. there is a change in the direction of the ray iii. the speed of the ray changes. Which of the statements above is', 'i only~i ad ii only~ii and iii only~i and iii only', 'i ad ii only', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(256, '255', 'Which of the following relations about the focal length fo of the objective and focal length fe of the eye piece of a compound is correct?', 'fo = fe~fo ~fo ~fe = 2fo', 'fo ', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(257, '256', 'The functional difference between a lens and a mirror is that a lens', 'reflects a beam of light while a mirror refracts it~refracts a beam of light while a mirror reflects it~absorbs incident rays while a mirror transmit them~transmits incidents ray whle a mirror absorbs them', 'refracts a beam of light while a mirror reflects it', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(258, '257', 'The diagram above illustrates an electromagnetic wave travelling with speed 3.0 x 108ms-1. Calculate the wave length of the wave', '0.05m~0.15m~0.16m~0.40m', '0.16m', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(259, '258', 'A fish inside a pond appears to be at a depth of 1.5m when viewed vertically from above. The refractive index of the water in the pound is 1.3. Calculate the apparent displacement of the fish', '2.50m~1.95m~1.50m~0.45m', '0.45m', 'Real depth = n x apparent depth \n\n= 1.3 x 1.5 = 1.95m \n\nApparent displacement = 1.95 - 1.5 = 0.45m', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(260, '259', 'an observer hears an echo 1.26 seconds after blowing a whistle near a cliff. calculate the distance of the observer from the cliff. [speed of sound in air = 330ms-1]', '104.4m~207.9m~415.8m~523.8m', '207.9m', 'S = \\(\\frac{vt}{2} = \\frac{330 \\times 1.26}{2} = 207.9\\)', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(261, '260', 'An object is placed in front of two plane mirrors inclined at 60o to each other. Determine the number of the images formed', '2~3~5~7', '5', 'n = \\(\\frac{360}{\\theta}\\) - 1\n\n= \\(\\frac{360}{60} -1\\)\n\n= 6 - 1 = 5', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(262, '261', 'An ammeter can be adapted to measure potential difference by using a', 'shunt~multiplier~rheostat~resistance box', 'multiplier', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(263, '262', 'The region around a magnet in which magnetic force can be expressed is known as', 'declination~flux density~field~flux', 'field', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(264, '263', 'In an ac circuit when the supply voltage frequency is equal to the resonant frequency, the current', 'leads the supply voltge by 90o~lags behind the supply voltage by 90o~leads the supply voltage by 45o~is in phase with the supply voltage', 'is in phase with the supply voltage', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(265, '264', 'The energy stored in a simple cell is', 'electrical~nuclear~thermal~chemical', 'chemical', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(266, '265', 'Which of the following conditions occur at resonance in a series RLC circuit? i. Impedance equal resistance ii. Current is maximum iii. Reactance are maximum iv. Current and voltage are 90o out of phase', 'i and ii only~i and ii only~i, ii and iii only~i, ii, iii and iv', 'i and ii only', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(267, '266', 'An electric motor converts', 'electrical energy to mechanical energy~mechanical energy to electrical energy~mechanical energy to chemical energy~electrical energy to thermal energy', 'electrical energy to mechanical energy', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(268, '267', 'A 15 \\(\\mu F\\) capacitor is connected to a 240V, 50Hz ac. source. Calculate the reactance of the capacitance [\\(\\pi = 3.142\\)]', '16\\(\\Omega\\)~68\\(\\Omega\\)~106\\(\\Omega\\)~212\\(\\Omega\\)', '212\\(\\Omega\\)', '\\(X_c = \\frac{1}{2 \\pi fc}\\)\n\n= 2 x 3.142 x 50 x 15 x 10-6\n\n= 212.179\\(\\Omega\\)', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(269, '268', 'Two identical charges situated 20cm apart in vacuum repel each other with a force of 1.0N.Calculate the value of each other with a force of 1.0N. Calculate the value of each charge. [(14 \\(\\pi \\varepsilon_o)^{-1}\\) = 9 x 109Nm2C-2]', '21\\(\\mu C\\)~3.6\\(\\mu C\\)~4.0\\(\\mu C\\)~4.4\\(\\mu C\\)', '21\\(\\mu C\\)', 'F = \\(\\frac{Q^2}{4 \\pi \\varepsilon_o r^2}\\)\n\nI = 9 x 109 x \\(\\frac{Q^2}{0.2^2}\\)\n\nQ = \\(\\sqrt{\\frac{0.04}{9 \\times 10^9}}\\)\n\n= 2.11 x 10-6', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(270, '269', 'In the circuit diagram above, E is a battery of negligible internal resistance. If its emf is 9.0V. Calculate the current in the circuit ', '1.8A~1.0A~0.8A~0.3A', '1.0A', '\\(\\frac{1}{r} = \\frac{1}{r_1} + \\frac{1}{r_2}\\)\n\n= \\(\\frac{1}{5} + \\frac{1}{20}\\)\n\n= \\(\\frac{4 + 1}{20} = \\frac{5}{20}\\)\n\nr = \\(\\frac{20}{5}\\)\n\n= 4\\(\\Omega\\)\n\nR = R1 + R2\n\n= 5 + 4 \n\n= 9\\(\\Omega\\)\n\nbut V = IR \n\nI = \\(\\frac{V}{R} = \\frac{9}{9}\\)\n\n= 1A', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(271, '270', 'A wire of length 100 cm has a resistance of 10\\(\\Omega\\). If its cross-sectional area is 0.005cm2, determine its resistivity', '0.0005\\(\\Omega\\)cm~0.0015\\(\\Omega\\)cm~0.0016\\(\\Omega\\)cm~0.0700\\(\\Omega\\)cm', '0.0005\\(\\Omega\\)cm', 'e = \\(\\frac{RA}{L} = \\frac{10 \\times 0.005}{100} = 0.0005\\)', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(272, '271', 'A transformer has 400 turns of wire in the primary coil and 40 turns in the secondary col. If the input voltage is 150 volts. Calculate the magnitude of the output voltage', '150V~55V~36V~15V', '15V', '\\(\\frac{ES}{EP} = \\frac{Ns}{Np} = \\frac{Es}{150} = \\frac{40}{400}\\)\n\nEs = \\(\\frac{150 \\times 40}{400}\\)\n\n= 15V', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(273, '272', 'The circuit above illustrates a standard resistor R, voltage source E and a lamp L connected in series. If the temperature of R is increased, the brightness of the lamp will', 'increase sharply~decrease slightly~remains the same~increase gradually', 'decrease slightly', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(274, '273', 'The energy required to separate the nucleus in an atom completely is known as', 'mass defect of the atom~electron binding energy~excitation energy~nuclear binding energy', 'nuclear binding energy', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(275, '274', 'Which of the following statements is the major advantage of nuclear fusion over nuclear fission?', 'nuclear fusion releases more energy~more neutrons are released in fusion than in fission~fussion does not release as much dangerous radiation as fission~fusion reactions occur more readily than fission', 'fussion does not release as much dangerous radiation as fission', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(276, '275', 'An aluminum foil is placed across a beam of radiation from a radioactive source. Which of the following types of radiation will be stopped by it?', 'alpha and beta particles~alpha and gamma particles~beta and gamma particles~gamma particles only', 'alpha and beta particles', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(277, '276', 'An element of nucleon number P and atomic number Q emits an alpha particle from its nucleus. The resultant numbers of the new element formed are respectively', 'P - 4 and Q + 2~P - 4 and Q - 2~P + 2 and Q + 2~P + 2 and Q - 2', 'P - 4 and Q - 2', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(278, '277', 'Which of the following statements about mass and weight are correct? i. Weight is the force of gravity on a body. ii. The mass of a body is the quantity of matter in the body. iii. The weight of a body is greatest at the equator. iv. The mass of a body is greatest at the poles', 'i and ii only~i and iii only~ii and iv only~iii and iv only', 'i and ii only', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(279, '278', 'Materials that can be stretched and still return to their original forms when the stresses are removed are said be', 'elastic~elastomer~plastic~thermoplastic', 'elastic', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(280, '279', 'Which of the following units is derived?', 'kg~m~K~N', 'N', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(281, '280', 'The barometric reading at a place is 73.5m Hg. Calculate the pressure at a point 30m below the surface of water contained in a reservoir at the place. [g = ms-2, density = 1.2 x 104kg m-3, density of water = 1.0 x 103m-3]', '4.0 x 105 Nm-2~3.0 x 10 5 Nm-2~2.0 x 105 Nm-2~1.0 x 105 Nm-2', '3.0 x 10 5 Nm-2', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(282, '281', 'An object floats in a fluid when it displaces it\'s', 'volume of liquid in which it floats~mass of fluid in which it foats~weith of fluid in which it foats~density of fluid in which it foats', 'weith of fluid in which it foats', 'A floating object displaces a weight of fluid equal to its own weigh', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(283, '282', 'The resultant force in a couple is', 'zero~infinite~the sum of the forces~thr product of the forces', 'zero', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(284, '283', 'The slope of a straight-line velocity-time graph represents', 'uniform acceleration~uniform speed~total distance travelled~workdone', 'uniform acceleration', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(285, '284', 'A body is projected with an initial velocity U at an angle O to the horizontal. The time taken by it to reach its maximum height is given by the expression', '\\(\\frac{2u \\text{sin}\\theta}{g}\\)~\\(\\frac{u^2 \\text{sin}^2\\theta}{2g}\\)~\\(\\frac{u \\text{sin}\\theta}{g}\\)~\\(\\frac{u \\text{sin}\\theta}{2g}\\)', '\\(\\frac{u \\text{sin}\\theta}{g}\\)', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(286, '285', 'Which of the following statements describes a body in a stable equilibrium correctly?', 'a person walking on a tight-rope~ball on a smooth horizontal table~ball resting on an inverted hemisphere bowl~ball in the middle of a nemispherical bowl', 'ball in the middle of a nemispherical bowl', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(287, '286', 'In a school compound a girl walks 40km due east from the laboratory to the staff room to submit her report. Then she returns and walks 30m due north to her classroom. Determine the magnitude of her displacement from the10m laboratory', '10m~35m~50m~70m', '50m', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(288, '287', 'Two strings each inclined at an angle 30o to the horizontal are used to hold a bucket of water weighing 20N. Calculate the tension i n each string.', '20\\(sqrt{3}\\)N~20N~10\\(sqrt{3}\\)N~10N', '10\\(sqrt{3}\\)N', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(289, '288', 'A bullet fired vertically upwards reaches a height of 500m. Neglecting air resistance, calculate the magnitude of the initial velocity of the bullet. [g = 10ms-2]', '500.0ms-1~100.0ms-1~70.0ms-1~50.0ms-1', '100.0ms-1', 'V2 = U2 + 2gs\n\nV2 = 0\n\nV2 = 2gs\n\nh = 500m\n\ng = 10ms-2\n\nV2 2 x 10 x 500\n\nV2 = 10,000 \n\nV = \\(\\sqrt{10000}\\)\n\nV = 100ms-1', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(290, '289', 'A uniform bar AB is balanced on a knife-edge which is 60cm from B by a mass of 22g which hangs at C 10cm from A. Calculate the mass of the bar.', '133.2g~66.0g~60.0g~22.0g', '66.0g', 'clockwise movement = anticlockwise movement \n\nw x 10 = 22 x 30\n\nw = \\(\\frac{22 \\times 30}{10}\\)\n\nw = 66.0g', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(291, '290', 'A body of mass 1000kg is released from a height of 10m above the ground. Determine its kinetic energy just before it strikes the ground .[g = 10ms-2]', '10J~103J~104J~105J', '105J', 'Ke = mgh\n\nKe = Pe\n\n\\(\\frac{1}{2}\\)MV2 = mgh \n\nKe = 1000 x 10 x 10\n\nKe = 100000J\n\nKe = 105J', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(292, '291', 'The crackling noise produced by aluminum roofing sheets on a house during a hot sunny day is a result of', 'thermal equilibrium of the sheets~conduction of heat by the sheets~contraction of the sheets~expansion of the sheets', 'expansion of the sheets', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(293, '292', 'Water is unsuitable for use as a thermometric liquid because it', 'expands unevenly between 0oC and 40oC~has narrow temperature range~has a concave meniscus~msintsin s fixed density', 'expands unevenly between 0oC and 40oC', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(294, '293', 'The diagram above illustrates a block ans tackle pulley system in which an effort E supports a load of 100.0N. If the efficiency of the machine is 75%, calculate the value of E', '22.2N~38.0N~67.0N~75.0N', '22.2N', 'Given', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(295, '294', 'A quantity of hot water at 100oC is added to 400g of water at 10oC until the temperature of the mixture is 60oC.', '200g~320g~400g~500g', '500g', 'Heat lost by hot water = Heat gained by cold water \n\nM x 4200 x (100 - 60 = 0.4 x 4200 x (60 - 10)\n\n4200m x 40 = 0.4 x 4200 x 50 \n\n40m = 0.4 x 50 \n\nm = \\(\\frac{0.4 \\times 50}{40}\\) = 0.5kg\n\n= 500g', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(296, '295', 'A battery of emf 24V is connected to three resistor P, Q and R as illustrated in the diagram. Determine the voltage across the resistor Q', '5v~10v~14v~24v', '10v', 'E - V1 + V2\n\n24V = 14V + VQP \n\nVQP = 4 + 14V \n\nVQP =10V', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(297, '296', 'In an experiment in which a molten substance is allowed to cool, the cooling curve above was obtained. The temperature 60oC is known as the', 'vaporization point~cooling temperature~boiling point~melting point', 'melting point', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(298, '298', 'Which of the following concepts is a method of heat transfer that does not require a material medium?', 'conduction~radiation~diffusion~convection', 'radiation', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(299, '299', 'Which of the following units is the S.I. unit of heat capacity?', 'Jkg-1~Jkg-1 K-1~JK-1~Jg-1K-1', 'JK-1', 'Heat capacity = \\(\\frac{\\text{Heat energy supplied}}{\\text{Rise in temperature}}\\)\n= JK\\(^{-1}\\)', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(300, '300', 'The pressure applied to an enclosed fluid to one end id transmitted equally throughout the fluid and to the container walls. This statement is', 'Archimede\'s principle~Bernoulli\'s principle~Pascal\'s principle Heisenberg\'s~Heisenberg\'s uncertainty principle', 'Pascal\'s principle Heisenberg\'s', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(301, '301', 'The diagram given illustrates a wave form. Determine the speed of the wave', '5.4 ms-1~8.4 ms-1~9.6 ms-1~10.0 ms-1', '10.0 ms-1', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(302, '302', 'What type of wave is emitted by a loud speaker?', 'Transverse~Longitudinal~Gamma~Radio', 'Longitudinal', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(303, '303', 'An object is placed 15cm from a diverging lens of focal length 12cm. The image of the object formed by the lens in', 'real and 6.67cm from the lens~virtual and 6.67cm from the lens~real and 60.00cm from the lens~virtual and 60.00cm from the lens', 'virtual and 6.67cm from the lens', 'The focal length of a diverging lens is negative.\nf = -12 cm', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(304, '304', 'A swimming pool is .1m deep. If it contains water of refractive index 1.3, calculate the apparent depth of pool', '3.4m~2.7m~1.6m~0.8m', '1.6m', 'n = \\(\\frac{\\text{real depth}}{\\text{apparent depth}}\\)\n\n1.3 = \\(\\frac{2.1}{\\text{apparent}}\\)\n\nA.D = \\(\\frac{2.1}{1.3} = 1.6\\)', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(305, '305', 'When an air column is set into vibrations, the distance between two consecutive nodes of the resultant wave is', 'one quarter of the wavelength~half of the wavelength~the wavelength~twice the wavelength', 'half of the wavelength', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(306, '306', 'A girl standing some distance from the cliff claps her hands and hears the echo 0.8s later. calculate her distance from the cliff. [speed of sound in air = 320 ms-1]', '23m~128m~288m~298m', '128m', 'V = \\(\\frac{2nx}{E}\\)\n\n= \\(\\frac{2 \\times 1 \\times X}{0.8} = 320\\)\n\n2x = 0.8 x 320\n\nx = \\(\\frac{0.8 \\times 320}{2}\\)\n\n= 128m', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(307, '307', 'Red light travels faster than blue light when both of them pass through a glass prism because the', 'refractive index of red light is grester than that of blue light~refractive index of blue light is greater than that of red light~red light is more intense than the blue light~blue light is more intense than the red light', 'blue light is more intense than the red light', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(308, '308', 'An object is placed 20cm from a concave mirror of focal length 15cm. Calculate the linear magnification of the image formed', '0.5~1.5~2~3', '3', '\\(\\frac{1}{U} + \\frac{1}{V} = \\frac{1}{F}\\)\n\n\\(\\frac{1}{V} = \\frac{1}{F} - \\frac{1}{U}\\)\n\n\\(\\frac{1}{V} = \\frac{1}{15} - \\frac{1}{20}\\)\n\n\\(\\frac{1}{V} = \\frac{\\text{4 - 3}}{60}\\)\n\n\n\\(\\frac{1}{V} = \\frac{1}{60}\\)\n\nV = 60cm\n\nM = \\(\\frac{V}{U} = \\frac{60}{20}\\)\n\nM = 3.0cm', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(309, '309', 'All electromagnetic waves in a vacuum have the same', 'wavelength~frequency~speed~amplitude', 'speed', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(310, '310', 'The diagram given illustrates two charged particles W and X. The charges on W and x are respectively', 'negative~negative~positive~positive', 'negative', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(311, '311', 'An alternating current supply is connected to an electric lamp which lights with the same brightness as it does with direct current source emf 6v. The peak potential difference of the a.c supply is', '4.6v~6.0v~8.5v~12.0v', '8.5v', 'Vo = V\\(\\_{rms}\\) x \\(\\sqrt{2}\\)\n\nVo = 6 x 1.414\n\nVo = 8.484\n\n= 8.5v', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(312, '312', 'An electric generator', '120 w~360 w~720 w~2400 w', '720 w', 'Power - IV\n\nI = \\(\\frac{P}{V}\\)\n\n= \\(\\frac{12000}{2000}\\)\n\nI = 6A\n\nPower loss = I\\(^2\\)R = 6\\(^2\\)', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(313, '313', 'Which of the following statements is correct? When capacitors of different values are connected in series', 'the same charge flows through them~the same voltage appears across each capacitor~different quantities of charges flow through them in different voltages across them~different quantities of charges flows through them with the same voltage across them', 'the same charge flows through them', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(314, '314', 'Which of the following statements about a three-pin plug is', 'i only~ii only~i and ii only~i, ii and iii', 'i and ii only', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(315, '315', 'The symbol illustrated above is that of a resistor', 'which absorb light~which emits light~which absorbs heat to function properly~whose resistance is light dependent', 'which absorbs heat to function properly', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(316, '316', 'A wire of cross-sectional area 0.60mm2 has a restivity of 7.2 x 10-7 \\(\\Omega\\). Calculate the length of wire that will have a resistance of 3\\(\\Omega\\).', '0.25m~2.50m~3.60m~36', '2.50m', 'R = \\(\\frac{PL}{A}\\)\n\nC = \\(\\frac{RA}{P}\\)\n\nC = \\(\\frac{0.60 \\times 10^{-6} \\times 3}{7.2 \\times 10^{-7}}\\)\n\nC = 2.50m', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(317, '317', 'A battery of emf 24V is connected to three resistor P, Q and R as illustrated in the given diagram. Determine the voltage across the resistor Q.', '5V~10V~14V~24V', '10V', 'E - V1 + V2\n\n24V = 14V + VQP\n\nVQP = 24 + 14V\n\nVQP = 10V', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(318, '318', 'The mass of the earth is 6.0 x 1024kg and that of the moon is 7.0 x 1022kg. If the distance between them is 4.0 x 108m, calculate the force of attraction between them. [G = 6.7 x 10-11Nm2kg-2]', '1.8 x 105N~1.8 x 1010N~1.8 x 1015N~1.8 x 1020N', '1.8 x 1020N', 'F = \\(\\frac{GM_1M_2}{12^2}\\)\n\nF = 6.7 x 10-11x\n\nF = \\(\\frac{M_1M_2}{R^2}\\)\n\nF = \\(\\frac{6.7 \\times 10^{-11} \\times 6.0 \\times 10^{24} \\times 7.0 \\times 10^{22}}{(4 \\times 10^8)^2}\\) \n\n= 1.8 x 1020N', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(319, '319', 'The angle which the direction of the earth magnetic field makes with the horizontal at a palace is know as.', 'angle of contact~angle of dip~angle of declination~magnetic meridian', 'angle of dip', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(320, '320', 'What must be connected between the points P and Q to establish a steady current through the incomplete circuit diagram given?', 'Fuse~ammeter~Cell~voltmeter', 'Cell', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(321, '321', 'When current flows through a moving-coil galvanometer, the force exerted on the pointer depends on the', 'i only~ii only~i and iii only~i, ii and iii', 'i and iii only', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(322, '322', 'in a nuclear fission process, the mass defect was 1.2 x 10-5kg. Calculate the energy released. [speed of the light in vacuum = c = 3.0 x 108ms-1]', '1.08 x 1011J~5.20 x 1011J~1.08 x 1012J~2.50 x 1013J', '1.08 x 1012J', 'E - Mec2\n\nE = 1.2 x 10-5 x (3 x 108)2\n\nE = 1.08 x 1012J', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(323, '323', 'Which of the following statements about diode is correct?', 'reverse bias diodes have low resistance~forward bias diodes have high resistance~forward bias diodes produce high current~forward bias diodes function as a result of heat', 'forward bias diodes have high resistance', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(324, '324', 'Which of the following radiations constitutes a stream of electrons?', 'Ramma rays~X-rays~Cathode rays~Radio waves', 'Cathode rays', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(325, '325', '\\(^{226}_{88}Ra\\) emits two alpha particles to produce polonium(po) nuclide. The correct formula for the nuclide?', '\\(^{224}_{86}po\\)~\\(^{222}_{86}po\\)~\\(^{222}_{84}po\\)~\\(^{218}_{84}po\\)', '\\(^{218}_{84}po\\)', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(326, '326', 'The dimensions of momentum are', 'MLT~ML-1T-1~MLT-1~ML-1T', 'MLT-1', 'Momentum = kgms-1 = MLT-1', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(327, '327', 'A student measures the volume of a liquid using a measuring cylinder. What else needs to be measured by the student in order to determine the density of the liquid?', 'depth of the liquid in the cylinder~mass of the cylinder~mass of the liquid~tempersture of the liquid', 'mass of the liquid', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(328, '328', 'The diagram given, represents the graph of stress against strain for an elastic wire. The point Q on the graph is the', 'elastic linit~breaking point~yield point~proportional limit', 'breaking point', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(329, '329', 'A ball is dropped from the top of a tower. Due to air resistance,it reaches terminal velocity. Which of the following statement(s) about its motion is', 'i only~i and ii only~ii and iii only~i, ii and iii', 'i only', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(330, '330', 'Which of the following substances lowers the surface tension of water?', 'metal~sand~detergent~paper', 'detergent', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(331, '331', 'An object of volume 400cm3 and 2.5gcm-3 is suspended from a spring balance with half its volume immersed in water. Determine the reading on the spring balance. (Density of water = 1gcm-3)', '1200g~1000g~800g~400g', '800g', 'Mass = density x volume \n\n400 x 2.5 = 1000g\n\nLoss in mass = volume x density \n\n= \\(\\frac{400}{2}\\) x 1 = 200g\n\nReading on spring balance = 1000 - 200g = 800g', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(332, '332', 'The diagram given illustrates a force-distance graph for the motion of a wooden block. Determine the work done on the block when moved through a distance of 5m.', '4J~15J~5J~100J', '100J', 'W = FS = 20 X 5 \n\n= 100J', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(333, '333', 'The two person of a body undergoing a uniformly accelerated motion are (10s, 10ms-1) and (30s, 50ms-1). On the velocity-time graph pf the body.', '0.5ms-2~2.0ms-2~10.0ms-2~40.0ms-2', '2.0ms-2', 'Slope = a = \\(\\frac{\\deltav}{\\deltat}\\)\n\n= \\(\\frac{50 - 10}{30 - 10}\\) \n\n= 2.0ms-2', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(334, '334', 'At a birthday party, the celebrant pops a corked fruit wine. If the cork shoots out of the bottle at an angle of 40o to the horizontal and travels a horizontal distance of 4.50m in 1.25s. Calculate the initial speed of the cork.', '4.2ms-1~4.7ms-1~5.6ms-1~7.1ms-1', '4.7ms-1', 'R = Ucos\\(\\theta\\) x t \n\nU = \\(\\frac{R}{Cos \\theta \\times t}\\)\n\n= \\(\\frac{4.50}{Cos40N.25}\\)\n\n= 4.699m', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(335, '335', 'A uniform metre rule is balanced on a fulcrum placed at the 35cm mark by suspending a mass of 120g at the 10cm mark. Calculate the mass of the metre rule.', '60g~80g~120g~200g', '200g', 'Clock-wise moment = Anti-clock wise \n\n15 x m = 5 x 10 \n\nm = 200g', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(336, '336', 'A plank is placed along the path on which a wheel barrow containing sand is pushed at a construction site to prevent it from sticking as illustrated in the diagram given. The large area of the plank prevents the wheel barrow from getting stuck by', 'increasing the reaction on the ground~increasing the pressure on the ground~decreasing the pressure on the ground~decreasing the weight on the ground', 'decreasing the pressure on the ground', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(337, '337', 'When a body is thrown vertically upwards, its velocity at the maximum height is', 'maximium~zero~double its initial value~half its initial value', 'zero', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(338, '338', 'Resonance occurs when one vibrating object causes a second object to vibrate at its own natural', 'amplitude~speed~frequency~intensity', 'frequency', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(339, '339', 'The mouth piece of a telephone handset converts', 'electrical energy to sound energy~sound energy to electrical energy~sound energy to radiowave~radiowave to sound energy', 'sound energy to electrical energy', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(340, '340', 'In the clinical thermometer, the function of the kink is to i. Prevent the back flow of mercury after use. ii. Ensure the back flow of mercury after use. iii. Maintain the thermometric property of mercury. iv. Allow the temperature attained to be read.', 'i only~i and ii only~i and iv only~iii and iv only', 'i and iv only', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(341, '341', 'Which of the following statements correctly defines the boiling point of a liquid? The temperature at which the', 'saturated vapour pressure equals the atmospheric pressure~molecules leaves the liquid at a rate equal to the rate at which they return~molecules leave the liquid at a rate higher than that at which they return~molecules leave the liquid at a rate lower than the rate at which they return', 'saturated vapour pressure equals the atmospheric pressure', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(342, '342', 'The diagram given is used to determine the', 'boiling point of water~atmospheric pressure~upper fixed point of a thermometer~amount of water in the atmosphere', 'upper fixed point of a thermometer', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(343, '343', 'An aluminium rod of length 1.8m at 10', '155oC~160oC~169oC~179oC', '179oC', '\\(\\alpha = \\frac{L_2 - L_1}{L_1(\\theta_2 - \\theta_1)}\\)\n\nL\\(_2\\) - L\\(_1\\) = \\(\\alpha L_1 (\\theta_2 - \\theta_1)\\)\n\n\\(\\theta_2 = \\frac{0.007}{2.3 \\times 10^{-5} \\times 1.8}\\) + 10\n\n= 179', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(344, '344', 'A mercury-in-glass thermometer read 4cm at ice point and 29cm at steam point. Calculate the temperature when the mercury level is at 9cm', '13oC~20oC~33oC~38oC', '20oC', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(345, '345', 'The continuous stirring in the method of mixtures to determine the specific thermal capacity of a substance ensures', 'continuous dissipation of heat to the room~uniform distribution of thermal energy to all parts of the mixture~that the thermal energy is confined to the mixture~that there is rapid heat exchange', 'uniform distribution of thermal energy to all parts of the mixture', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(346, '346', 'Which of the following statements is correct about the effect of dissolved salt on the freezing point of water?', 'the freezing point is lowered~the freezing point is increased~there is no change in the freezing point~the change in the freezing point depends on the temperature of the surrounding', 'the freezing point is lowered', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY');
INSERT INTO `labelling1` (`id`, `examYear`, `questions`, `options`, `answer`, `explaination`, `imageDir`, `topic`, `package_id`, `subject_id`) VALUES
(347, '347', 'A pressurized perfume bottle is left on the window pane of a room. What happens to he gas molecules of the perfume on a sunny day? They', 'expand~collide less often~move more rapidly~contract', 'move more rapidly', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(348, '348', 'Given that v, f and \\(\\lambda\\) are the velocity, frequency and wavelength of a wave respectively. Which of the following equations is correct?', 'v = f2\\(\\lambda\\)~f = \\(\\frac{v}{\\lambda}\\)~f = \\(\\frac{v}{\\lambda^2}\\)~\\(\\lambda = \\frac{f}{v^2}\\)', 'f = \\(\\frac{v}{\\lambda}\\)', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(349, '349', 'The distance between two successive trough of a wave is 0.4m. If the frequency of the source is 825Hz, Calculate the speed of the wave', '165.0 ms-1~330.0ms-1~41.5ms-1~85.0ms-1', '330.0ms-1', 'v = f\\(\\lambda\\) \n\n= 825 x 0.4 \n\n= 330.0ms-1', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(350, '350', 'X-rays and infrared rays are both electromagnetic. Which common property do the waves have? Both waves', 'are longitudinal~have same frequency~have the same wavelength~travel at the same speed in a vacuum', 'travel at the same speed in a vacuum', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(351, '351', 'The image formed by a concave mirror is real, inverted and magnified, when object is placed', 'at the focus~at the centre of curvature~beyond the centre of curvature~between the centre of curvature and the focus', 'between the centre of curvature and the focus', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(352, '352', 'Total internal reflection. i. is a phenomenon of refraction of light. ii. occurs when light rays travel into a denser medium. iii. occurs when the critical angle is just exceeded. iv. is a phenomenon of reflection of light. Which of the statements above are correct?', 'i and ii only~i and iii only~i, ii and iii only~i, iii and iv only', 'i and iii only', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(353, '353', 'Complementary colours are those which', 'have the same refractive index~have the same wavelength~add-up to produce black light~add-up to produce white light', 'add-up to produce white light', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(354, '354', 'The diagram given illustrates the waveform of a note produced by vibrations in an air column of length L. If the speed of sound in air is V, derive an expression for the frequency of the notes', '\\(\\frac{V}{L}\\)~\\(\\frac{5VL}{2}\\)~\\(\\frac{5L}{4V}\\)~\\(\\frac{5V}{4L}\\)', '\\(\\frac{5V}{4L}\\)', 'L = \\(\\frac{5\\lambda}{4}\\)\n\n\\(\\lambda = \\frac{4L}{5}\\)\n\nBut \\(\\lambda = f\\lambda\\)\n\nf = \\(\\frac{v}{\\lambda} = \\frac{v}{\\frac{4L}{5}}\\)\n\n= \\(\\frac{5v}{4L}\\)', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(355, '355', 'The pair of musical instruments that works on the vibration of air in pipes is', 'piano and the organ~guitar and the flute~trumpet and the violin~flute and the trumpet', 'flute and the trumpet', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(356, '356', 'An astronomical telescope has objectives and eye-piece lenses of focal length 3.5m and 5cm respectively. Determine the magnifying power of the telescope when in normal adjustment', '70~17.5~7~0.7', '70', 'Magnify power = \\(\\frac{f_o}{f_e}\\)\n\n= \\(\\frac{3.5 \\times 100}{5.0}\\)\n\n= 70', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(357, '357', 'An aluminium cable of diameter 4 x 10-3m and resistivity 3.0 x 10-8\\(\\omega\\)m has a resistance of 21\\(\\Omega\\). Calculate the length of the cable. (\\(\\pi = 3.14\\))', '8.0 x 102m~8.8 x 103m~8.0 x 104m~8.8 x 104m', '8.8 x 103m', 'R = \\(\\frac{4eL}{\\pid^2}\\)\n\nL = \\(\\frac{R\\pid^2}{4e}\\)\n\n= \\(\\frac{21 \\times 3.14(4 \\times 10^{-3})^2}{4 \\times 3.0 x 10^{-8}}\\)\n\n= 8.8 x 103m', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(358, '358', 'The electricity meters in houses measure energy unit consumed in', 'kilowatt-hour~volt~ampere~coulomb', 'kilowatt-hour', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(359, '359', 'A man and his friend have masses 70kg and 60kg respectively. If they are seated 1.0m apart, calculate the gravitational force of attraction between them. (G = 6.67 x 10-11 Nm2 kg-2)', '1.59 x 10-14 N~2.80 x 10-7 N~1.30 x 10-2 N~6.30 x 1013 N', '2.80 x 10-7 N', 'F = \\(\\frac{GM_1M_}{r^2}\\)\n\n= \\(\\6.67 \\times 10^{-11} \\times 70 \\times 60}{1^2}\\)\n\n= 2.8014 x 10-7 N', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(360, '360', 'The p.d across a parallel-plate capacitor is 103V. If the distance between the two plates is 10cm. Calculate the magnitude of the electric field strength between the plates.', '1.0 x 104Vm-1~1.0 x 105Vm-1~1.5 x 105Vm-1~2.0 x 105Vm-1', '1.0 x 104Vm-1', 'E = \\(\\frac{v}{d} = \\frac{10^3}{0.1}\\)\n\n= 10000\n\n= 1.0 x 104Vm-1', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(361, '361', 'Two different materials, rubbed against each other acquired opposite charges when separated. This is an example of charging by', 'induction~friction~conduction~convection', 'friction', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(362, '363', 'Which of the following factors does not affect the e.m.f of a primary cell? Its', 'size~internal resistance~operating temperature~duration of usage', 'size', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(363, '364', 'Two magnets are used to magnetize a soft iron bar PQ as illustrated in the diagram given. The correct polarity at P and Q respectively', 'S and N~N and N~S and S~N and S', 'N and N', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(364, '365', 'In storing magnets, keepers are used to', 'reduced self-demagnetization~cancel the effect of the earth\'s magnetic field~protect the magnet from stray electric field~increase the strangth of the magnets', 'reduced self-demagnetization', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(365, '366', 'A 10\\(\\mu\\)C charge moves with a velocity of 1.0 x 105 ms-1 at right angle to a uniform magnetic field of flux density 5.0 x 10-4T. Calculate the force on the charge', '5.0 x 10-5N~5.0 x 10-4N~5.0 x 105N~5.0 x 106N', '5.0 x 10-4N', 'F = qvB\n\n= 10 x 10-6 x 1.0 x 105 x 10-4\n\n= 5.0 x 10-4N', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(366, '367', 'Which of the following statements is not correct about steel and soft iron?', 'steel is more magnetized than soft iron~permanent magnets are usually made of steel~soft iron is more readily magnetized than steel~soft iron more readily loses its magnetism than steel', 'steel is more magnetized than soft iron', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(367, '368', 'What determines the polarity at the ends of an electromagnet? The', 'magnitude of the current passing through the wire~material of the core of the magnet~material of the coil~direction of current in the wire', 'direction of current in the wire', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(368, '369', 'How many beta particle(s) are emitted in the radioactive decay of \\(^{198}_{79}Au \\leftarrow ^{198}_{80}Hg\\)?', '1~2~3~5', '1', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(369, '370', 'The phenomenon by which two light atomic nuclear combine to form a heavy nuclide with the release of energy is known as', 'radioactivity~nuclear fusion~nuclear fission~chain reaction', 'nuclear fusion', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(370, '371', 'In a p-type semiconductor, the', 'number of holes are equal to the number of electrons~electrical resistivity increases~electrons are the majority charge carriers~holes are the majority charge carriers', 'holes are the majority charge carriers', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(371, '372', 'Let \\(\\Delta\\)x be the uncertainty in the measurements of position and \\(\\Delta\\)p the uncertainty in measurement of momentum. The uncertainty principle relation is given as', '\\(\\Delta\\)x . \\(\\Delta\\)p = h~\\(\\Delta\\)x . \\(\\Delta\\)p \\(\\leq\\) = h~\\(\\Delta\\)x . \\(\\Delta\\)p \\(\\geq\\) = h~\\(\\Delta\\)x . \\(\\Delta\\)p ', '\\(\\Delta\\)x . \\(\\Delta\\)p \\(\\geq\\) = h', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(372, '373', 'Two angles of a pentagon are in the ratio 2', '72o~100o~120o~144o', '144o', '\n\n\nThe diagram given simple illustrates that a pentagon contains three \\(\\Delta\\)s. \n\nTwo angles which are in the ratio 2', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(373, '374', 'The S.I unit for sound energy is', 'Hz~cd~dB~J', 'J', 'Every form of energy is measured in joules (J).', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(374, '375', 'The general definition of elastic modulus is', '\\(\\frac{stress}{strain}\\)~\\(\\frac{strain}{stress}\\)~\\(stress \\times strain\\)~\\(\\sqrt{\\frac{stress}{strain}}\\)', '\\(\\frac{stress}{strain}\\)', 'Elastic modulus is the ratio of pressure (stress) applied to a body to the resistance (strain) produced by the body.\n= \\(\\frac{stress}{strain}\\)', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(375, '376', 'The diagram above illustrates a simple barometer. Which distance measures the atmospheric pressure?', 'PQ~QR~RS~QS', 'QR', 'The height of the mercury column in a simple barometer is calculated as the atmospheric pressure.', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(376, '377', 'The property of a body to remain at rest or to continue in uniform motion in a straight line is called', 'momentum~Inertia~impulse~Energy', 'Inertia', 'Inertia is the resistance of the object to any change in its motion, including a change in direction. An object will stay still or keep moving at the same speed and in a straight line, unless it is acted upon by an external unbalanced force.', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(377, '378', 'During a training session, two footballers pass a ball repeatedly between each other. The \'to and fro\' motion of the ball is not simple harmonic because the', 'I and III only~I and II only~II and III only~I, II and III', 'I and III only', 'In SHM, the body must have acceleration in a direction opposite to the displacement and the acceleration must be directly proportional to displacement. Also, the acceleration must be directed towards its mean position. This is not the case with a football on the pitch.', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(378, '379', 'A dam is able to hold a large quantity of water because its wall is', 'thickest at the top~thickest at the middle~thickest at the bottom~of the same thickness throughout', 'thickest at the bottom', 'The pressure of the water is much greater deeper down and the dam needs to be thick at the bottom so that it is strong enough to withstand this larger pressure.', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(379, '380', 'A body of mass m moving around a circle of radius r with a uniform speed v experiences a centripetal force F. The work done by the centripetal force on it is', 'Fv~zero~Fmr~\\(\\frac{Fr}{m}\\)', 'zero', 'The work done by centripetal force in the case of a uniform circular motion is 0 joules.', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(380, '381', 'A block is acted upon by TWO horizontal forces as illustrated in the diagram above. The block accelerates at 1.5\\(ms^{-2}\\). Calculate the mass of the block.', '6kg~9kg~10kg~15kg', '6kg', 'Total force exerted on the block = (10 - 1)N =9N\nForce = mass x acceleration\n9 = m x 1.5\nm = 9', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(381, '382', 'Which of the following quantities are dimensionally independent?', 'I and II~II, III and IV~I, II, III and IV~I, III and IV', 'I, III and IV', 'The quantities Efficiency, Dielectric constant and Refractive index are dimensionless.', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(382, '383', 'A body is projected with an initial velocity u at angle \\(\\theta\\) to the horizontal. If \\(R_{max}\\) is the maximum range of the projectile, what does the relation \\(\\frac{u^{2}}{R_{max}}\\) represent?', 'The vertical distance covered~Acceleration due to gravity~The horizontal distance covered~The acceleration of the body', 'Acceleration due to gravity', '\\(R_{max} = \\frac{u^{2}}{g}\\)\nHence, \\(g = \\frac{u^{2}}{R_{max}}\\)', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(383, '384', 'An object at rest is said to possess', 'potential energy~kinetic energy~chemical energy~electrical energy', 'potential energy', 'Potential energy is the energy that is stored in an object due to its position relative to some zero position.', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(384, '385', 'According to Newton\'s law of cooling, the heat energy lost per unit area of a body depends on the', 'I and II only~II and IV only~I,II and III~I, II and IV', 'I,II and III', 'The rate of cooling of liduid according to Newton\'s law of cooling depends on', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(385, '386', 'The graph of density against temperature for water is correctly illustrated by', 'I~II~III~IV', 'III', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(386, '387', 'A football is kicked at an angle of 45', '0.0\\(ms^{-1}\\)~5.6\\(ms^{-1}\\)~10.6\\(ms^{-1}\\)~15.0\\(ms^{-1}\\)', '10.6\\(ms^{-1}\\)', 'The horizontal component of velocity, \\(V_{x}\\), is unaffected by the acceleration of free fall and remains constant.\n\\(V_{x} = U_{x} = Ucos\\theta\\)\n= \\(15 \\times cos45 = 15\\times 0.7071\\)\n\\(\\approxeq 10.6ms^{-1}\\)', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(387, '388', 'The ice point on the absolute scale of temperature is', '0K~~100K~273K', '0K', 'The absolute zero of the scale of temperature being the ice point of the absolute scale of temperature is 0K, which is -273', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(388, '389', 'Which of the following factors does not increase the rate of evaporation of water in a lake?', 'Increase in the pressure of the atmosphere~Rise in temperature~Increase in the surface area of the lake~Increase in the speed of the wind', 'Increase in the pressure of the atmosphere', 'The rate of evaporation is increased by the lowering of atmospheric pressure and not its increase. Every other factor stands, for the increase of evaporation process.', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(389, '390', 'The bob of a simple pendulum takes 8.0s to complete 10 oscillations. Determine the frequency of oscillation of the bob.', '0.125Hz~1.25Hz~7.50Hz~8.00Hz', '1.25Hz', '10 complete oscillations = 8.0s\n1 complete oscillation (period) = \\(\\frac{8}{10}\\)s\nFrequency = \\(\\frac{1}{period}\\) = \\(\\frac{1}{0.8} = 1.25Hz\\)', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(390, '391', 'The diagram above illustrates the mercury-in-glass thermometer used for determining the temperature of a room. Use the data on it to determine the room temperature.', '3.3~7~13~30', '30', 'Let the room temperature be X.\nWe have, \\(\\frac{3-0}{10-0} = \\frac{X-0}{100-0}\\)\n\\(\\frac{3}{10} = \\frac{X}{100}\\)\n\\(X = \\frac{3 \\times 100}{10}\\)\n= 30', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(391, '392', 'Frequency is measured in', 'meter per second~seconds~hertz~farad', 'hertz', 'The unit of frequency is hertz, abbreviated Hz.', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(392, '393', 'Which of the following electromagnetic waves is most energetic?', 'Radio waves~X-ray~Gamma rays~Ultra-violet rays', 'Gamma rays', 'The gamma rays have the shortest wavelength and therefore, impart the highest photon energy.', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(393, '394', 'Rainbow formation is a natural phenomenon illustrating that white light', 'splits into three components after rainfall~is dispersed by glass prisms~splits into its constituent colours before rainfall~is dispersed into its constituent colours after rainfall', 'is dispersed into its constituent colours after rainfall', 'A rainbow is caused by the dispersion of sunlight by tiny water droplets present in the atmosphere, which can be seen after the rain.', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(394, '395', 'The lens illustrated above can best be described as a', 'converging meniscus~plano-convex~diverging meniscus~bi-convex', 'plano-convex', 'The diagram is that of a plano-convex lens', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(395, '396', 'Two plane mirrors are inclined to each other such that an object placed between them has 11 images. Determine the angle of inclination', '30~45~60~90', '30', 'Formula for number of images = \\(\\frac{360}{n} - 1\\)\nwhere n is the angle of inclination.\nGiven the number of images = 11, we have\n\\(\\frac{360}{n} - 1 = 11\\)\n\\(\\frac{360}{n} = 12\\)\n\\(n = \\frac{360}{12} =30', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(396, '397', 'The pitch of a note is not affected by', 'frequency~ tension in a vibrating string~mass of a vibrating string~amplitude of sound wave', 'amplitude of sound wave', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(397, '398', 'When two flat plate conductors are arranged in such a way that they possess equal and opposite charges seperated by a dielectric, they form a', 'electroscope~electrophorus~capacitor~cell', 'capacitor', 'Most capacitors contain at least two electrical conductors often in the form of metallic plates or surfaces separated by a dielectric medium.', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(398, '399', 'Which electrical device is illustrated above?', 'a.c. generator~a.c. motor~d.c. generator~d.c. motor', 'd.c. generator', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(399, '400', 'A simple barometer is constructed using a liquid \\(Q_{1}\\) of density 16.2\\(g', '1358mm~957mm~760mm~638mm', '638mm', 'Let \\(h_{Q}\\) and \\(\\rho_{Q}\\) be the least length and the density of \\(Q_{1}\\)', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(400, '401', 'A bar AB is balanced horizontally on two knife edges as illustrated as in the diagram above. Determine the weight of the bar.', '10.0N~20.0N~40.0N~50.0N', '40.0N', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(401, '402', 'To obtain a virtual, erect and magnified image from a thin converging lens, an object must be placed', 'between the focus and the lens~at the focus~between the focal length and twice the focal length~beyond twice the focal length', 'between the focus and the lens', 'When the object is placed between the optical centre of the lens and the focal length, the image formed is virtual, erect and magnified.', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(402, '403', 'The diagram above represents a transverse travelling wave. Which two points are 180', 'A and E~B and D~C and F~D and H', 'D and H', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(403, '404', 'Two objects P and Q of masses 100kg and 20kg respectively are 1.2m apart on a horizontal surface. Calculate the net gravitational force acting on Q. ', '\\(1.11\\times 10^{-7} N\\) towards P~\\(1.11\\times 10^{-7} N\\) towards Q~\\(9.26\\times 10^{-8} N\\) towards P~\\(9.26\\times 10^{-8} N\\) towards Q', '\\(9.26\\times 10^{-8} N\\) towards Q', '\\(F= \\frac{Gm_{1}m_{2}}{r^{2}}\\)\n\\(m_{1} = 100kg\\)\n\\(m_{2} = 20kg', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(404, '405', 'The primary of a transformer has 100 turns and its secondary has 200 turns. If the voltage at the primary is 100V, determine the voltage at the secondary.', '50V~100V~200V~400V', '200V', 'The ideal transformer (either step-up or step-down) works with the equation', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(405, '406', 'In the diagram illustrated a block of mass M is at rest on a plane inclined at an angle \\(\\theta\\) to the horizontal. As \\(\\theta\\) increases, the velocity ratio of the plane', 'increases~decreases~remain the same~decreases and later increases', 'decreases', 'The velocity ratio and therefore, the mechanical advantage of an inclined plane system increases as \\(\\theta\\) decreases and vice-versa.', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(406, '407', 'When the speed of a car is halved, its kinetic energy is', 'doubled~quartered~halved~quadrupled', 'quartered', 'Given \\(K_{1}\\) = \\(\\frac{mv^{2}}{2}\\).\nWhen v is halved, we have\n\\(K_{2}\\) = \\(\\frac{m\\times (\\frac{v}{2})^{2}}{2}\\)\n= \\(\\frac{K_{1}}{4}\\)\nHence, the initial kinetic energy is quartered.', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(407, '408', 'A wire of length 400cm is stretched between two fixed points. When plucked, its fundamental frequency is 150Hz. Calculate the speed of the wave produced.', '250\\(ms^{-1}\\)~625\\(ms^{-1}\\)~1200\\(ms^{-1}\\)~1500\\(ms^{-1}\\)', '1200\\(ms^{-1}\\)', 'The fundamental frequency \\((f_{0})\\) = \\(\\frac{v}{2l}\\)\n\\(f_{0} = 150Hz', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(408, '409', 'The diagram above illustrates a waveform. Determine the number of wavelengths in it', '4~3\\(\\frac{1}{2}\\)~2\\(\\frac{1}{2}\\)~2', '2\\(\\frac{1}{2}\\)', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(409, '410', 'A resistor with fixed resistance value is called a', 'resistance box~standard resistor~shunt resistor~multiplier resistor', 'standard resistor', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(410, '411', 'Which of the following statements is not an advantage of an alkaline accumulator?', 'The electrolyte does not need attention~It can be recharged~It has low internal resistance~It has a much longer life than lead-acid accumulator', 'The electrolyte does not need attention', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(411, '412', 'The diagram above illustrates the wire connections to a three-pin plug. The wires P, Q and R respectively are', 'live, neutral and earth~neutral, earth and live~earth, live and neutral~earth, neutral and live', 'neutral, earth and live', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(412, '413', 'Which of the following statements about parallel plate capacitors is', 'I only~I and II only~II and III only~I, II and III', 'II and III only', 'Capacitors pass AC but block DC signals (when charged up to the applied DC voltage), they are often used to separate the AC and DC components of a signal. Capacitors are also primarily used to store energy.', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(413, '414', 'The circuit contains three ammeters A1, A2 and A3 with readings of A2 and A3 shown as indicated in the diagram. Determine the reading of A1.', '2A~3A~5A~8A', '3A', 'Ammeters are connected in series so,\nA3= A2 + A1\nA1 = A3 - A1\n= 5A - 2A\n= 3A', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(414, '415', 'Which of the following statements about magnetic lines of force is not correct? They', 'pass through even non-magnetic materials~run from the north pole to the south pole~are in a state of tension and tend to be shorted~intersect one another', 'intersect one another', 'Two magnetic lines of force can not intersect each other.', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(415, '416', 'In which of the following activities is an induction coil not useful?', 'Investigation of high voltages~Study of electric discharge~Operation of X-ray tubes~A.C. power transmission', 'A.C. power transmission', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(416, '417', 'In a series R-L-C circuit, R = 10\\(\\Omega\\), \\(X_{c}\\)= 4\\(\\Omega\\) and \\(X_{L}\\) = 9\\(\\Omega\\). The impedance of the circuit is', '4.1\\(\\Omega\\)~5.0\\(\\Omega\\)~10.8\\(\\Omega\\)~11.2\\(\\Omega\\)', '11.2\\(\\Omega\\)', 'The impedance for a RLC circuit is\n\\(Z = \\sqrt{R^{2} + (X_{L} - X_{C})^{2}}\\)\n= \\(\\sqrt{10^{2} + (9 - 4)^{2}}\\)\n= \\(\\sqrt{125}\\)\n= 11.18\\(\\Omega\\) \\(\\approxeq\\) 11.2\\(\\Omega\\)', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(417, '418', 'A student uses two compass needles to investigate the magnetic field around a bar magnet. Which of the following diagrams show the correct directions of the needles?', 'A~B~C~D', 'B', 'By convention, the field direction is taken to be outward from the North pole and in to the South pole of the magnet. Also, they form closed lines.', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(418, '419', 'Which of the following is emitted in a process of natural radioactivity?', '\\(\\alpha\\)- particles and \\(\\beta\\)- particles~\\(\\alpha\\)- particles and X-rays~\\(\\beta\\)- particles and X-rays~\\(\\lambda\\)- rays and X-rays', '\\(\\alpha\\)- particles and \\(\\beta\\)- particles', 'In the course of natural radioactivity, alpha, beta and gamma rays are emitted.', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(419, '420', 'In which of the following situations is photoelectric effect employed?', 'I, II and IV only~I, III and IV only~III and IV only~I and II only', 'I, II and IV only', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(420, '421', 'Which of the following radiations has the longest wavelength?', 'Gamma ray~Radio wave~Infrared ray~X-ray', 'Radio wave', 'Radio wave has the longest wavelength and shortest frequency.', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(421, '422', 'In which of the following fields is radioisotopes not used?', 'Medicine~Oil industry~Agriculture~Weather forecast', 'Weather forecast', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(422, '423', 'A nuclide is represented by \\(_{32}^{70}B\\). Determine its neutron-proton ratio', '0.5~0.8~1.2~1.5', '1.2', 'The element B has a mass number of 70 with atomic number 32. Hence, B has 32 protons and (70-32) = 38 neutrons.\nThe neutron- proton ratio is 38', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(423, '424', 'The diagram above is a micrometer screw gauge. Determine its reading.', '2.44mm~2.46mm~2.86mm~2.96mm', '2.46mm', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(424, '425', 'Which of the following is the dimension for impulse?', 'MLT\\(^{-1}\\)~MLT\\(^{-2}\\)~MLT~ML', 'MLT\\(^{-1}\\)', 'Impulse = Force \\(\\times\\) time\nForce has the dimension \\(\\frac{ML}{T^{2}}\\), hence', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(425, '426', 'A body accelerates uniformly from rest at 2\\(ms^{-2}\\). Calculate its velocity when it has travelled a distance of 9m.', '3.0\\(ms^{-1}\\)~4.5\\(ms^{-1}\\)~6.0\\(ms^{-1}\\)~18.0\\(ms^{-1}\\)', '6.0\\(ms^{-1}\\)', 'Given that \\(u = 0ms^{-1}, a = 2ms^{-2}, s = 9m\\)\nWe can use the equation, \\(v^{2}=u^{2} +2as\\) so that we have,\n\\(v^{2} = 0^{2} + 2\\times 2\\times 9\\)\n\\(v^{2} = 36', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(426, '427', 'Which of the following statements about matter is not correct?', 'Molecules of solids move more freely than molecules of liquids and gases~Molecules of solids are more closely packed than those of liquids~Energy is required to break the intermolecular forces of attraction between molecules~Molecules of liquids move about within the liquid and they are in constant motion', 'Molecules of solids move more freely than molecules of liquids and gases', 'All other properties of the different states of matter holds except that the molecules of solids don\'t move freely due to the fact that the particles in the solids are closely packed so it inhibits free motion.', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(427, '428', 'A ball is projected horizontally from the top of a tower. Neglecting air resistance, which of the following statements about its motion is', 'I only~II only~I and II only~II and III only', 'II and III only', 'The body while coming down is acted upon by acceleration due to gravity, hence, the vertical force is constant. Also, at maximum height, the vertical velocity is 0 and then increases as the body comes downward.', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(428, '429', 'Two forces 100N and 60N act on an object of mass 10kg as illustrated in the diagram above. Neglecting friction, calculate the acceleration of the object.', '4.0\\(ms^{-2}\\)~13.1\\(ms^{-2}\\)~16.0\\(ms^{-2}\\)~22.6\\(ms^{-2}\\)', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(429, '430', 'A body weighing 14N in air is partially immersed in water. If the mass of water displaced in the process is 200g, calculate the upthrust on the body. [g=10\\(m', '2.0N~3.0N~3.5N~7.0N', '2.0N', 'Upthrust = weight of liquid displaced\n= mass of liquid displaced \\(\\times\\) acceleration due to gravity\n= \\(\\frac{200}{1000} \\times 10\\)\n= 2N', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(430, '431', 'Which of the following processes is not a surface phenomenon?', 'Condensation~Evaporation~Photo Emission~Thermionic Emission', 'Condensation', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(431, '432', 'A chemical balance is used for measuring', 'volume~mass~thickness~density', 'mass', 'It is a type of beam balance with great precision, and it can pick up the slightest mass placed on it.', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(432, '433', 'A body is whirled round a circular path at constant speed. Which of the following diagrams correctly indicates the direction of the body\'s velocity (v) and its acceleration (a)?', 'I~II~III~IV', 'II', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(433, '434', 'A motorist travelling at 72\\(kmh^{-1}\\) had his eyes shut for 0.4s during a hard sneeze. Calculate the distance covered by him during this time interval.', '50.0m~28.8m~18.0m~8.0m', '8.0m', 'Convert velocity from', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(434, '435', 'The angle at which a projectile must be fired to cover maximum range is', '30~45~60~90', '45', 'The formula is \\(\\frac{v^{2}sin2\\theta}{g}\\)', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(435, '436', 'A body can undergo the following types of motion except', 'random~rotational~translational~relative', 'relative', 'Relative motion is the calculation of the motion of an object with regard to some other moving object. Hence, relative motion is not a type of motion.', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(436, '437', 'Which of the following graphs correctly represents the relationship between the kinetic energy (K.E) and the displacement (d) from point of release of a swinging pendulum bob?', 'I~II~III~IV', 'II', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(437, '438', 'The energy stored in a spring of stiffness constant k = 2000\\(Nm^{-1}\\) when extended 4cm is', '0.16J~1.60J~16.00J~160.00J', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(438, '439', 'Ice of mass 50g at 0', '2400J~6800J~7251J~24000J', '24000J', 'The quantity of heat needed to melt ice = mL (where m is the mass of ice and L is the specific latent heat of fusion of ice)\nQ = \\(50 \\times 336 = 16800J\\) but this is 70% of the total heat supplied so that we have,\n70% total heat = 16800J\n\\(\\frac{70}{100}\\) of total', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(439, '440', 'A plane is inclined at an angle \\(\\theta\\) to the horizontal. Its velocity ratio is', '\\(sin\\theta\\)~\\(tan\\theta\\)~\\(\\frac{1}{sin\\theta}\\)~\\(\\frac{1}{tan\\theta}\\)', '\\(\\frac{1}{sin\\theta}\\)', 'Velocity ratio = \\(\\frac{Effort distance}{Load distance}\\)\nOn an inclined plane, it is the inverse of \\(sin\\theta\\) = \\(\\frac{1}{sin\\theta}\\)', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(440, '441', 'The diagram above illustrates a beaker of water being heated. It is observed that as the bubbles rise they get bigger in size.The reason for this observation is', 'water pressure on the bubbles decreases~density of water increases with rise in temperature~volume of water increases with rise in temperature~atmospheric pressure on the bubbles decreases', 'water pressure on the bubbles decreases', 'When a bubble is deep under water, it has both atmospheric pressure and water pressure (giving it depth), acting on it but as it rises, the water pressure decreases. At this point, the basic pressre acting on the bubble is the atmospheric pressure. Recall that pressure is inversely proportional to volume (Boyles\' law), hence, the less the pressure, the more the volume.', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(441, '442', 'Which of the following devices converts light energy to electrical energy?', 'Bulb~Television~Solar cell~Light emitting diode (LED)', 'Solar cell', 'The solar cell converts light from the sun to electricity.', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(442, '443', 'A motor of a corn mill machine operates on electrical energy of \\(1.44 \\times 10^{5}\\)J. If one-quarter of the energy is wasted on sound and heat, determine the efficiency of the machine.', '0.25~0.36~0.64~0.75', '0.75', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(443, '444', 'Thermal energy added or removed from a substance that changes the state of the substance is called', 'latent heat~heat of reaction~calorimetry~specific heat', 'latent heat', 'Latent heat is thermal energy released or absorbed, by a body or a thermodynamic system, during a constant-temperature process.', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(444, '445', 'The maximum density of water occurs at a temperature of', '0~4~37~273', '4', 'This is as a result of the Hydrogen bonding in water. Due to the high Kinetic Energy of water, the hydrogen bonds can\'t hold for too long but from 4', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(445, '446', 'A vapour whose molecules are in dynamic equilibrium with those of its own liquid is said to be', 'unsaturated~gaseous~saturated~diffused', 'saturated', 'A saturated vapour is one which is in a dynamic equilibrium with its own liquid.', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(446, '447', 'The diagram above illustrates two waves of equal amplitudes A and frequencies approaching each other. When the two waves meet at a point I midway between them, the vertical displacement of the resulting wave will be', '0~\\(\\frac{A}{2}\\)~\\(\\frac{A}{4}\\)~\\(2A\\)', '\\(2A\\)', 'This is a type of constructive interference. When', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(447, '448', 'A rainbow is formed when sunlight is incident on water droplets suspended in the air due to', 'interference~refraction~dispersion~diffraction', 'dispersion', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(448, '449', 'Which of the following statements about the 3rd overtone of a vibrating air column of an open pipe is correct? It has', '4 nodes~5 nodes~3 antinodes~4 antinodes', '4 nodes', 'The 3rd overtone for an open pipe has 5 antinodes and 4 nodes.', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(449, '450', 'Consider the wave equation', 'Acceleration~Speed~Amplitude~Wavelength', 'Amplitude', 'Comparing the given equation with the wave equation', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(450, '451', 'Plane waves through a narrow gap emerge as circular waves. This phenomenon is known as', 'interference~dispersion~refraction~diffraction', 'diffraction', 'Diffraction refers to the various things that occur when a wave encounters an obstacle. This bending of the wave after it passes a small gap is an example of diffraction.', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(451, '452', 'A ray of light incident at an angle \\(\\theta\\) in a rectangular prism grazes the surface of the prism on emerging from the prism. Determine the value of the angle. [Absolute refractive index of the material of the prism is 1.5]', '41.8~48.2~60.8~90', '41.8', '\\(\\eta = \\frac{1}{sin\\theta}\\)\n\\(1.5 = \\frac{1}{sin\\theta}\\)\n\\(sin\\theta = \\frac{1}{1.5} = 0.667\\)\n\\(\\theta = sin^{-1}(0.667) = 41.835', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(452, '453', 'The diagram above illustrates a wave setup between two fixed ends 4.0m apart. If the speed of the wave is 1.0\\(ms^{-1}\\), its wavelength and frequency respectively are', '1m~2m~2m~4m', '2m', 'For the 4th harmonic, \\(L = 2\\lambda\\)\n\\(4m = 2\\lambda \\implies \\lambda = \\frac{4m}{2}\\)\n=\\(2m\\)\nRecall, \\(v = f\\lambda\\)\n\\(1 = f \\times 2 \\implies f = \\frac{1}{2}\\)\n= 0.50Hz', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(453, '454', 'Two plane mirrors are inclined at an angle 20', '17~18~19~20', '17', 'The number of images formed = \\(\\frac{360}{n}\\) where the value gotten is odd\nelse, = \\(\\frac{360}{n} -1\\).\nSolving, we have that \\(\\frac{360}{20} = 18\\)\nHence, the no of images formed is 18 - 1 = 17.', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(454, '455', 'A converging lens of focal length 10cm forms an erect image three times the size of the real object. Calculate the distance between the image and the object.', '6.6cm~11.1cm~13.3cm~20.0cm', '13.3cm', 'Given, image size = 3U\nobject size = U\nfocal length = 10cm\nlens to object distance = \\(\\frac{focal length \\times object size}{image size}\\)\n= \\(\\frac{10 \\times u}{3u} = 3.33\\)\ndistance between image and object = 10 + 3.33 = 13.33cm', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(455, '456', 'The inverse of the time required for a wave to complete one full cycle is called', 'wavelength~period~frequency~amplitude', 'frequency', 'The time required to complete one full cycle is the period', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(456, '457', 'Two bar magnets are placed near each other. Which of the following diagrams correctly illustrates the magnetic field pattern formed by the pair?', 'I~II~III~IV', 'II', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(457, '458', 'The force per unit charge experienced at a point in a field is the', 'gravitational field strength~electric potential~electric field intensity~magnetic field strength', 'electric field intensity', 'Electric intensity at a point is defined as the force experienced per unit positive charge at a point placed in the electric field.', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(458, '459', 'Which of the following objects is not a conductor of electricity?', 'The Earth~Human body~Iron rod~Dry wood', 'Dry wood', 'Dry wood is rather an insulator and not a conductor.', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(459, '460', 'A circuit is set up as shown in the diagram above. When the key is closed, the ammeter reading will be', '6A~4A~2A~1A', '2A', 'The resistors are connected both in parallel and series. To calculate the total resistance, we have', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(460, '461', 'Which of the following statements is', 'I, II and III~III only~II only~I only', 'I only', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(461, '462', 'The diagrams above illustrate electrical connections to the element of an electric pressing iron.In which of the connections is the fuse correctly fixed?', 'I~II~III~IV', 'II', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(462, '463', 'A transformer connected to a 240\\(V_{r.m.s}\\) has 3000 turns in its primary coil and 500 turns in its secondary coil. Calculate the output voltage.', '4000V~400V~40V~4V', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(463, '464', 'A lamp rated 100W, 240V is lit for 5hours. Calculate the cost of lighting the lamp if 1kWh of electrical energy cost N5.', 'N2.50~N3.20~N6.50~N9.60', 'N2.50', 'Power = 100W', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(464, '465', 'A battery of e.m.f 3.0V is connected across a potentiometer wire AB of length 10\\(\\Omega m^{-1}\\) as illustrated in the diagram above. If the jockey J makes contact at the 30cm mark, determine the resistance of length AJ and voltage across AJ.', '3.0\\(\\Omega\\)~3.0\\(\\Omega\\)~3.3\\(\\Omega\\)~3.3\\(\\Omega\\)', '3.0\\(\\Omega\\)', 'E = 3.0V', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(465, '466', 'The main reason why a.c. is transmitted at very high voltage and low current is that', 'flows faster through the conductor~can be stepped down~is cheaper to generate~reduces heat loss', 'reduces heat loss', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(466, '467', 'The diagram above illustrates two charged bodies, X and Y seperated by a distance r. Each body has charge q and mass m. Which of the following statements about the electrostatic force \\(F_{e}\\) and fravitational force \\(F_{g}\\) acting between the bodies is correct?', '\\(F_{e}\\) is attraction while \\(F_{g}\\) is repulsion~Both \\(F_{e}\\) and \\(F_{g}\\) are that of repulsion~Both \\(F_{e}\\) and \\(F_{g}\\) is that of attraction~\\(F_{e}\\) is repulsion while \\(F_{g}\\) is attraction', '\\(F_{e}\\) is repulsion while \\(F_{g}\\) is attraction', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(467, '468', 'The opposition offered to an alternating current in a C-R series circuit is known as', 'impedance~resistance~reactance~friction', 'impedance', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(468, '469', 'Which of the following pairs of concepts constitutes complementary variables as expressess by the Heinsberg uncertainty principle?', 'Momentum and time~Energy and acceleration~Position and momentum~Velocity and Momentum', 'Position and momentum', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(469, '470', 'The nucleon number of an atom is the total number of', 'electrons and protons~electrons and neutrons~neutrons minus electrons~protons and neutrons', 'protons and neutrons', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(470, '471', 'n = \\(\\alpha\\)', '+21.2eV~+10.4eV~-10.4eV~-21.2eV', '+10.4eV', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(471, '472', 'Which of the following statements about Gamma radiation is correct? Gamma radiation can', 'be seen by the naked eye~not pass through an aluminium foil~be present naturally in our surroundings~be used as a tracer', 'be used as a tracer', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY');
INSERT INTO `labelling1` (`id`, `examYear`, `questions`, `options`, `answer`, `explaination`, `imageDir`, `topic`, `package_id`, `subject_id`) VALUES
(472, '473', 'Radio wave', 'Visible, ultraviolet, X-ray~X-ray, visible, ultraviolet~Ultraviolet, visible, X-ray~X-ray, ultraviolet, visible', 'Visible, ultraviolet, X-ray', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY');

-- --------------------------------------------------------

--
-- Table structure for table `labelling_byuser`
--

CREATE TABLE `labelling_byuser` (
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  `examYear` varchar(200) NOT NULL,
  `questions` longtext NOT NULL,
  `options` longtext NOT NULL,
  `answer` longtext NOT NULL,
  `explaination` longtext NOT NULL,
  `imageDir` varchar(500) NOT NULL,
  `topic` varchar(500) NOT NULL,
  `package_id` varchar(200) NOT NULL,
  `subject_id` varchar(200) NOT NULL
) ENGINE=InnoDB DEFAULT CHARSET=utf8mb4;

-- --------------------------------------------------------

--
-- Table structure for table `label_acceptance`
--

CREATE TABLE `label_acceptance` (
  `id` int(11) NOT NULL,
  `user_id` varchar(200) NOT NULL,
  `label_id` varchar(200) NOT NULL,
  `limitation` int(200) NOT NULL,
  `status` int(1) NOT NULL,
  `timeStmp` timestamp NOT NULL DEFAULT current_timestamp() ON UPDATE current_timestamp()
) ENGINE=InnoDB DEFAULT CHARSET=utf8mb4;

--
-- Dumping data for table `label_acceptance`
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INSERT INTO `label_acceptance` (`id`, `user_id`, `label_id`, `limitation`, `status`, `timeStmp`) VALUES
(17, 'DL-USER-2', 'DL-1', 0, 0, '2021-07-05 11:01:32'),
(18, 'DL-USER-3', 'DL-1', 0, 0, '2021-07-05 11:29:51'),
(19, 'DL-USER-3', 'DL-2', 0, 0, '2021-07-05 13:12:23'),
(20, 'DL-USER-3', 'DL-3', 0, 0, '2021-07-13 11:01:20'),
(21, 'DL-USER-2', 'DL-2', 0, 0, '2021-07-19 11:37:53');

-- --------------------------------------------------------

--
-- Table structure for table `label_bank_details`
--

CREATE TABLE `label_bank_details` (
  `id` int(11) NOT NULL,
  `labeller_id` varchar(200) NOT NULL,
  `account_name` varchar(500) NOT NULL,
  `account_number` varchar(10) NOT NULL,
  `bank_sort_code` varchar(100) NOT NULL,
  `email` varchar(500) NOT NULL,
  `bank_name` varchar(500) NOT NULL
) ENGINE=InnoDB DEFAULT CHARSET=utf8mb4;

--
-- Dumping data for table `label_bank_details`
--

INSERT INTO `label_bank_details` (`id`, `labeller_id`, `account_name`, `account_number`, `bank_sort_code`, `email`, `bank_name`) VALUES
(4, 'DL-USER-2', 'Abubakar Bello', '123456', '124', 'bank@bank.com', 'Gt Bank');

-- --------------------------------------------------------

--
-- Table structure for table `label_package`
--

CREATE TABLE `label_package` (
  `id` int(11) NOT NULL,
  `database_name` varchar(200) NOT NULL,
  `file_name` varchar(200) NOT NULL,
  `label_name` varchar(2000) NOT NULL,
  `label_id` varchar(2000) NOT NULL,
  `label_descr` longtext NOT NULL,
  `label_timeline` date NOT NULL,
  `label_price` varchar(200) NOT NULL,
  `timeStmp` timestamp NOT NULL DEFAULT current_timestamp() ON UPDATE current_timestamp()
) ENGINE=InnoDB DEFAULT CHARSET=utf8mb4;

--
-- Dumping data for table `label_package`
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INSERT INTO `label_package` (`id`, `database_name`, `file_name`, `label_name`, `label_id`, `label_descr`, `label_timeline`, `label_price`, `timeStmp`) VALUES
(1, 'labelling', 'topics.txt', 'WAEC Mathematics Labelling', 'DL-1', '', '2021-05-12', '7000', '2021-07-04 13:51:14'),
(4, 'labelling1', 'topics2.txt', 'WAEC Physics Labelling', 'DL-2', '', '2021-05-12', '7000', '2021-07-04 13:51:27');

-- --------------------------------------------------------

--
-- Table structure for table `label_payments`
--

CREATE TABLE `label_payments` (
  `id` int(11) NOT NULL,
  `user_id` varchar(20) NOT NULL,
  `label_id` varchar(20) NOT NULL,
  `amount_paid` decimal(20,2) NOT NULL,
  `queCount` int(11) DEFAULT NULL,
  `pay_at` date NOT NULL,
  `payment_refrence` text DEFAULT NULL,
  `status` int(1) NOT NULL DEFAULT 1,
  `paid_by` varchar(20) NOT NULL
) ENGINE=InnoDB DEFAULT CHARSET=latin1;

--
-- Dumping data for table `label_payments`
--

INSERT INTO `label_payments` (`id`, `user_id`, `label_id`, `amount_paid`, `queCount`, `pay_at`, `payment_refrence`, `status`, `paid_by`) VALUES
(1, 'DL-USER-3', 'DL-1', '21000.00', 3, '2021-07-08', 'xhjxjhx', 1, 'Admin'),
(2, 'DL-USER-3', 'DL-2', '7000.00', 1, '2021-07-08', 'Direct Bank Transfer to GTB 090998889', 1, 'Admin'),
(3, 'DL-USER-3', 'DL-1', '21000.00', 3, '2021-07-08', 'yuyuuhjmn  iu', 1, 'Admin'),
(4, 'DL-USER-2', 'DL-2', '7000.00', 1, '2021-07-09', 'POS', 1, 'Admin');

-- --------------------------------------------------------

--
-- Table structure for table `label_users`
--

CREATE TABLE `label_users` (
  `id` int(11) NOT NULL,
  `fname` varchar(200) NOT NULL,
  `lname` varchar(200) NOT NULL,
  `email` varchar(500) NOT NULL,
  `password` varchar(200) NOT NULL,
  `state` varchar(200) NOT NULL,
  `phone` varchar(20) NOT NULL,
  `card_id` varchar(200) NOT NULL,
  `agree` varchar(20) NOT NULL
) ENGINE=InnoDB DEFAULT CHARSET=utf8mb4;

--
-- Dumping data for table `label_users`
--

INSERT INTO `label_users` (`id`, `fname`, `lname`, `email`, `password`, `state`, `phone`, `card_id`, `agree`) VALUES
(5, 'Abubakar', 'Bello', 'abubakarbello@steamledge.com', '12345', 'Kano', '9053447098', 'DL-USER-2', 'on'),
(6, 'Abdul', 'Abdul', 'py@test.com', '123456@', 'Abia', '09088776655', 'DL-USER-3', 'on'),
(7, 'TEST ', 'ADMIN', 'admin@ymail.com', '12345@', 'Kano', '00900', 'Admin', '--');

-- --------------------------------------------------------

--
-- Table structure for table `learn_lessons`
--

CREATE TABLE `learn_lessons` (
  `id` int(11) NOT NULL,
  `active_lesson` varchar(200) NOT NULL,
  `lesson_id` varchar(200) NOT NULL,
  `lesson_name` varchar(1000) NOT NULL,
  `file_name` varchar(200) NOT NULL,
  `topic_id` varchar(200) NOT NULL,
  `package_id` varchar(200) NOT NULL,
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  `images` longtext NOT NULL,
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  `lesson_type` int(2) NOT NULL,
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) ENGINE=InnoDB DEFAULT CHARSET=utf8mb4;

--
-- Dumping data for table `learn_lessons`
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INSERT INTO `learn_lessons` (`id`, `active_lesson`, `lesson_id`, `lesson_name`, `file_name`, `topic_id`, `package_id`, `subject_name`, `content_file`, `images`, `subject_id`, `lesson_type`, `package_name`) VALUES
(1, '', 'WAEC-MATH-LS-1', 'Conversion from Other Bases to Base 10', '1', 'WAEC-MATH-TP-1', 'WAEC-PK-1', 'Mathematics', '<fieldset>                     <div class=\"mySlides\">                      <!-- <p class=\"lesson_exp_head\">                         <span>Example 1 :</span>                         convert \\(111_{10}\\) to base 100                       </p>-->                                              <div class=\"lessons_step\">                         <p class=\"lesson_exp_head\">                           Step 1                         </p>                         <p class=\"lesson_explain\">converting \\(111_{10}\\) to its nearest base.</p>                         <p class=\"lesson-equation\">                           \\(x_{1,\\:2}=\\frac{-\\left(-1\\right)\\pm \\sqrt{\\left(-1\\right)^2-4\\cdot \\:1\\cdot                           \\left(-6\\right)}}{2\\cdot \\:1}\\)                         </p>                                                  <div class=\"row\" style=\"justify-content: space-between;\">                           <a href=\"#\" class=\" controlsBtn btn-previous\"><i class=\"fa fa-arrow-left\"></i> Example 1</a>                           <a href=\"#\" class=\" controlsBtn btn-next\"> Example 2 <i class=\"fa fa-arrow-right\"></i></a>                         </div>                       </div>                     </div>                                        </fieldset>', '', 'WAEC-MATH', 1, 'WAEC'),
(2, '', 'WAEC-MATH-LS-2', 'Converting from Base Ten to Other Bases', '2', 'WAEC-MATH-TP-1', 'WAEC-PK-1', 'Mathematics', '', '', 'WAEC-MATH', 1, 'WAEC'),
(3, '', 'WAEC-MATH-LS-3', 'Addition in other bases', '3', 'WAEC-MATH-TP-1', 'WAEC-PK-1', 'Mathematics', '', '', 'WAEC-MATH', 1, 'WAEC'),
(4, '', 'WAEC-MATH-LS-5', 'Multiplication in other Bases', '5', 'WAEC-MATH-TP-1', 'WAEC-PK-1', 'Mathematics', '', '', 'WAEC-MATH', 1, 'WAEC'),
(5, '', 'WAEC-MATH-LS-6', 'Division in Other Bases', '6', 'WAEC-MATH-TP-1', 'WAEC-PK-1', 'Mathematics', '', '', 'WAEC-MATH', 1, 'WAEC'),
(6, '', 'WAEC-MATH-LS-7', 'Bicimals', '7', 'WAEC-MATH-TP-1', 'WAEC-PK-1', 'Mathematics', '', '', 'WAEC-MATH', 1, 'WAEC'),
(7, '', 'NECO-MATH-LS-1', 'Conversion from Other Bases to Base 10', '1', 'NECO-MATH-TP-1', 'NECO-PK-1', 'Mathematics', '', '', 'NECO-MATH', 1, 'NECO'),
(8, '', 'NECO-MATH-LS-2', 'Converting from Base Ten to Other Bases', '2', 'NECO-MATH-TP-1', 'NECO-PK-1', 'Mathematics', '', '', 'NECO-MATH', 1, 'NECO'),
(9, '', 'NECO-MATH-LS-3', 'Addition in other bases', '3', 'NECO-MATH-TP-1', 'NECO-PK-1', 'Mathematics', '', '', 'NECO-MATH', 1, 'NECO'),
(10, '', 'NECO-MATH-LS-5', 'Multiplication in other Bases', '5', 'NECO-MATH-TP-1', 'NECO-PK-1', 'Mathematics', '', '', 'NECO-MATH', 1, 'NECO'),
(11, '', 'NECO-MATH-LS-6', 'Division in Other Bases', '6', 'NECO-MATH-TP-1', 'NECO-PK-1', 'Mathematics', '', '', 'NECO-MATH', 1, 'NECO'),
(12, '', 'NECO-MATH-LS-7', 'Bicimals', '7', 'NECO-MATH-TP-1', 'NECO-PK-1', 'Mathematics', '', '', 'NECO-MATH', 1, 'NECO'),
(13, 'active', 'JAMB-MATH-LS-1', 'Conversion from Other Bases to Base 10', '1', 'JAMB-MATH-TP-1', 'JAMB-PK-1', 'Mathematics', '', '', 'JAMB-MATH', 1, 'JAMB'),
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(912, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'If A=<latex>egin{pmatrix}8&-8&-10\\-5&6&5\\-9&7&10end{pmatrix}</latex>, find the Transpose of A (<latex>A^{T}</latex>).\n', '', 1, 'math', 'matrix'),
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(916, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'If A=<latex>egin{pmatrix}-2&-7&-7\\-5&-3&2\\2&8&-2end{pmatrix}</latex>, find the Transpose of A (<latex>A^{T}</latex>).\n', '', 1, 'math', 'matrix'),
(917, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'If A=<latex>egin{pmatrix}-5&6&-9\\8&8&-3\\10&3&-6end{pmatrix}</latex>, find the Transpose of A (<latex>A^{T}</latex>).\n', '', 1, 'math', 'matrix'),
(918, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'If A=<latex>egin{pmatrix}-9&2&-7\\8&3&-8\\-9&3&9end{pmatrix}</latex>, find the Transpose of A (<latex>A^{T}</latex>).\n', '', 1, 'math', 'matrix'),
(919, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'If A=<latex>egin{pmatrix}-3&7&-5\\2&-5&-5\\-10&8&-5end{pmatrix}</latex>, find the Transpose of A (<latex>A^{T}</latex>).\n', '', 1, 'math', 'matrix'),
(920, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'If A=<latex>egin{pmatrix}10&4&-5\\7&7&5\\10&2&-2end{pmatrix}</latex>, find the Transpose of A (<latex>A^{T}</latex>).\n', '', 1, 'math', 'matrix'),
(921, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'If A=<latex>egin{pmatrix}3&-7&7\\5&-2&7\\2&-5&9end{pmatrix}</latex>, find the Transpose of A (<latex>A^{T}</latex>).\n', '', 1, 'math', 'matrix'),
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(925, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'If A=<latex>egin{pmatrix}7&4&-2\\-10&5&4\\6&-2&2end{pmatrix}</latex>, find the Transpose of A (<latex>A^{T}</latex>).\n', '', 1, 'math', 'matrix'),
(926, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'If A=<latex>egin{pmatrix}-3&-3&8\\3&-10&10\\-8&-3&7end{pmatrix}</latex>, find the Transpose of A (<latex>A^{T}</latex>).\n', '', 1, 'math', 'matrix'),
(927, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'If A=<latex>egin{pmatrix}5&9&8\\3&-5&5\\-8&-6&3end{pmatrix}</latex>, find the Transpose of A (<latex>A^{T}</latex>).\n', '', 1, 'math', 'matrix'),
(928, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'If A=<latex>egin{pmatrix}-2&9&8\\8&-2&10\\3&-3&-9end{pmatrix}</latex>, find the Transpose of A (<latex>A^{T}</latex>).\n', '', 1, 'math', 'matrix'),
(929, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'If A=<latex>egin{pmatrix}-6&8&10\\-8&10&-9\\7&-10&8end{pmatrix}</latex>, find the Transpose of A (<latex>A^{T}</latex>).\n', '', 1, 'math', 'matrix'),
(930, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'If A=<latex>egin{pmatrix}8&5&-5\\-6&-3&8\\-9&-7&6end{pmatrix}</latex>, find the Transpose of A (<latex>A^{T}</latex>).\n', '', 1, 'math', 'matrix'),
(931, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'If A=<latex>egin{pmatrix}-8&-6&-8\\-7&-7&-7\\2&-7&-6end{pmatrix}</latex>, find the Transpose of A (<latex>A^{T}</latex>).\n', '', 1, 'math', 'matrix'),
(932, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'If A=<latex>egin{pmatrix}3&-7&2\\9&7&-3\\-7&2&-3end{pmatrix}</latex>, find the Transpose of A (<latex>A^{T}</latex>).\n', '', 1, 'math', 'matrix'),
(933, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'If A=<latex>egin{pmatrix}-7&-7&3\\7&-10&-8\\8&8&3end{pmatrix}</latex>, find the Transpose of A (<latex>A^{T}</latex>).\n', '', 1, 'math', 'matrix'),
(934, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'If A=<latex>egin{pmatrix}-3&2&4\\-9&7&-2\\-2&8&-6end{pmatrix}</latex>, find the Transpose of A (<latex>A^{T}</latex>).\n', '', 1, 'math', 'matrix'),
(935, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'If A=<latex>egin{pmatrix}4&-10&-7\\-10&-2&-5\\-10&8&10end{pmatrix}</latex>, find the Transpose of A (<latex>A^{T}</latex>).\n', '', 1, 'math', 'matrix'),
(936, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'If A=<latex>egin{pmatrix}3&-7&4\\3&-7&-5\\-9&8&-2end{pmatrix}</latex>, find the Transpose of A (<latex>A^{T}</latex>).\n', '', 1, 'math', 'matrix'),
(937, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'If A=<latex>egin{pmatrix}4&10&-6\\9&7&6\\4&9&10end{pmatrix}</latex>, find the Transpose of A (<latex>A^{T}</latex>).\n', '', 1, 'math', 'matrix'),
(938, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'If A=<latex>egin{pmatrix}-7&3&3\\-5&-10&6\\-2&9&-7end{pmatrix}</latex>, find the Transpose of A (<latex>A^{T}</latex>).\n', '', 1, 'math', 'matrix'),
(939, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'If A=<latex>egin{pmatrix}-9&-9&-8\\-2&-9&-5\\8&5&-3end{pmatrix}</latex>, find the Transpose of A (<latex>A^{T}</latex>).\n', '', 1, 'math', 'matrix'),
(940, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'If A=<latex>egin{pmatrix}3&6&-3\\6&4&3\\-10&6&6end{pmatrix}</latex>, find the Transpose of A (<latex>A^{T}</latex>).\n', '', 1, 'math', 'matrix'),
(941, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'If A=<latex>egin{pmatrix}-7&-6&10\\4&7&10\\-6&6&3end{pmatrix}</latex>, find the Transpose of A (<latex>A^{T}</latex>).\n', '', 1, 'math', 'matrix'),
(942, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'If A=<latex>egin{pmatrix}8&10&6\\-10&-3&-5\\-10&4&10end{pmatrix}</latex>, find the Transpose of A (<latex>A^{T}</latex>).\n', '', 1, 'math', 'matrix'),
(943, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'If A=<latex>egin{pmatrix}7&10&-9\\-6&6&8\\-6&-9&-3end{pmatrix}</latex>, find the Transpose of A (<latex>A^{T}</latex>).\n', '', 1, 'math', 'matrix'),
(944, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'If A=<latex>egin{pmatrix}6&3&-7\\8&8&10\\-5&8&4end{pmatrix}</latex>, find the Transpose of A (<latex>A^{T}</latex>).\n', '', 1, 'math', 'matrix'),
(945, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'If A=<latex>egin{pmatrix}10&4&-9\\-8&7&-2\\3&3&-10end{pmatrix}</latex>, find the Transpose of A (<latex>A^{T}</latex>).\n', '', 1, 'math', 'matrix'),
(946, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'If A=<latex>egin{pmatrix}-10&6&-10\\-2&-7&-3\\-7&7&-8end{pmatrix}</latex>, find the Transpose of A (<latex>A^{T}</latex>).\n', '', 1, 'math', 'matrix'),
(947, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'If A=<latex>egin{pmatrix}-9&9&-6\\-3&-10&-10\\-6&3&10end{pmatrix}</latex>, find the Transpose of A (<latex>A^{T}</latex>).\n', '', 1, 'math', 'matrix'),
(948, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'If A=<latex>egin{pmatrix}-8&-7&7\\-10&9&-7\\-8&-10&-2end{pmatrix}</latex>, find the Transpose of A (<latex>A^{T}</latex>).\n', '', 1, 'math', 'matrix'),
(949, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'If A=<latex>egin{pmatrix}-5&6&-8\\-5&5&6\\2&-6&10end{pmatrix}</latex>, find the Transpose of A (<latex>A^{T}</latex>).\n', '', 1, 'math', 'matrix'),
(950, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'If A=<latex>egin{pmatrix}3&7&4\\6&5&-8\\4&4&2end{pmatrix}</latex>, find the Transpose of A (<latex>A^{T}</latex>).\n', '', 1, 'math', 'matrix'),
(951, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'If A=<latex>egin{pmatrix}2&2&-2\\3&5&-6\\-2&10&-2end{pmatrix}</latex>, find the Transpose of A (<latex>A^{T}</latex>).\n', '', 1, 'math', 'matrix'),
(952, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'If A=<latex>egin{pmatrix}9&-8&10\\9&3&-8\\-8&9&-10end{pmatrix}</latex>, find the Transpose of A (<latex>A^{T}</latex>).\n', '', 1, 'math', 'matrix'),
(953, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'If A=<latex>egin{pmatrix}-10&-10&9\\5&-7&-10\\7&4&-9end{pmatrix}</latex>, find the Transpose of A (<latex>A^{T}</latex>).\n', '', 1, 'math', 'matrix'),
(954, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'If A=<latex>egin{pmatrix}-6&-9&-7\\-9&7&-6\\10&-9&3end{pmatrix}</latex>, find the Transpose of A (<latex>A^{T}</latex>).\n', '', 1, 'math', 'matrix'),
(955, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'If A=<latex>egin{pmatrix}-5&3&-9\\6&7&-2\\-3&4&-8end{pmatrix}</latex>, find the Transpose of A (<latex>A^{T}</latex>).\n', '', 1, 'math', 'matrix'),
(956, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'If A=<latex>egin{pmatrix}6&-10&5\\-3&-8&4\\3&6&8end{pmatrix}</latex>, find the Transpose of A (<latex>A^{T}</latex>).\n', '', 1, 'math', 'matrix'),
(957, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'Calculate the Determinant of A, if A=<latex>egin{pmatrix}4&6&3\\8&-5&10\\-6&-8&2end{pmatrix}</latex>.\n', '', 1, 'math', 'matrix'),
(958, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'Calculate the Determinant of A, if A=<latex>egin{pmatrix}-3&2&-5\\-3&-7&6\\5&-10&3end{pmatrix}</latex>.\n', '', 1, 'math', 'matrix'),
(959, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'Calculate the Determinant of A, if A=<latex>egin{pmatrix}8&-10&-6\\7&6&5\\-9&7&-6end{pmatrix}</latex>.\n', '', 1, 'math', 'matrix'),
(960, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'Calculate the Determinant of A, if A=<latex>egin{pmatrix}7&5&-10\\-8&5&10\\-3&-9&-10end{pmatrix}</latex>.\n', '', 1, 'math', 'matrix'),
(961, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'Calculate the Determinant of A, if A=<latex>egin{pmatrix}-7&8&-9\\-6&4&2\\-3&-5&-7end{pmatrix}</latex>.\n', '', 1, 'math', 'matrix'),
(962, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'Calculate the Determinant of A, if A=<latex>egin{pmatrix}-9&-9&10\\3&-5&-5\\10&10&-8end{pmatrix}</latex>.\n', '', 1, 'math', 'matrix'),
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(964, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'Calculate the Determinant of A, if A=<latex>egin{pmatrix}-10&9&-3\\-8&-8&8\\-2&-5&-7end{pmatrix}</latex>.\n', '', 1, 'math', 'matrix'),
(965, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'Calculate the Determinant of A, if A=<latex>egin{pmatrix}-7&6&4\\4&10&-3\\-10&6&-2end{pmatrix}</latex>.\n', '', 1, 'math', 'matrix'),
(966, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'Calculate the Determinant of A, if A=<latex>egin{pmatrix}8&4&-10\\-2&-5&4\\-8&6&-3end{pmatrix}</latex>.\n', '', 1, 'math', 'matrix'),
(967, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'Calculate the Determinant of A, if A=<latex>egin{pmatrix}-5&-2&-9\\5&-6&6\\-10&-5&2end{pmatrix}</latex>.\n', '', 1, 'math', 'matrix'),
(968, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'Calculate the Determinant of A, if A=<latex>egin{pmatrix}3&9&-2\\10&3&-2\\2&2&-10end{pmatrix}</latex>.\n', '', 1, 'math', 'matrix'),
(969, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'Calculate the Determinant of A, if A=<latex>egin{pmatrix}-6&-5&-3\\-2&-3&5\\-7&4&-5end{pmatrix}</latex>.\n', '', 1, 'math', 'matrix'),
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(972, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'Calculate the Determinant of A, if A=<latex>egin{pmatrix}8&6&-10\\-8&8&6\\-7&6&3end{pmatrix}</latex>.\n', '', 1, 'math', 'matrix'),
(973, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'Calculate the Determinant of A, if A=<latex>egin{pmatrix}2&5&10\\6&-6&4\\-8&-7&7end{pmatrix}</latex>.\n', '', 1, 'math', 'matrix'),
(974, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'Calculate the Determinant of A, if A=<latex>egin{pmatrix}-9&7&6\\-5&-2&-6\\7&-8&9end{pmatrix}</latex>.\n', '', 1, 'math', 'matrix'),
(975, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'Calculate the Determinant of A, if A=<latex>egin{pmatrix}10&-6&-6\\-6&-10&-8\\2&7&-10end{pmatrix}</latex>.\n', '', 1, 'math', 'matrix'),
(976, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'Calculate the Determinant of A, if A=<latex>egin{pmatrix}-10&10&3\\8&-3&-10\\10&-9&7end{pmatrix}</latex>.\n', '', 1, 'math', 'matrix'),
(977, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'Calculate the Determinant of A, if A=<latex>egin{pmatrix}-8&-8&-6\\9&-6&-3\\3&9&8end{pmatrix}</latex>.\n', '', 1, 'math', 'matrix'),
(978, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'Calculate the Determinant of A, if A=<latex>egin{pmatrix}-3&-5&-3\\-10&-8&-3\\-2&10&-10end{pmatrix}</latex>.\n', '', 1, 'math', 'matrix'),
(979, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'Calculate the Determinant of A, if A=<latex>egin{pmatrix}3&4&-5\\-9&-2&-7\\-7&-7&-5end{pmatrix}</latex>.\n', '', 1, 'math', 'matrix'),
(980, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'Calculate the Determinant of A, if A=<latex>egin{pmatrix}-6&-3&6\\-5&8&-6\\-8&-3&7end{pmatrix}</latex>.\n', '', 1, 'math', 'matrix'),
(981, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'Calculate the Determinant of A, if A=<latex>egin{pmatrix}-9&-3&10\\8&2&6\\2&-8&-9end{pmatrix}</latex>.\n', '', 1, 'math', 'matrix'),
(982, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'Calculate the Determinant of A, if A=<latex>egin{pmatrix}9&-8&-5\\5&6&-6\\5&9&-3end{pmatrix}</latex>.\n', '', 1, 'math', 'matrix'),
(983, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'Calculate the Determinant of A, if A=<latex>egin{pmatrix}2&10&-9\\-9&-7&6\\4&8&4end{pmatrix}</latex>.\n', '', 1, 'math', 'matrix'),
(984, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'Calculate the Determinant of A, if A=<latex>egin{pmatrix}3&10&7\\4&9&10\\-5&-7&4end{pmatrix}</latex>.\n', '', 1, 'math', 'matrix'),
(985, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'Calculate the Determinant of A, if A=<latex>egin{pmatrix}5&6&7\\4&5&5\\-3&-3&3end{pmatrix}</latex>.\n', '', 1, 'math', 'matrix'),
(986, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'Calculate the Determinant of A, if A=<latex>egin{pmatrix}-3&-10&8\\9&-9&-7\\4&7&-2end{pmatrix}</latex>.\n', '', 1, 'math', 'matrix'),
(987, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'Calculate the Determinant of A, if A=<latex>egin{pmatrix}8&-2&10\\-3&-6&5\\3&-7&10end{pmatrix}</latex>.\n', '', 1, 'math', 'matrix'),
(988, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'Calculate the Determinant of A, if A=<latex>egin{pmatrix}9&-6&6\\10&-2&-10\\-5&6&-3end{pmatrix}</latex>.\n', '', 1, 'math', 'matrix'),
(989, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'Calculate the Determinant of A, if A=<latex>egin{pmatrix}5&10&9\\-8&10&10\\5&-2&-8end{pmatrix}</latex>.\n', '', 1, 'math', 'matrix'),
(990, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'Calculate the Determinant of A, if A=<latex>egin{pmatrix}-2&6&3\\2&7&3\\-8&-5&5end{pmatrix}</latex>.\n', '', 1, 'math', 'matrix'),
(991, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'Calculate the Determinant of A, if A=<latex>egin{pmatrix}-5&6&-10\\4&3&-8\\-8&9&4end{pmatrix}</latex>.\n', '', 1, 'math', 'matrix'),
(992, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'Calculate the Determinant of A, if A=<latex>egin{pmatrix}9&10&-8\\8&-8&4\\8&9&9end{pmatrix}</latex>.\n', '', 1, 'math', 'matrix'),
(993, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'Calculate the Determinant of A, if A=<latex>egin{pmatrix}5&-9&3\\7&5&7\\-9&10&4end{pmatrix}</latex>.\n', '', 1, 'math', 'matrix'),
(994, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'Calculate the Determinant of A, if A=<latex>egin{pmatrix}-9&10&-6\\9&5&-3\\9&7&-3end{pmatrix}</latex>.\n', '', 1, 'math', 'matrix'),
(995, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'Calculate the Determinant of A, if A=<latex>egin{pmatrix}9&10&-2\\-6&-6&-2\\6&8&10end{pmatrix}</latex>.\n', '', 1, 'math', 'matrix'),
(996, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'Calculate the Determinant of A, if A=<latex>egin{pmatrix}3&6&10\\-7&-3&-5\\-6&7&5end{pmatrix}</latex>.\n', '', 1, 'math', 'matrix'),
(997, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'Calculate the Determinant of A, if A=<latex>egin{pmatrix}6&-3&-2\\7&-5&-10\\6&-6&9end{pmatrix}</latex>.\n', '', 1, 'math', 'matrix'),
(998, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'Calculate the Determinant of A, if A=<latex>egin{pmatrix}3&10&9\\-3&-8&3\\-7&9&-8end{pmatrix}</latex>.\n', '', 1, 'math', 'matrix'),
(999, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'Calculate the Determinant of A, if A=<latex>egin{pmatrix}-5&-10&9\\8&9&7\\-2&7&-3end{pmatrix}</latex>.\n', '', 1, 'math', 'matrix'),
(1000, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'Calculate the Determinant of A, if A=<latex>egin{pmatrix}8&-5&-3\\6&-5&-10\\-5&-5&-9end{pmatrix}</latex>.\n', '', 1, 'math', 'matrix'),
(1001, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'Calculate the Determinant of A, if A=<latex>egin{pmatrix}-5&3&5\\-5&6&-10\\6&5&2end{pmatrix}</latex>.\n', '', 1, 'math', 'matrix'),
(1002, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'Calculate the Determinant of A, if A=<latex>egin{pmatrix}7&-3&-9\\-9&-5&-2\\9&-10&5end{pmatrix}</latex>.\n', '', 1, 'math', 'matrix'),
(1003, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'Calculate the Determinant of A, if A=<latex>egin{pmatrix}4&5&6\\9&9&6\\8&6&-9end{pmatrix}</latex>.\n', '', 1, 'math', 'matrix'),
(1004, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'Calculate the Determinant of A, if A=<latex>egin{pmatrix}-2&-8&2\\-8&-6&-8\\-8&-2&4end{pmatrix}</latex>.\n', '', 1, 'math', 'matrix'),
(1005, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'Calculate the Determinant of A, if A=<latex>egin{pmatrix}-10&10&-5\\-6&8&8\\-3&-2&-10end{pmatrix}</latex>.\n', '', 1, 'math', 'matrix'),
(1006, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'Determine the Minor of the matrix, <latex>egin{pmatrix}10&-3&10\\6&9&-7\\-3&6&7end{pmatrix}</latex>.\n', '', 1, 'math', 'matrix'),
(1007, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'Determine the Minor of the matrix, <latex>egin{pmatrix}-5&-6&9\\2&-7&7\\-3&6&-8end{pmatrix}</latex>.\n', '', 1, 'math', 'matrix'),
(1008, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'Determine the Minor of the matrix, <latex>egin{pmatrix}3&-7&6\\3&9&3\\3&2&-6end{pmatrix}</latex>.\n', '', 1, 'math', 'matrix'),
(1009, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'Determine the Minor of the matrix, <latex>egin{pmatrix}3&-7&2\\7&4&3\\-7&-6&-9end{pmatrix}</latex>.\n', '', 1, 'math', 'matrix'),
(1010, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'Determine the Minor of the matrix, <latex>egin{pmatrix}-5&8&3\\-3&10&2\\2&9&-8end{pmatrix}</latex>.\n', '', 1, 'math', 'matrix'),
(1011, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'Determine the Minor of the matrix, <latex>egin{pmatrix}7&-8&9\\-6&9&-3\\4&-6&4end{pmatrix}</latex>.\n', '', 1, 'math', 'matrix'),
(1012, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'Determine the Minor of the matrix, <latex>egin{pmatrix}7&-10&6\\8&6&10\\-5&-2&-2end{pmatrix}</latex>.\n', '', 1, 'math', 'matrix'),
(1013, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'Determine the Minor of the matrix, <latex>egin{pmatrix}-3&2&5\\8&9&-2\\10&-5&6end{pmatrix}</latex>.\n', '', 1, 'math', 'matrix'),
(1014, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'Determine the Minor of the matrix, <latex>egin{pmatrix}-10&-9&9\\4&-3&-2\\10&-6&-9end{pmatrix}</latex>.\n', '', 1, 'math', 'matrix'),
(1015, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'Determine the Minor of the matrix, <latex>egin{pmatrix}-7&7&8\\-6&10&-3\\7&-10&9end{pmatrix}</latex>.\n', '', 1, 'math', 'matrix'),
(1016, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'Determine the Minor of the matrix, <latex>egin{pmatrix}-10&-10&8\\-10&7&-2\\-6&7&-2end{pmatrix}</latex>.\n', '', 1, 'math', 'matrix'),
(1017, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'Determine the Minor of the matrix, <latex>egin{pmatrix}-8&2&3\\3&3&-10\\2&-3&-8end{pmatrix}</latex>.\n', '', 1, 'math', 'matrix'),
(1018, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'Determine the Minor of the matrix, <latex>egin{pmatrix}5&6&-10\\-2&-2&4\\2&2&-3end{pmatrix}</latex>.\n', '', 1, 'math', 'matrix'),
(1019, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'Determine the Minor of the matrix, <latex>egin{pmatrix}5&-9&-8\\-6&-8&-9\\-8&7&4end{pmatrix}</latex>.\n', '', 1, 'math', 'matrix'),
(1020, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'Determine the Minor of the matrix, <latex>egin{pmatrix}2&5&3\\-5&5&-5\\2&-9&-3end{pmatrix}</latex>.\n', '', 1, 'math', 'matrix'),
(1021, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'Determine the Minor of the matrix, <latex>egin{pmatrix}4&-5&7\\-3&6&-9\\-9&2&2end{pmatrix}</latex>.\n', '', 1, 'math', 'matrix'),
(1022, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'Determine the Minor of the matrix, <latex>egin{pmatrix}5&5&-2\\5&-10&-10\\3&9&-10end{pmatrix}</latex>.\n', '', 1, 'math', 'matrix'),
(1023, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'Determine the Minor of the matrix, <latex>egin{pmatrix}8&-8&-2\\9&-7&3\\-7&-5&-8end{pmatrix}</latex>.\n', '', 1, 'math', 'matrix'),
(1024, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'Determine the Minor of the matrix, <latex>egin{pmatrix}5&-2&10\\-9&-9&-5\\7&-9&-3end{pmatrix}</latex>.\n', '', 1, 'math', 'matrix'),
(1025, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'Determine the Minor of the matrix, <latex>egin{pmatrix}3&-2&6\\-10&-9&-9\\-6&-9&7end{pmatrix}</latex>.\n', '', 1, 'math', 'matrix'),
(1026, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'Determine the Minor of the matrix, <latex>egin{pmatrix}3&3&7\\-8&8&-8\\4&-10&7end{pmatrix}</latex>.\n', '', 1, 'math', 'matrix'),
(1027, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'Determine the Minor of the matrix, <latex>egin{pmatrix}-6&4&10\\-9&8&-7\\7&-2&7end{pmatrix}</latex>.\n', '', 1, 'math', 'matrix'),
(1028, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'Determine the Minor of the matrix, <latex>egin{pmatrix}-5&-9&7\\5&-10&5\\4&9&-8end{pmatrix}</latex>.\n', '', 1, 'math', 'matrix'),
(1029, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'Determine the Minor of the matrix, <latex>egin{pmatrix}4&8&7\\3&-6&-2\\-3&8&-6end{pmatrix}</latex>.\n', '', 1, 'math', 'matrix'),
(1030, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'Determine the Minor of the matrix, <latex>egin{pmatrix}2&4&9\\-6&4&6\\-5&-3&3end{pmatrix}</latex>.\n', '', 1, 'math', 'matrix'),
(1031, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'Determine the Minor of the matrix, <latex>egin{pmatrix}-10&4&-10\\6&8&-10\\-9&8&-2end{pmatrix}</latex>.\n', '', 1, 'math', 'matrix'),
(1032, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'Determine the Minor of the matrix, <latex>egin{pmatrix}9&4&6\\-9&-6&-3\\7&9&6end{pmatrix}</latex>.\n', '', 1, 'math', 'matrix'),
(1033, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'Determine the Minor of the matrix, <latex>egin{pmatrix}-3&-3&-9\\9&-5&-5\\-2&-3&-5end{pmatrix}</latex>.\n', '', 1, 'math', 'matrix'),
(1034, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'Determine the Minor of the matrix, <latex>egin{pmatrix}-10&-9&-8\\-2&5&-2\\-3&10&3end{pmatrix}</latex>.\n', '', 1, 'math', 'matrix'),
(1035, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'Determine the Minor of the matrix, <latex>egin{pmatrix}6&-10&10\\8&-3&-3\\-8&-8&9end{pmatrix}</latex>.\n', '', 1, 'math', 'matrix'),
(1036, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'Determine the Minor of the matrix, <latex>egin{pmatrix}-8&-6&-5\\-7&-7&-8\\6&3&-7end{pmatrix}</latex>.\n', '', 1, 'math', 'matrix'),
(1037, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'Determine the Minor of the matrix, <latex>egin{pmatrix}6&5&-2\\-9&-9&-2\\4&-2&7end{pmatrix}</latex>.\n', '', 1, 'math', 'matrix'),
(1038, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'Determine the Minor of the matrix, <latex>egin{pmatrix}5&-3&-9\\-2&-2&-5\\-10&4&-8end{pmatrix}</latex>.\n', '', 1, 'math', 'matrix'),
(1039, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'Determine the Minor of the matrix, <latex>egin{pmatrix}-6&7&8\\-8&-10&4\\-3&3&10end{pmatrix}</latex>.\n', '', 1, 'math', 'matrix'),
(1040, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'Determine the Minor of the matrix, <latex>egin{pmatrix}3&-10&9\\-8&3&-7\\9&-3&10end{pmatrix}</latex>.\n', '', 1, 'math', 'matrix'),
(1041, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'Determine the Minor of the matrix, <latex>egin{pmatrix}2&4&-3\\3&7&2\\2&-7&-5end{pmatrix}</latex>.\n', '', 1, 'math', 'matrix'),
(1042, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'Determine the Minor of the matrix, <latex>egin{pmatrix}-3&-3&-6\\-9&7&6\\-3&6&9end{pmatrix}</latex>.\n', '', 1, 'math', 'matrix'),
(1043, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'Determine the Minor of the matrix, <latex>egin{pmatrix}7&2&-8\\4&6&-8\\-7&7&-5end{pmatrix}</latex>.\n', '', 1, 'math', 'matrix'),
(1044, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'Determine the Minor of the matrix, <latex>egin{pmatrix}7&4&-6\\-6&8&3\\3&3&4end{pmatrix}</latex>.\n', '', 1, 'math', 'matrix'),
(1045, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'Determine the Minor of the matrix, <latex>egin{pmatrix}8&-3&-6\\-8&10&-9\\-8&4&-2end{pmatrix}</latex>.\n', '', 1, 'math', 'matrix'),
(1046, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'Determine the Minor of the matrix, <latex>egin{pmatrix}10&-10&-10\\-5&3&6\\-2&-2&10end{pmatrix}</latex>.\n', '', 1, 'math', 'matrix'),
(1047, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'Determine the Minor of the matrix, <latex>egin{pmatrix}-3&10&-7\\10&-8&-5\\5&2&3end{pmatrix}</latex>.\n', '', 1, 'math', 'matrix'),
(1048, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'Determine the Minor of the matrix, <latex>egin{pmatrix}-3&-9&4\\6&9&2\\-6&3&3end{pmatrix}</latex>.\n', '', 1, 'math', 'matrix'),
(1049, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'Determine the Minor of the matrix, <latex>egin{pmatrix}-8&-9&-6\\7&2&8\\6&-2&8end{pmatrix}</latex>.\n', '', 1, 'math', 'matrix'),
(1050, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'Determine the Minor of the matrix, <latex>egin{pmatrix}-2&-9&7\\-3&3&8\\2&-9&9end{pmatrix}</latex>.\n', '', 1, 'math', 'matrix'),
(1051, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'Determine the Minor of the matrix, <latex>egin{pmatrix}-2&-5&-8\\-9&6&-2\\-2&-7&7end{pmatrix}</latex>.\n', '', 1, 'math', 'matrix'),
(1052, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'Determine the Minor of the matrix, <latex>egin{pmatrix}-3&-8&10\\3&-9&10\\-6&3&6end{pmatrix}</latex>.\n', '', 1, 'math', 'matrix'),
(1053, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'Determine the Minor of the matrix, <latex>egin{pmatrix}8&-7&-7\\-2&6&9\\9&5&-6end{pmatrix}</latex>.\n', '', 1, 'math', 'matrix'),
(1054, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'Determine the Minor of the matrix, <latex>egin{pmatrix}5&-3&-2\\-8&10&9\\4&9&-9end{pmatrix}</latex>.\n', '', 1, 'math', 'matrix'),
(1055, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'Calculate the Inverse of the matrix, <latex>egin{pmatrix}8&-3&-6\\-10&-5&-6\\4&6&8end{pmatrix}</latex>.\n', '', 1, 'math', 'matrix'),
(1056, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'Calculate the Inverse of the matrix, <latex>egin{pmatrix}-6&2&-10\\10&7&-6\\2&7&-3end{pmatrix}</latex>.\n', '', 1, 'math', 'matrix'),
(1057, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'Calculate the Inverse of the matrix, <latex>egin{pmatrix}2&-5&2\\7&9&-7\\2&-8&10end{pmatrix}</latex>.\n', '', 1, 'math', 'matrix'),
(1058, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'Calculate the Inverse of the matrix, <latex>egin{pmatrix}3&-7&-7\\6&-3&-9\\-3&3&8end{pmatrix}</latex>.\n', '', 1, 'math', 'matrix'),
(1059, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'Calculate the Inverse of the matrix, <latex>egin{pmatrix}10&2&10\\9&6&-10\\-8&3&-5end{pmatrix}</latex>.\n', '', 1, 'math', 'matrix'),
(1060, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'Calculate the Inverse of the matrix, <latex>egin{pmatrix}10&-2&-2\\-7&-9&7\\10&8&-3end{pmatrix}</latex>.\n', '', 1, 'math', 'matrix'),
(1061, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'Calculate the Inverse of the matrix, <latex>egin{pmatrix}6&-2&-9\\3&-5&-10\\9&-7&-9end{pmatrix}</latex>.\n', '', 1, 'math', 'matrix'),
(1062, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'Calculate the Inverse of the matrix, <latex>egin{pmatrix}-3&10&-9\\-9&10&-5\\9&2&2end{pmatrix}</latex>.\n', '', 1, 'math', 'matrix'),
(1063, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'Calculate the Inverse of the matrix, <latex>egin{pmatrix}-8&-8&10\\-7&7&8\\-6&8&-3end{pmatrix}</latex>.\n', '', 1, 'math', 'matrix'),
(1064, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'Calculate the Inverse of the matrix, <latex>egin{pmatrix}-2&-7&2\\-9&9&5\\-2&-9&10end{pmatrix}</latex>.\n', '', 1, 'math', 'matrix'),
(1065, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'Calculate the Inverse of the matrix, <latex>egin{pmatrix}3&10&-5\\-6&-3&3\\2&-2&-3end{pmatrix}</latex>.\n', '', 1, 'math', 'matrix'),
(1066, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'Calculate the Inverse of the matrix, <latex>egin{pmatrix}-9&-7&-6\\-2&-10&9\\9&-2&-5end{pmatrix}</latex>.\n', '', 1, 'math', 'matrix'),
(1067, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'Calculate the Inverse of the matrix, <latex>egin{pmatrix}3&-3&-6\\10&8&-9\\8&2&9end{pmatrix}</latex>.\n', '', 1, 'math', 'matrix'),
(1068, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'Calculate the Inverse of the matrix, <latex>egin{pmatrix}3&7&-8\\2&3&3\\4&7&10end{pmatrix}</latex>.\n', '', 1, 'math', 'matrix'),
(1069, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'Calculate the Inverse of the matrix, <latex>egin{pmatrix}4&-6&-5\\6&4&-3\\-10&-10&-6end{pmatrix}</latex>.\n', '', 1, 'math', 'matrix'),
(1070, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'Calculate the Inverse of the matrix, <latex>egin{pmatrix}-10&-8&2\\-6&4&3\\-3&-9&7end{pmatrix}</latex>.\n', '', 1, 'math', 'matrix'),
(1071, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'Calculate the Inverse of the matrix, <latex>egin{pmatrix}3&8&-6\\4&-8&-5\\8&-2&3end{pmatrix}</latex>.\n', '', 1, 'math', 'matrix'),
(1072, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'Calculate the Inverse of the matrix, <latex>egin{pmatrix}-9&-7&-7\\8&9&7\\7&-2&-5end{pmatrix}</latex>.\n', '', 1, 'math', 'matrix'),
(1073, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'Calculate the Inverse of the matrix, <latex>egin{pmatrix}-9&2&4\\-7&10&7\\7&-10&9end{pmatrix}</latex>.\n', '', 1, 'math', 'matrix'),
(1074, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'Calculate the Inverse of the matrix, <latex>egin{pmatrix}6&6&6\\-8&9&9\\2&4&3end{pmatrix}</latex>.\n', '', 1, 'math', 'matrix'),
(1075, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'Calculate the Inverse of the matrix, <latex>egin{pmatrix}-2&-3&6\\6&-2&-8\\-7&5&8end{pmatrix}</latex>.\n', '', 1, 'math', 'matrix'),
(1076, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'Calculate the Inverse of the matrix, <latex>egin{pmatrix}4&4&10\\6&10&-2\\-9&-6&4end{pmatrix}</latex>.\n', '', 1, 'math', 'matrix'),
(1077, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'Calculate the Inverse of the matrix, <latex>egin{pmatrix}-7&-3&3\\-9&-5&-6\\7&-7&8end{pmatrix}</latex>.\n', '', 1, 'math', 'matrix'),
(1078, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'Calculate the Inverse of the matrix, <latex>egin{pmatrix}3&-10&6\\6&-3&7\\-9&9&5end{pmatrix}</latex>.\n', '', 1, 'math', 'matrix'),
(1079, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'Calculate the Inverse of the matrix, <latex>egin{pmatrix}-8&-7&-10\\8&-5&10\\2&9&10end{pmatrix}</latex>.\n', '', 1, 'math', 'matrix'),
(1080, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'Calculate the Inverse of the matrix, <latex>egin{pmatrix}3&6&-8\\6&9&-8\\-2&-7&4end{pmatrix}</latex>.\n', '', 1, 'math', 'matrix'),
(1081, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'Calculate the Inverse of the matrix, <latex>egin{pmatrix}8&10&10\\3&-9&-6\\6&-10&7end{pmatrix}</latex>.\n', '', 1, 'math', 'matrix'),
(1082, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'Calculate the Inverse of the matrix, <latex>egin{pmatrix}-2&9&-6\\6&-9&10\\8&3&5end{pmatrix}</latex>.\n', '', 1, 'math', 'matrix'),
(1083, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'Calculate the Inverse of the matrix, <latex>egin{pmatrix}-6&7&4\\-2&5&5\\-10&-10&7end{pmatrix}</latex>.\n', '', 1, 'math', 'matrix'),
(1084, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'Calculate the Inverse of the matrix, <latex>egin{pmatrix}9&2&3\\5&-3&4\\3&-9&-5end{pmatrix}</latex>.\n', '', 1, 'math', 'matrix'),
(1085, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'Calculate the Inverse of the matrix, <latex>egin{pmatrix}8&9&4\\8&-3&4\\-2&9&4end{pmatrix}</latex>.\n', '', 1, 'math', 'matrix'),
(1086, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'Calculate the Inverse of the matrix, <latex>egin{pmatrix}2&-2&3\\8&-10&9\\6&-5&3end{pmatrix}</latex>.\n', '', 1, 'math', 'matrix'),
(1087, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'Calculate the Inverse of the matrix, <latex>egin{pmatrix}-10&8&-3\\-5&-9&6\\-8&7&-2end{pmatrix}</latex>.\n', '', 1, 'math', 'matrix'),
(1088, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'Calculate the Inverse of the matrix, <latex>egin{pmatrix}7&8&3\\-2&8&2\\-2&-5&-6end{pmatrix}</latex>.\n', '', 1, 'math', 'matrix'),
(1089, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'Calculate the Inverse of the matrix, <latex>egin{pmatrix}3&-2&-2\\4&-10&-7\\5&-9&-2end{pmatrix}</latex>.\n', '', 1, 'math', 'matrix'),
(1090, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'Calculate the Inverse of the matrix, <latex>egin{pmatrix}6&8&-5\\-5&-9&4\\6&6&-3end{pmatrix}</latex>.\n', '', 1, 'math', 'matrix'),
(1091, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'Calculate the Inverse of the matrix, <latex>egin{pmatrix}-10&3&-9\\-6&10&8\\-8&3&3end{pmatrix}</latex>.\n', '', 1, 'math', 'matrix'),
(1092, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'Calculate the Inverse of the matrix, <latex>egin{pmatrix}-10&-3&7\\-3&4&8\\2&-3&-5end{pmatrix}</latex>.\n', '', 1, 'math', 'matrix'),
(1093, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'Calculate the Inverse of the matrix, <latex>egin{pmatrix}-10&4&-7\\-3&-9&9\\4&5&6end{pmatrix}</latex>.\n', '', 1, 'math', 'matrix'),
(1094, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'Calculate the Inverse of the matrix, <latex>egin{pmatrix}2&-9&8\\-3&-7&8\\5&10&-8end{pmatrix}</latex>.\n', '', 1, 'math', 'matrix'),
(1095, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'Calculate the Inverse of the matrix, <latex>egin{pmatrix}-2&-5&3\\5&-5&7\\-8&8&4end{pmatrix}</latex>.\n', '', 1, 'math', 'matrix'),
(1096, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'Calculate the Inverse of the matrix, <latex>egin{pmatrix}4&9&6\\5&-2&-10\\-7&3&-8end{pmatrix}</latex>.\n', '', 1, 'math', 'matrix'),
(1097, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'Calculate the Inverse of the matrix, <latex>egin{pmatrix}4&-7&-8\\7&-3&-7\\-9&4&3end{pmatrix}</latex>.\n', '', 1, 'math', 'matrix'),
(1098, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'Calculate the Inverse of the matrix, <latex>egin{pmatrix}2&3&8\\-8&-2&9\\8&-7&-3end{pmatrix}</latex>.\n', '', 1, 'math', 'matrix'),
(1099, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'Calculate the Inverse of the matrix, <latex>egin{pmatrix}3&4&-9\\-8&3&10\\-10&10&6end{pmatrix}</latex>.\n', '', 1, 'math', 'matrix'),
(1100, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'Calculate the Inverse of the matrix, <latex>egin{pmatrix}4&10&-3\\-10&-7&4\\9&-10&-9end{pmatrix}</latex>.\n', '', 1, 'math', 'matrix'),
(1101, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'Calculate the Inverse of the matrix, <latex>egin{pmatrix}-7&-5&5\\-8&9&-7\\-5&-7&-6end{pmatrix}</latex>.\n', '', 1, 'math', 'matrix'),
(1102, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'Calculate the Inverse of the matrix, <latex>egin{pmatrix}9&-2&-7\\-3&-6&-10\\5&5&-9end{pmatrix}</latex>.\n', '', 1, 'math', 'matrix'),
(1103, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'Calculate the Inverse of the matrix, <latex>egin{pmatrix}9&-7&-5\\-7&3&9\\-3&-8&-7end{pmatrix}</latex>.\n', '', 1, 'math', 'matrix'),
(1104, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'If C=<latex>egin{pmatrix}9&5\\8&-3end{pmatrix}</latex> and D=<latex>egin{pmatrix}9&5\\8&-3end{pmatrix}</latex>, Calculate C<latex>	imes</latex>D.\n', '', 1, 'math', 'matrix'),
(1105, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'If C=<latex>egin{pmatrix}2&-6\\7&-6end{pmatrix}</latex> and D=<latex>egin{pmatrix}2&-6\\7&-6end{pmatrix}</latex>, Calculate C<latex>	imes</latex>D.\n', '', 1, 'math', 'matrix'),
(1106, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'If C=<latex>egin{pmatrix}2&5\\5&8end{pmatrix}</latex> and D=<latex>egin{pmatrix}2&5\\5&8end{pmatrix}</latex>, Calculate C<latex>	imes</latex>D.\n', '', 1, 'math', 'matrix'),
(1107, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'If C=<latex>egin{pmatrix}-8&6\\-10&-10end{pmatrix}</latex> and D=<latex>egin{pmatrix}-8&6\\-10&-10end{pmatrix}</latex>, Calculate C<latex>	imes</latex>D.\n', '', 1, 'math', 'matrix'),
(1108, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'If C=<latex>egin{pmatrix}4&8\\-6&8end{pmatrix}</latex> and D=<latex>egin{pmatrix}4&8\\-6&8end{pmatrix}</latex>, Calculate C<latex>	imes</latex>D.\n', '', 1, 'math', 'matrix'),
(1109, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'If C=<latex>egin{pmatrix}-2&9\\-5&-7end{pmatrix}</latex> and D=<latex>egin{pmatrix}-2&9\\-5&-7end{pmatrix}</latex>, Calculate C<latex>	imes</latex>D.\n', '', 1, 'math', 'matrix'),
(1110, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'If C=<latex>egin{pmatrix}-2&-5\\10&5end{pmatrix}</latex> and D=<latex>egin{pmatrix}-2&-5\\10&5end{pmatrix}</latex>, Calculate C<latex>	imes</latex>D.\n', '', 1, 'math', 'matrix'),
(1111, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'If C=<latex>egin{pmatrix}-8&10\\-2&-5end{pmatrix}</latex> and D=<latex>egin{pmatrix}-8&10\\-2&-5end{pmatrix}</latex>, Calculate C<latex>	imes</latex>D.\n', '', 1, 'math', 'matrix'),
(1112, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'If C=<latex>egin{pmatrix}-10&-7\\-6&-8end{pmatrix}</latex> and D=<latex>egin{pmatrix}-10&-7\\-6&-8end{pmatrix}</latex>, Calculate C<latex>	imes</latex>D.\n', '', 1, 'math', 'matrix'),
(1113, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'If C=<latex>egin{pmatrix}-5&-6\\-2&-10end{pmatrix}</latex> and D=<latex>egin{pmatrix}-5&-6\\-2&-10end{pmatrix}</latex>, Calculate C<latex>	imes</latex>D.\n', '', 1, 'math', 'matrix'),
(1114, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'If C=<latex>egin{pmatrix}5&-2\\10&6end{pmatrix}</latex> and D=<latex>egin{pmatrix}5&-2\\10&6end{pmatrix}</latex>, Calculate C<latex>	imes</latex>D.\n', '', 1, 'math', 'matrix'),
(1115, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'If C=<latex>egin{pmatrix}5&9\\-10&-9end{pmatrix}</latex> and D=<latex>egin{pmatrix}5&9\\-10&-9end{pmatrix}</latex>, Calculate C<latex>	imes</latex>D.\n', '', 1, 'math', 'matrix'),
(1116, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'If C=<latex>egin{pmatrix}-3&10\\-9&5end{pmatrix}</latex> and D=<latex>egin{pmatrix}-3&10\\-9&5end{pmatrix}</latex>, Calculate C<latex>	imes</latex>D.\n', '', 1, 'math', 'matrix'),
(1117, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'If C=<latex>egin{pmatrix}2&-6\\10&7end{pmatrix}</latex> and D=<latex>egin{pmatrix}2&-6\\10&7end{pmatrix}</latex>, Calculate C<latex>	imes</latex>D.\n', '', 1, 'math', 'matrix'),
(1118, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'If C=<latex>egin{pmatrix}-2&9\\10&8end{pmatrix}</latex> and D=<latex>egin{pmatrix}-2&9\\10&8end{pmatrix}</latex>, Calculate C<latex>	imes</latex>D.\n', '', 1, 'math', 'matrix'),
(1119, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'If C=<latex>egin{pmatrix}-6&-7\\10&9end{pmatrix}</latex> and D=<latex>egin{pmatrix}-6&-7\\10&9end{pmatrix}</latex>, Calculate C<latex>	imes</latex>D.\n', '', 1, 'math', 'matrix'),
(1120, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'If C=<latex>egin{pmatrix}8&3\\-7&4end{pmatrix}</latex> and D=<latex>egin{pmatrix}8&3\\-7&4end{pmatrix}</latex>, Calculate C<latex>	imes</latex>D.\n', '', 1, 'math', 'matrix'),
(1121, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'If C=<latex>egin{pmatrix}-8&-2\\-10&10end{pmatrix}</latex> and D=<latex>egin{pmatrix}-8&-2\\-10&10end{pmatrix}</latex>, Calculate C<latex>	imes</latex>D.\n', '', 1, 'math', 'matrix'),
(1122, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'If C=<latex>egin{pmatrix}5&-5\\6&-6end{pmatrix}</latex> and D=<latex>egin{pmatrix}5&-5\\6&-6end{pmatrix}</latex>, Calculate C<latex>	imes</latex>D.\n', '', 1, 'math', 'matrix'),
(1123, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'If C=<latex>egin{pmatrix}6&7\\10&-9end{pmatrix}</latex> and D=<latex>egin{pmatrix}6&7\\10&-9end{pmatrix}</latex>, Calculate C<latex>	imes</latex>D.\n', '', 1, 'math', 'matrix'),
(1124, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'If C=<latex>egin{pmatrix}-8&-9\\5&4end{pmatrix}</latex> and D=<latex>egin{pmatrix}-8&-9\\5&4end{pmatrix}</latex>, Calculate C<latex>	imes</latex>D.\n', '', 1, 'math', 'matrix'),
(1125, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'If C=<latex>egin{pmatrix}-7&-3\\-7&3end{pmatrix}</latex> and D=<latex>egin{pmatrix}-7&-3\\-7&3end{pmatrix}</latex>, Calculate C<latex>	imes</latex>D.\n', '', 1, 'math', 'matrix'),
(1126, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'If C=<latex>egin{pmatrix}-9&7\\7&-6end{pmatrix}</latex> and D=<latex>egin{pmatrix}-9&7\\7&-6end{pmatrix}</latex>, Calculate C<latex>	imes</latex>D.\n', '', 1, 'math', 'matrix'),
(1127, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'If C=<latex>egin{pmatrix}5&7\\8&-5end{pmatrix}</latex> and D=<latex>egin{pmatrix}5&7\\8&-5end{pmatrix}</latex>, Calculate C<latex>	imes</latex>D.\n', '', 1, 'math', 'matrix'),
(1128, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'If C=<latex>egin{pmatrix}9&-3\\4&-7end{pmatrix}</latex> and D=<latex>egin{pmatrix}9&-3\\4&-7end{pmatrix}</latex>, Calculate C<latex>	imes</latex>D.\n', '', 1, 'math', 'matrix'),
(1129, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'If C=<latex>egin{pmatrix}-6&-2\\9&5end{pmatrix}</latex> and D=<latex>egin{pmatrix}-6&-2\\9&5end{pmatrix}</latex>, Calculate C<latex>	imes</latex>D.\n', '', 1, 'math', 'matrix'),
(1130, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'If C=<latex>egin{pmatrix}5&4\\9&-8end{pmatrix}</latex> and D=<latex>egin{pmatrix}5&4\\9&-8end{pmatrix}</latex>, Calculate C<latex>	imes</latex>D.\n', '', 1, 'math', 'matrix'),
(1131, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'If C=<latex>egin{pmatrix}5&9\\-7&-2end{pmatrix}</latex> and D=<latex>egin{pmatrix}5&9\\-7&-2end{pmatrix}</latex>, Calculate C<latex>	imes</latex>D.\n', '', 1, 'math', 'matrix'),
(1132, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'If C=<latex>egin{pmatrix}8&9\\9&4end{pmatrix}</latex> and D=<latex>egin{pmatrix}8&9\\9&4end{pmatrix}</latex>, Calculate C<latex>	imes</latex>D.\n', '', 1, 'math', 'matrix'),
(1133, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'If C=<latex>egin{pmatrix}-6&9\\9&-9end{pmatrix}</latex> and D=<latex>egin{pmatrix}-6&9\\9&-9end{pmatrix}</latex>, Calculate C<latex>	imes</latex>D.\n', '', 1, 'math', 'matrix'),
(1134, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'If C=<latex>egin{pmatrix}6&-6\\-2&3end{pmatrix}</latex> and D=<latex>egin{pmatrix}6&-6\\-2&3end{pmatrix}</latex>, Calculate C<latex>	imes</latex>D.\n', '', 1, 'math', 'matrix'),
(1135, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'If C=<latex>egin{pmatrix}9&10\\-8&8end{pmatrix}</latex> and D=<latex>egin{pmatrix}9&10\\-8&8end{pmatrix}</latex>, Calculate C<latex>	imes</latex>D.\n', '', 1, 'math', 'matrix'),
(1136, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'If C=<latex>egin{pmatrix}3&2\\4&-2end{pmatrix}</latex> and D=<latex>egin{pmatrix}3&2\\4&-2end{pmatrix}</latex>, Calculate C<latex>	imes</latex>D.\n', '', 1, 'math', 'matrix'),
(1137, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'If C=<latex>egin{pmatrix}6&-10\\-9&-3end{pmatrix}</latex> and D=<latex>egin{pmatrix}6&-10\\-9&-3end{pmatrix}</latex>, Calculate C<latex>	imes</latex>D.\n', '', 1, 'math', 'matrix'),
(1138, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'If C=<latex>egin{pmatrix}-3&-2\\4&5end{pmatrix}</latex> and D=<latex>egin{pmatrix}-3&-2\\4&5end{pmatrix}</latex>, Calculate C<latex>	imes</latex>D.\n', '', 1, 'math', 'matrix'),
(1139, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'If C=<latex>egin{pmatrix}-3&7\\-8&5end{pmatrix}</latex> and D=<latex>egin{pmatrix}-3&7\\-8&5end{pmatrix}</latex>, Calculate C<latex>	imes</latex>D.\n', '', 1, 'math', 'matrix'),
(1140, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'If C=<latex>egin{pmatrix}2&10\\6&-2end{pmatrix}</latex> and D=<latex>egin{pmatrix}2&10\\6&-2end{pmatrix}</latex>, Calculate C<latex>	imes</latex>D.\n', '', 1, 'math', 'matrix'),
(1141, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'If C=<latex>egin{pmatrix}3&-10\\-9&4end{pmatrix}</latex> and D=<latex>egin{pmatrix}3&-10\\-9&4end{pmatrix}</latex>, Calculate C<latex>	imes</latex>D.\n', '', 1, 'math', 'matrix'),
(1142, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'If C=<latex>egin{pmatrix}-8&-8\\2&-10end{pmatrix}</latex> and D=<latex>egin{pmatrix}-8&-8\\2&-10end{pmatrix}</latex>, Calculate C<latex>	imes</latex>D.\n', '', 1, 'math', 'matrix'),
(1143, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'If C=<latex>egin{pmatrix}-3&9\\-9&3end{pmatrix}</latex> and D=<latex>egin{pmatrix}-3&9\\-9&3end{pmatrix}</latex>, Calculate C<latex>	imes</latex>D.\n', '', 1, 'math', 'matrix'),
(1144, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'If C=<latex>egin{pmatrix}-6&5\\6&6end{pmatrix}</latex> and D=<latex>egin{pmatrix}-6&5\\6&6end{pmatrix}</latex>, Calculate C<latex>	imes</latex>D.\n', '', 1, 'math', 'matrix'),
(1145, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'If C=<latex>egin{pmatrix}10&3\\-8&-2end{pmatrix}</latex> and D=<latex>egin{pmatrix}10&3\\-8&-2end{pmatrix}</latex>, Calculate C<latex>	imes</latex>D.\n', '', 1, 'math', 'matrix'),
(1146, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'If C=<latex>egin{pmatrix}-3&2\\-7&-9end{pmatrix}</latex> and D=<latex>egin{pmatrix}-3&2\\-7&-9end{pmatrix}</latex>, Calculate C<latex>	imes</latex>D.\n', '', 1, 'math', 'matrix'),
(1147, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'If C=<latex>egin{pmatrix}-10&-9\\-9&2end{pmatrix}</latex> and D=<latex>egin{pmatrix}-10&-9\\-9&2end{pmatrix}</latex>, Calculate C<latex>	imes</latex>D.\n', '', 1, 'math', 'matrix'),
(1148, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'If C=<latex>egin{pmatrix}6&4\\-6&3end{pmatrix}</latex> and D=<latex>egin{pmatrix}6&4\\-6&3end{pmatrix}</latex>, Calculate C<latex>	imes</latex>D.\n', '', 1, 'math', 'matrix'),
(1149, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'If C=<latex>egin{pmatrix}-10&-3\\-10&-2end{pmatrix}</latex> and D=<latex>egin{pmatrix}-10&-3\\-10&-2end{pmatrix}</latex>, Calculate C<latex>	imes</latex>D.\n', '', 1, 'math', 'matrix'),
(1150, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'If C=<latex>egin{pmatrix}3&7\\2&-2end{pmatrix}</latex> and D=<latex>egin{pmatrix}3&7\\2&-2end{pmatrix}</latex>, Calculate C<latex>	imes</latex>D.\n', '', 1, 'math', 'matrix'),
(1151, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'If C=<latex>egin{pmatrix}6&-7\\6&6end{pmatrix}</latex> and D=<latex>egin{pmatrix}6&-7\\6&6end{pmatrix}</latex>, Calculate C<latex>	imes</latex>D.\n', '', 1, 'math', 'matrix');
INSERT INTO `practiceq` (`id`, `subject_id`, `topic_id`, `pract_id`, `question`, `answer`, `q_type`, `subject`, `sub_topic`) VALUES
(1152, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'If C=<latex>egin{pmatrix}-8&-5\\-3&-6end{pmatrix}</latex> and D=<latex>egin{pmatrix}-8&-5\\-3&-6end{pmatrix}</latex>, Calculate C<latex>	imes</latex>D.\n', '', 1, 'math', 'matrix'),
(1153, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'If A=<latex>egin{pmatrix}2&8&-5\\7&-7&3\\4&2&-9end{pmatrix}</latex> and B=<latex>egin{pmatrix}2&8&-5\\7&-7&3\\4&2&-9end{pmatrix}</latex>, Calculate 8A+3B.\n', '', 1, 'math', 'matrix'),
(1154, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'If A=<latex>egin{pmatrix}-10&5&7\\8&8&-7\\6&7&10end{pmatrix}</latex> and B=<latex>egin{pmatrix}-10&5&7\\8&8&-7\\6&7&10end{pmatrix}</latex>, Calculate 7A-2B.\n', '', 1, 'math', 'matrix'),
(1155, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'If A=<latex>egin{pmatrix}5&6&-3\\-10&7&-3\\-6&6&8end{pmatrix}</latex> and B=<latex>egin{pmatrix}5&6&-3\\-10&7&-3\\-6&6&8end{pmatrix}</latex>, Calculate -7A-6B.\n', '', 1, 'math', 'matrix'),
(1156, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'If A=<latex>egin{pmatrix}7&9&6\\10&2&-9\\-9&-8&-8end{pmatrix}</latex> and B=<latex>egin{pmatrix}7&9&6\\10&2&-9\\-9&-8&-8end{pmatrix}</latex>, Calculate 4A-7B.\n', '', 1, 'math', 'matrix'),
(1157, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'If A=<latex>egin{pmatrix}-5&9&9\\-7&8&8\\6&-5&3end{pmatrix}</latex> and B=<latex>egin{pmatrix}-5&9&9\\-7&8&8\\6&-5&3end{pmatrix}</latex>, Calculate -10A-6B.\n', '', 1, 'math', 'matrix'),
(1158, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'If A=<latex>egin{pmatrix}2&-9&-3\\8&9&-5\\9&9&-2end{pmatrix}</latex> and B=<latex>egin{pmatrix}2&-9&-3\\8&9&-5\\9&9&-2end{pmatrix}</latex>, Calculate -2A-2B.\n', '', 1, 'math', 'matrix'),
(1159, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'If A=<latex>egin{pmatrix}2&-8&2\\-7&-9&7\\3&2&2end{pmatrix}</latex> and B=<latex>egin{pmatrix}2&-8&2\\-7&-9&7\\3&2&2end{pmatrix}</latex>, Calculate -2A-5B.\n', '', 1, 'math', 'matrix'),
(1160, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'If A=<latex>egin{pmatrix}7&8&-10\\-8&-8&-8\\-3&9&-5end{pmatrix}</latex> and B=<latex>egin{pmatrix}7&8&-10\\-8&-8&-8\\-3&9&-5end{pmatrix}</latex>, Calculate -10A-10B.\n', '', 1, 'math', 'matrix'),
(1161, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'If A=<latex>egin{pmatrix}8&9&4\\-2&-9&7\\10&9&8end{pmatrix}</latex> and B=<latex>egin{pmatrix}8&9&4\\-2&-9&7\\10&9&8end{pmatrix}</latex>, Calculate -5A-8B.\n', '', 1, 'math', 'matrix'),
(1162, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'If A=<latex>egin{pmatrix}9&2&6\\-2&10&6\\-5&9&5end{pmatrix}</latex> and B=<latex>egin{pmatrix}9&2&6\\-2&10&6\\-5&9&5end{pmatrix}</latex>, Calculate 10A+10B.\n', '', 1, 'math', 'matrix'),
(1163, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'If A=<latex>egin{pmatrix}8&9&9\\-8&-6&-9\\-9&-6&3end{pmatrix}</latex> and B=<latex>egin{pmatrix}8&9&9\\-8&-6&-9\\-9&-6&3end{pmatrix}</latex>, Calculate 5A-3B.\n', '', 1, 'math', 'matrix'),
(1164, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'If A=<latex>egin{pmatrix}4&-3&-5\\-6&-9&-3\\-9&-6&-8end{pmatrix}</latex> and B=<latex>egin{pmatrix}4&-3&-5\\-6&-9&-3\\-9&-6&-8end{pmatrix}</latex>, Calculate -10A-7B.\n', '', 1, 'math', 'matrix'),
(1165, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'If A=<latex>egin{pmatrix}6&-10&-10\\2&-8&10\\7&-5&9end{pmatrix}</latex> and B=<latex>egin{pmatrix}6&-10&-10\\2&-8&10\\7&-5&9end{pmatrix}</latex>, Calculate 3A+5B.\n', '', 1, 'math', 'matrix'),
(1166, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'If A=<latex>egin{pmatrix}6&10&-8\\8&8&3\\-7&-5&-10end{pmatrix}</latex> and B=<latex>egin{pmatrix}6&10&-8\\8&8&3\\-7&-5&-10end{pmatrix}</latex>, Calculate -9A-5B.\n', '', 1, 'math', 'matrix'),
(1167, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'If A=<latex>egin{pmatrix}8&6&10\\-6&-9&6\\-8&9&-9end{pmatrix}</latex> and B=<latex>egin{pmatrix}8&6&10\\-6&-9&6\\-8&9&-9end{pmatrix}</latex>, Calculate -9A+10B.\n', '', 1, 'math', 'matrix'),
(1168, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'If A=<latex>egin{pmatrix}-8&8&-5\\-6&5&-7\\2&-3&5end{pmatrix}</latex> and B=<latex>egin{pmatrix}-8&8&-5\\-6&5&-7\\2&-3&5end{pmatrix}</latex>, Calculate 10A+2B.\n', '', 1, 'math', 'matrix'),
(1169, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'If A=<latex>egin{pmatrix}-8&-7&-9\\10&8&-2\\-2&-8&6end{pmatrix}</latex> and B=<latex>egin{pmatrix}-8&-7&-9\\10&8&-2\\-2&-8&6end{pmatrix}</latex>, Calculate 4A+4B.\n', '', 1, 'math', 'matrix'),
(1170, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'If A=<latex>egin{pmatrix}-10&9&-2\\-2&9&4\\-3&3&4end{pmatrix}</latex> and B=<latex>egin{pmatrix}-10&9&-2\\-2&9&4\\-3&3&4end{pmatrix}</latex>, Calculate -3A+3B.\n', '', 1, 'math', 'matrix'),
(1171, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'If A=<latex>egin{pmatrix}5&-5&10\\9&-10&-2\\-9&10&10end{pmatrix}</latex> and B=<latex>egin{pmatrix}5&-5&10\\9&-10&-2\\-9&10&10end{pmatrix}</latex>, Calculate 7A+7B.\n', '', 1, 'math', 'matrix'),
(1172, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'If A=<latex>egin{pmatrix}-6&10&2\\6&-10&6\\7&8&-8end{pmatrix}</latex> and B=<latex>egin{pmatrix}-6&10&2\\6&-10&6\\7&8&-8end{pmatrix}</latex>, Calculate -3A-2B.\n', '', 1, 'math', 'matrix'),
(1173, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'If A=<latex>egin{pmatrix}2&-5&-8\\9&4&-8\\7&7&4end{pmatrix}</latex> and B=<latex>egin{pmatrix}2&-5&-8\\9&4&-8\\7&7&4end{pmatrix}</latex>, Calculate 9A+4B.\n', '', 1, 'math', 'matrix'),
(1174, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'If A=<latex>egin{pmatrix}-5&2&10\\-2&-9&-3\\-9&8&9end{pmatrix}</latex> and B=<latex>egin{pmatrix}-5&2&10\\-2&-9&-3\\-9&8&9end{pmatrix}</latex>, Calculate 4A+3B.\n', '', 1, 'math', 'matrix'),
(1175, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'If A=<latex>egin{pmatrix}10&-5&-8\\-7&5&2\\10&4&8end{pmatrix}</latex> and B=<latex>egin{pmatrix}10&-5&-8\\-7&5&2\\10&4&8end{pmatrix}</latex>, Calculate -7A-8B.\n', '', 1, 'math', 'matrix'),
(1176, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'If A=<latex>egin{pmatrix}4&6&10\\7&-5&7\\5&2&5end{pmatrix}</latex> and B=<latex>egin{pmatrix}4&6&10\\7&-5&7\\5&2&5end{pmatrix}</latex>, Calculate -8A+3B.\n', '', 1, 'math', 'matrix'),
(1177, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'If A=<latex>egin{pmatrix}5&2&10\\4&4&-3\\-9&-3&-8end{pmatrix}</latex> and B=<latex>egin{pmatrix}5&2&10\\4&4&-3\\-9&-3&-8end{pmatrix}</latex>, Calculate -2A+8B.\n', '', 1, 'math', 'matrix'),
(1178, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'If A=<latex>egin{pmatrix}6&5&-2\\-8&-3&-6\\7&-5&-5end{pmatrix}</latex> and B=<latex>egin{pmatrix}6&5&-2\\-8&-3&-6\\7&-5&-5end{pmatrix}</latex>, Calculate 7A-10B.\n', '', 1, 'math', 'matrix'),
(1179, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'If A=<latex>egin{pmatrix}6&-3&-6\\5&7&-9\\-5&2&-6end{pmatrix}</latex> and B=<latex>egin{pmatrix}6&-3&-6\\5&7&-9\\-5&2&-6end{pmatrix}</latex>, Calculate 2A-5B.\n', '', 1, 'math', 'matrix'),
(1180, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'If A=<latex>egin{pmatrix}-3&7&-3\\-7&-2&2\\10&-7&4end{pmatrix}</latex> and B=<latex>egin{pmatrix}-3&7&-3\\-7&-2&2\\10&-7&4end{pmatrix}</latex>, Calculate 10A+4B.\n', '', 1, 'math', 'matrix'),
(1181, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'If A=<latex>egin{pmatrix}-8&2&4\\-2&4&10\\-7&3&-9end{pmatrix}</latex> and B=<latex>egin{pmatrix}-8&2&4\\-2&4&10\\-7&3&-9end{pmatrix}</latex>, Calculate 5A-6B.\n', '', 1, 'math', 'matrix'),
(1182, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'If A=<latex>egin{pmatrix}-6&-6&9\\-9&8&-7\\3&3&9end{pmatrix}</latex> and B=<latex>egin{pmatrix}-6&-6&9\\-9&8&-7\\3&3&9end{pmatrix}</latex>, Calculate 9A-10B.\n', '', 1, 'math', 'matrix'),
(1183, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'If A=<latex>egin{pmatrix}-5&6&-7\\-10&4&-3\\-5&2&-8end{pmatrix}</latex> and B=<latex>egin{pmatrix}-5&6&-7\\-10&4&-3\\-5&2&-8end{pmatrix}</latex>, Calculate 7A+9B.\n', '', 1, 'math', 'matrix'),
(1184, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'If A=<latex>egin{pmatrix}10&4&5\\-5&4&-8\\-5&7&-7end{pmatrix}</latex> and B=<latex>egin{pmatrix}10&4&5\\-5&4&-8\\-5&7&-7end{pmatrix}</latex>, Calculate -6A-2B.\n', '', 1, 'math', 'matrix'),
(1185, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'If A=<latex>egin{pmatrix}-3&-6&-9\\6&-3&4\\5&-8&-5end{pmatrix}</latex> and B=<latex>egin{pmatrix}-3&-6&-9\\6&-3&4\\5&-8&-5end{pmatrix}</latex>, Calculate -6A-2B.\n', '', 1, 'math', 'matrix'),
(1186, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'If A=<latex>egin{pmatrix}7&2&-10\\8&-3&-7\\8&4&-6end{pmatrix}</latex> and B=<latex>egin{pmatrix}7&2&-10\\8&-3&-7\\8&4&-6end{pmatrix}</latex>, Calculate 4A+3B.\n', '', 1, 'math', 'matrix'),
(1187, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'If A=<latex>egin{pmatrix}2&3&7\\-10&6&4\\-2&9&7end{pmatrix}</latex> and B=<latex>egin{pmatrix}2&3&7\\-10&6&4\\-2&9&7end{pmatrix}</latex>, Calculate 6A+2B.\n', '', 1, 'math', 'matrix'),
(1188, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'If A=<latex>egin{pmatrix}-6&6&-5\\-10&-2&4\\4&7&-5end{pmatrix}</latex> and B=<latex>egin{pmatrix}-6&6&-5\\-10&-2&4\\4&7&-5end{pmatrix}</latex>, Calculate -5A+9B.\n', '', 1, 'math', 'matrix'),
(1189, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'If A=<latex>egin{pmatrix}6&-6&-9\\9&10&-9\\-2&7&-3end{pmatrix}</latex> and B=<latex>egin{pmatrix}6&-6&-9\\9&10&-9\\-2&7&-3end{pmatrix}</latex>, Calculate 9A-8B.\n', '', 1, 'math', 'matrix'),
(1190, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'If A=<latex>egin{pmatrix}3&-10&-7\\5&-2&-3\\-7&9&5end{pmatrix}</latex> and B=<latex>egin{pmatrix}3&-10&-7\\5&-2&-3\\-7&9&5end{pmatrix}</latex>, Calculate -8A-5B.\n', '', 1, 'math', 'matrix'),
(1191, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'If A=<latex>egin{pmatrix}3&7&6\\7&10&8\\-5&-6&3end{pmatrix}</latex> and B=<latex>egin{pmatrix}3&7&6\\7&10&8\\-5&-6&3end{pmatrix}</latex>, Calculate -9A-10B.\n', '', 1, 'math', 'matrix'),
(1192, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'If A=<latex>egin{pmatrix}-9&7&7\\5&4&-2\\7&-9&4end{pmatrix}</latex> and B=<latex>egin{pmatrix}-9&7&7\\5&4&-2\\7&-9&4end{pmatrix}</latex>, Calculate 7A-9B.\n', '', 1, 'math', 'matrix'),
(1193, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'If A=<latex>egin{pmatrix}7&-2&-3\\5&3&9\\4&4&5end{pmatrix}</latex> and B=<latex>egin{pmatrix}7&-2&-3\\5&3&9\\4&4&5end{pmatrix}</latex>, Calculate -8A-2B.\n', '', 1, 'math', 'matrix'),
(1194, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'If A=<latex>egin{pmatrix}2&7&9\\-7&-10&2\\-9&3&-10end{pmatrix}</latex> and B=<latex>egin{pmatrix}2&7&9\\-7&-10&2\\-9&3&-10end{pmatrix}</latex>, Calculate -7A+5B.\n', '', 1, 'math', 'matrix'),
(1195, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'If A=<latex>egin{pmatrix}-2&4&-9\\9&-3&2\\-7&-8&5end{pmatrix}</latex> and B=<latex>egin{pmatrix}-2&4&-9\\9&-3&2\\-7&-8&5end{pmatrix}</latex>, Calculate 10A-6B.\n', '', 1, 'math', 'matrix'),
(1196, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'If A=<latex>egin{pmatrix}-8&-10&-5\\4&-10&5\\7&-10&-8end{pmatrix}</latex> and B=<latex>egin{pmatrix}-8&-10&-5\\4&-10&5\\7&-10&-8end{pmatrix}</latex>, Calculate -10A-9B.\n', '', 1, 'math', 'matrix'),
(1197, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'If A=<latex>egin{pmatrix}2&-2&7\\-10&3&10\\-7&4&3end{pmatrix}</latex> and B=<latex>egin{pmatrix}2&-2&7\\-10&3&10\\-7&4&3end{pmatrix}</latex>, Calculate -2A+5B.\n', '', 1, 'math', 'matrix'),
(1198, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'If A=<latex>egin{pmatrix}4&6&9\\8&5&-8\\6&4&-6end{pmatrix}</latex> and B=<latex>egin{pmatrix}4&6&9\\8&5&-8\\6&4&-6end{pmatrix}</latex>, Calculate 6A-7B.\n', '', 1, 'math', 'matrix'),
(1199, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'If A=<latex>egin{pmatrix}5&2&9\\7&-6&3\\4&-9&-10end{pmatrix}</latex> and B=<latex>egin{pmatrix}5&2&9\\7&-6&3\\4&-9&-10end{pmatrix}</latex>, Calculate 4A-5B.\n', '', 1, 'math', 'matrix'),
(1200, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'If A=<latex>egin{pmatrix}10&10&-6\\7&10&8\\-2&2&-2end{pmatrix}</latex> and B=<latex>egin{pmatrix}10&10&-6\\7&10&8\\-2&2&-2end{pmatrix}</latex>, Calculate 6A+5B.\n', '', 1, 'math', 'matrix'),
(1201, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'If A=<latex>egin{pmatrix}-9&3&-9\\-6&-6&3\\10&3&9end{pmatrix}</latex> and B=<latex>egin{pmatrix}-9&3&-9\\-6&-6&3\\10&3&9end{pmatrix}</latex>, Calculate -10A+10B.\n', '', 1, 'math', 'matrix'),
(1202, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'Solve the following pairs of equations using matrix method 2x+6y-4z=2, 2x-4y+4z=6, 8x-8y-6z=10.\n', '', 1, 'math', 'matrix'),
(1203, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'Solve the following pairs of equations using matrix method 2x+6y-4z=2, 2x-4y+4z=6, 7x-6y+2z=6.\n', '', 1, 'math', 'matrix'),
(1204, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'Solve the following pairs of equations using matrix method 2x+6y-4z=2, 2x-4y+4z=6, -10x+6y+4z=10.\n', '', 1, 'math', 'matrix'),
(1205, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'Solve the following pairs of equations using matrix method 2x+6y-4z=2, 2x-4y+4z=6, -7x+8y-10z=3.\n', '', 1, 'math', 'matrix'),
(1206, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'Solve the following pairs of equations using matrix method 2x+6y-4z=2, 2x-4y+4z=6, 7x-10y+9z=6.\n', '', 1, 'math', 'matrix'),
(1207, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'Solve the following pairs of equations using matrix method 2x+6y-4z=2, 2x-4y+4z=6, -9x-8y-2z=6.\n', '', 1, 'math', 'matrix'),
(1208, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'Solve the following pairs of equations using matrix method 2x+6y-4z=2, 2x-4y+4z=6, 7x-5y-6z=3.\n', '', 1, 'math', 'matrix'),
(1209, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'Solve the following pairs of equations using matrix method 2x+6y-4z=2, 2x-4y+4z=6, -10x+9y+8z=-9.\n', '', 1, 'math', 'matrix'),
(1210, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'Solve the following pairs of equations using matrix method 2x+6y-4z=2, 2x-4y+4z=6, 4x+2y+6z=-8.\n', '', 1, 'math', 'matrix'),
(1211, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'Solve the following pairs of equations using matrix method 2x+6y-4z=2, 2x-4y+4z=6, 6x-9y+10z=3.\n', '', 1, 'math', 'matrix'),
(1212, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'Solve the following pairs of equations using matrix method 2x+6y-4z=2, 2x-4y+4z=6, 6x-5y-9z=10.\n', '', 1, 'math', 'matrix'),
(1213, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'Solve the following pairs of equations using matrix method 2x+6y-4z=2, 2x-4y+4z=6, -7x-8y+5z=-10.\n', '', 1, 'math', 'matrix'),
(1214, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'Solve the following pairs of equations using matrix method 2x+6y-4z=2, 2x-4y+4z=6, 9x+7y-8z=4.\n', '', 1, 'math', 'matrix'),
(1215, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'Solve the following pairs of equations using matrix method 2x+6y-4z=2, 2x-4y+4z=6, -10x+8y+9z=-5.\n', '', 1, 'math', 'matrix'),
(1216, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'Solve the following pairs of equations using matrix method 2x+6y-4z=2, 2x-4y+4z=6, 2x-5y+6z=9.\n', '', 1, 'math', 'matrix'),
(1217, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'Solve the following pairs of equations using matrix method 2x+6y-4z=2, 2x-4y+4z=6, 4x-10y+9z=2.\n', '', 1, 'math', 'matrix'),
(1218, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'Solve the following pairs of equations using matrix method 2x+6y-4z=2, 2x-4y+4z=6, 5x-2y-9z=3.\n', '', 1, 'math', 'matrix'),
(1219, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'Solve the following pairs of equations using matrix method 2x+6y-4z=2, 2x-4y+4z=6, -10x+10y-7z=-2.\n', '', 1, 'math', 'matrix'),
(1220, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'Solve the following pairs of equations using matrix method 2x+6y-4z=2, 2x-4y+4z=6, 5x+9y-9z=8.\n', '', 1, 'math', 'matrix'),
(1221, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'Solve the following pairs of equations using matrix method 2x+6y-4z=2, 2x-4y+4z=6, 5x-2y-3z=-5.\n', '', 1, 'math', 'matrix'),
(1222, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'Solve the following pairs of equations using matrix method 2x+6y-4z=2, 2x-4y+4z=6, 4x-7y+10z=-8.\n', '', 1, 'math', 'matrix'),
(1223, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'Solve the following pairs of equations using matrix method 2x+6y-4z=2, 2x-4y+4z=6, -7x+7y-10z=6.\n', '', 1, 'math', 'matrix'),
(1224, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'Solve the following pairs of equations using matrix method 2x+6y-4z=2, 2x-4y+4z=6, -10x+10y-9z=4.\n', '', 1, 'math', 'matrix'),
(1225, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'Solve the following pairs of equations using matrix method 2x+6y-4z=2, 2x-4y+4z=6, 8x+4y-3z=-6.\n', '', 1, 'math', 'matrix'),
(1226, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'Solve the following pairs of equations using matrix method 2x+6y-4z=2, 2x-4y+4z=6, 5x-5y+4z=-9.\n', '', 1, 'math', 'matrix'),
(1227, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'Solve the following pairs of equations using matrix method 2x+6y-4z=2, 2x-4y+4z=6, 7x+3y-8z=4.\n', '', 1, 'math', 'matrix'),
(1228, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'Solve the following pairs of equations using matrix method 2x+6y-4z=2, 2x-4y+4z=6, 5x-7y+7z=-9.\n', '', 1, 'math', 'matrix'),
(1229, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'Solve the following pairs of equations using matrix method 2x+6y-4z=2, 2x-4y+4z=6, 3x+8y-7z=-2.\n', '', 1, 'math', 'matrix'),
(1230, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'Solve the following pairs of equations using matrix method 2x+6y-4z=2, 2x-4y+4z=6, 3x+2y-2z=-8.\n', '', 1, 'math', 'matrix'),
(1231, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'Solve the following pairs of equations using matrix method 2x+6y-4z=2, 2x-4y+4z=6, -2x+4y+10z=-3.\n', '', 1, 'math', 'matrix'),
(1232, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'Solve the following pairs of equations using matrix method 2x+6y-4z=2, 2x-4y+4z=6, -3x-10y+3z=-9.\n', '', 1, 'math', 'matrix'),
(1233, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'Solve the following pairs of equations using matrix method 2x+6y-4z=2, 2x-4y+4z=6, 3x-2y+10z=-7.\n', '', 1, 'math', 'matrix'),
(1234, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'Solve the following pairs of equations using matrix method 2x+6y-4z=2, 2x-4y+4z=6, 9x+3y+5z=-10.\n', '', 1, 'math', 'matrix'),
(1235, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'Solve the following pairs of equations using matrix method 2x+6y-4z=2, 2x-4y+4z=6, 4x-3y-10z=8.\n', '', 1, 'math', 'matrix'),
(1236, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'Solve the following pairs of equations using matrix method 2x+6y-4z=2, 2x-4y+4z=6, -5x+2y-6z=10.\n', '', 1, 'math', 'matrix'),
(1237, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'Solve the following pairs of equations using matrix method 2x+6y-4z=2, 2x-4y+4z=6, -9x-8y-10z=-2.\n', '', 1, 'math', 'matrix'),
(1238, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'Solve the following pairs of equations using matrix method 2x+6y-4z=2, 2x-4y+4z=6, -6x+7y-10z=-3.\n', '', 1, 'math', 'matrix'),
(1239, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'Solve the following pairs of equations using matrix method 2x+6y-4z=2, 2x-4y+4z=6, 2x+5y+3z=7.\n', '', 1, 'math', 'matrix'),
(1240, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'Solve the following pairs of equations using matrix method 2x+6y-4z=2, 2x-4y+4z=6, -8x+5y+2z=9.\n', '', 1, 'math', 'matrix'),
(1241, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'Solve the following pairs of equations using matrix method 2x+6y-4z=2, 2x-4y+4z=6, -6x+10y+5z=7.\n', '', 1, 'math', 'matrix'),
(1242, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'Solve the following pairs of equations using matrix method 2x+6y-4z=2, 2x-4y+4z=6, 9x+2y+7z=-2.\n', '', 1, 'math', 'matrix'),
(1243, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'Solve the following pairs of equations using matrix method 2x+6y-4z=2, 2x-4y+4z=6, 3x+2y+4z=-2.\n', '', 1, 'math', 'matrix'),
(1244, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'Solve the following pairs of equations using matrix method 2x+6y-4z=2, 2x-4y+4z=6, -9x+6y+2z=3.\n', '', 1, 'math', 'matrix'),
(1245, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'Solve the following pairs of equations using matrix method 2x+6y-4z=2, 2x-4y+4z=6, -10x+8y-2z=6.\n', '', 1, 'math', 'matrix'),
(1246, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'Solve the following pairs of equations using matrix method 2x+6y-4z=2, 2x-4y+4z=6, -8x-3y-6z=5.\n', '', 1, 'math', 'matrix'),
(1247, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'Solve the following pairs of equations using matrix method 2x+6y-4z=2, 2x-4y+4z=6, 6x+8y-5z=9.\n', '', 1, 'math', 'matrix'),
(1248, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'Solve the following pairs of equations using matrix method 2x+6y-4z=2, 2x-4y+4z=6, -3x+3y-5z=2.\n', '', 1, 'math', 'matrix'),
(1249, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'Solve the following pairs of equations using matrix method 2x+6y-4z=2, 2x-4y+4z=6, 2x-6y+8z=-7.\n', '', 1, 'math', 'matrix'),
(1250, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'Solve the following pairs of equations using matrix method 2x+6y-4z=2, 2x-4y+4z=6, -2x-5y+3z=-3.\n', '', 1, 'math', 'matrix'),
(1251, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', 'Solve the following pairs of equations using matrix method 2x+6y-4z=2, 2x-4y+4z=6, -9x+7y-5z=8.\n', '', 1, 'math', 'matrix'),
(1252, 'WAEC-MATH', 'WAEC-MATH-TP-20', 'WAEC-MATH-TP-20', '', '', 1, 'math', 'matrix'),
(1253, 'WAEC-MATH', 'WAEC-MATH-TP-18', 'WAEC-MATH-TP-18', 'find the scalar product of the following vectors a=-2i+9j, b=-8i+3j\n', '', 1, 'math', 'vectors'),
(1254, 'WAEC-MATH', 'WAEC-MATH-TP-18', 'WAEC-MATH-TP-18', 'find the scalar product of the following vectors a=-5i-6j, b=-1i-8j\n', '', 1, 'math', 'vectors'),
(1255, 'WAEC-MATH', 'WAEC-MATH-TP-18', 'WAEC-MATH-TP-18', 'find the scalar product of the following vectors a=-2i+7j, b=-2i+5j\n', '', 1, 'math', 'vectors'),
(1256, 'WAEC-MATH', 'WAEC-MATH-TP-18', 'WAEC-MATH-TP-18', 'find the scalar product of the following vectors a=-6i+6j, b=2i-2j\n', '', 1, 'math', 'vectors'),
(1257, 'WAEC-MATH', 'WAEC-MATH-TP-18', 'WAEC-MATH-TP-18', 'find the scalar product of the following vectors a=9i+3j, b=-7i+9j\n', '', 1, 'math', 'vectors'),
(1258, 'WAEC-MATH', 'WAEC-MATH-TP-18', 'WAEC-MATH-TP-18', 'find the scalar product of the following vectors a=-7i-10j, b=9i+5j\n', '', 1, 'math', 'vectors'),
(1259, 'WAEC-MATH', 'WAEC-MATH-TP-18', 'WAEC-MATH-TP-18', 'calculate the scalar product of the following vectors a=-5i-1j, b=-4i-1j\n', '', 1, 'math', 'vectors'),
(1260, 'WAEC-MATH', 'WAEC-MATH-TP-18', 'WAEC-MATH-TP-18', 'calculate the scalar product of the following vectors a=-8i-3j, b=7i-5j\n', '', 1, 'math', 'vectors'),
(1261, 'WAEC-MATH', 'WAEC-MATH-TP-18', 'WAEC-MATH-TP-18', 'calculate the scalar product of the following vectors a=-2i-6j, b=6i-6j\n', '', 1, 'math', 'vectors'),
(1262, 'WAEC-MATH', 'WAEC-MATH-TP-18', 'WAEC-MATH-TP-18', 'calculate the scalar product of the following vectors a=2i-5j, b=7i-3j\n', '', 1, 'math', 'vectors'),
(1263, 'WAEC-MATH', 'WAEC-MATH-TP-18', 'WAEC-MATH-TP-18', 'calculate the scalar product of the following vectors a=-7i+6j, b=-8i+8j\n', '', 1, 'math', 'vectors'),
(1264, 'WAEC-MATH', 'WAEC-MATH-TP-18', 'WAEC-MATH-TP-18', 'calculate the scalar product of the following vectors a=9i+6j, b=4i-2j\n', '', 1, 'math', 'vectors'),
(1265, 'WAEC-MATH', 'WAEC-MATH-TP-18', 'WAEC-MATH-TP-18', 'calculate the scalar product of the following vectors a=-2i+9j, b=5i+3j\n', '', 1, 'math', 'vectors'),
(1266, 'WAEC-MATH', 'WAEC-MATH-TP-18', 'WAEC-MATH-TP-18', 'calculate the scalar product of the following vectors a=-2i-6j, b=-2i-2j\n', '', 1, 'math', 'vectors'),
(1267, 'WAEC-MATH', 'WAEC-MATH-TP-18', 'WAEC-MATH-TP-18', 'calculate the scalar product of the following vectors a=-4i+3j, b=9i-6j\n', '', 1, 'math', 'vectors'),
(1268, 'WAEC-MATH', 'WAEC-MATH-TP-18', 'WAEC-MATH-TP-18', 'calculate the scalar product of the following vectors a=2i-9j, b=-6i+5j\n', '', 1, 'math', 'vectors'),
(1269, 'WAEC-MATH', 'WAEC-MATH-TP-18', 'WAEC-MATH-TP-18', 'calculate the scalar product of the following vectors a=-1i+8j, b=3i-9j\n', '', 1, 'math', 'vectors'),
(1270, 'WAEC-MATH', 'WAEC-MATH-TP-18', 'WAEC-MATH-TP-18', 'calculate the scalar product of the following vectors a=-2i-6j, b=-8i-2j\n', '', 1, 'math', 'vectors'),
(1271, 'WAEC-MATH', 'WAEC-MATH-TP-18', 'WAEC-MATH-TP-18', 'calculate the scalar product of the following vectors a=2i-7j, b=-2i-10j\n', '', 1, 'math', 'vectors'),
(1272, 'WAEC-MATH', 'WAEC-MATH-TP-18', 'WAEC-MATH-TP-18', 'calculate the scalar product of the following vectors a=9i-8j, b=2i-1j\n', '', 1, 'math', 'vectors'),
(1273, 'WAEC-MATH', 'WAEC-MATH-TP-18', 'WAEC-MATH-TP-18', 'calculate the scalar product of the following vectors a=5i+8j, b=7i+6j\n', '', 1, 'math', 'vectors'),
(1274, 'WAEC-MATH', 'WAEC-MATH-TP-18', 'WAEC-MATH-TP-18', 'find the scalar product of the following vectors a=-8i+5j, b=-4i+6j\n', '', 1, 'math', 'vectors'),
(1275, 'WAEC-MATH', 'WAEC-MATH-TP-18', 'WAEC-MATH-TP-18', 'find the scalar product of the following vectors a=9i-9j, b=-2i-3j\n', '', 1, 'math', 'vectors'),
(1276, 'WAEC-MATH', 'WAEC-MATH-TP-18', 'WAEC-MATH-TP-18', 'find the scalar product of the following vectors a=4i-3j, b=2i-9j\n', '', 1, 'math', 'vectors'),
(1277, 'WAEC-MATH', 'WAEC-MATH-TP-18', 'WAEC-MATH-TP-18', 'find the scalar product of the following vectors a=9i-1j, b=-3i-5j\n', '', 1, 'math', 'vectors'),
(1278, 'WAEC-MATH', 'WAEC-MATH-TP-18', 'WAEC-MATH-TP-18', 'find the scalar product of the following vectors a=-4i-8j, b=-3i+7j\n', '', 1, 'math', 'vectors'),
(1279, 'WAEC-MATH', 'WAEC-MATH-TP-18', 'WAEC-MATH-TP-18', 'find the scalar product of the following vectors a=-4i+8j, b=8i-5j\n', '', 1, 'math', 'vectors'),
(1280, 'WAEC-MATH', 'WAEC-MATH-TP-18', 'WAEC-MATH-TP-18', 'find the scalar product of the following vectors a=-4i-10j, b=-9i+9j\n', '', 1, 'math', 'vectors'),
(1281, 'WAEC-MATH', 'WAEC-MATH-TP-18', 'WAEC-MATH-TP-18', 'find the scalar product of the following vectors a=4i+6j, b=-4i-4j\n', '', 1, 'math', 'vectors'),
(1282, 'WAEC-MATH', 'WAEC-MATH-TP-18', 'WAEC-MATH-TP-18', 'find the scalar product of the following vectors a=-5i-2j, b=-5i+6j\n', '', 1, 'math', 'vectors'),
(1283, 'WAEC-MATH', 'WAEC-MATH-TP-18', 'WAEC-MATH-TP-18', 'find the scalar product of the following vectors a=9i-2j, b=-8i-4j\n', '', 1, 'math', 'vectors'),
(1284, 'WAEC-MATH', 'WAEC-MATH-TP-18', 'WAEC-MATH-TP-18', 'find the scalar product of the following vectors a=7i-2j, b=2i+6j\n', '', 1, 'math', 'vectors'),
(1285, 'WAEC-MATH', 'WAEC-MATH-TP-18', 'WAEC-MATH-TP-18', 'find the scalar product of the following vectors a=2i+2j, b=6i+9j\n', '', 1, 'math', 'vectors'),
(1286, 'WAEC-MATH', 'WAEC-MATH-TP-18', 'WAEC-MATH-TP-18', 'find the scalar product of the following vectors a=7i-9j, b=2i+5j\n', '', 1, 'math', 'vectors'),
(1287, 'WAEC-MATH', 'WAEC-MATH-TP-18', 'WAEC-MATH-TP-18', 'find the scalar product of the following vectors a=4i-3j, b=-2i+7j\n', '', 1, 'math', 'vectors'),
(1288, 'WAEC-MATH', 'WAEC-MATH-TP-18', 'WAEC-MATH-TP-18', 'find the scalar product of the following vectors a=-5i+6j, b=-10i-8j\n', '', 1, 'math', 'vectors'),
(1289, 'WAEC-MATH', 'WAEC-MATH-TP-18', 'WAEC-MATH-TP-18', 'find the scalar product of the following vectors a=-10i-6j, b=-2i-3j\n', '', 1, 'math', 'vectors'),
(1290, 'WAEC-MATH', 'WAEC-MATH-TP-18', 'WAEC-MATH-TP-18', 'find the scalar product of the following vectors a=9i+9j, b=-7i+8j\n', '', 1, 'math', 'vectors'),
(1291, 'WAEC-MATH', 'WAEC-MATH-TP-18', 'WAEC-MATH-TP-18', 'find the scalar product of the following vectors a=2i-2j, b=-3i-6j\n', '', 1, 'math', 'vectors'),
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(1409, 'WAEC-MATH', 'WAEC-MATH-TP-18', 'WAEC-MATH-TP-18', 'Find the projection the vector a on the vector b if a=-4i-7j, b=9i-8j\n', '', 1, 'math', 'vectors'),
(1410, 'WAEC-MATH', 'WAEC-MATH-TP-18', 'WAEC-MATH-TP-18', 'Find the projection the vector a on the vector b if a=8i-3j, b=6i-8j\n', '', 1, 'math', 'vectors'),
(1411, 'WAEC-MATH', 'WAEC-MATH-TP-18', 'WAEC-MATH-TP-18', 'Find the projection the vector a on the vector b if a=3i-3j, b=8i-8j\n', '', 1, 'math', 'vectors'),
(1412, 'WAEC-MATH', 'WAEC-MATH-TP-18', 'WAEC-MATH-TP-18', 'Find the projection the vector a on the vector b if a=-9i+2j, b=-8i-2j\n', '', 1, 'math', 'vectors'),
(1413, 'WAEC-MATH', 'WAEC-MATH-TP-18', 'WAEC-MATH-TP-18', 'Find the projection the vector a on the vector b if a=8i-8j, b=-6i+7j\n', '', 1, 'math', 'vectors'),
(1414, 'WAEC-MATH', 'WAEC-MATH-TP-18', 'WAEC-MATH-TP-18', 'Find the projection the vector a on the vector b if a=5i-6j, b=6i+5j\n', '', 1, 'math', 'vectors'),
(1415, 'WAEC-MATH', 'WAEC-MATH-TP-18', 'WAEC-MATH-TP-18', 'Find the projection the vector a on the vector b if a=-4i-8j, b=-8i+8j\n', '', 1, 'math', 'vectors'),
(1416, 'WAEC-MATH', 'WAEC-MATH-TP-18', 'WAEC-MATH-TP-18', 'Find the projection the vector a on the vector b if a=6i+9j, b=-4i+9j\n', '', 1, 'math', 'vectors'),
(1417, 'WAEC-MATH', 'WAEC-MATH-TP-18', 'WAEC-MATH-TP-18', 'Find the projection the vector a on the vector b if a=8i-9j, b=-8i-4j\n', '', 1, 'math', 'vectors'),
(1418, 'WAEC-MATH', 'WAEC-MATH-TP-18', 'WAEC-MATH-TP-18', 'Find the projection the vector a on the vector b if a=-2i+4j, b=6i-8j\n', '', 1, 'math', 'vectors'),
(1419, 'WAEC-MATH', 'WAEC-MATH-TP-18', 'WAEC-MATH-TP-18', 'Find the projection the vector a on the vector b if a=-2i-3j, b=-1i-8j\n', '', 1, 'math', 'vectors'),
(1420, 'WAEC-MATH', 'WAEC-MATH-TP-18', 'WAEC-MATH-TP-18', 'Find the projection the vector a on the vector b if a=-10i+2j, b=2i-1j\n', '', 1, 'math', 'vectors'),
(1421, 'WAEC-MATH', 'WAEC-MATH-TP-18', 'WAEC-MATH-TP-18', 'Find the projection the vector a on the vector b if a=4i+7j, b=-2i+8j\n', '', 1, 'math', 'vectors'),
(1422, 'WAEC-MATH', 'WAEC-MATH-TP-18', 'WAEC-MATH-TP-18', 'Find the projection the vector a on the vector b if a=-3i+9j, b=-10i-7j\n', '', 1, 'math', 'vectors'),
(1423, 'WAEC-MATH', 'WAEC-MATH-TP-18', 'WAEC-MATH-TP-18', 'Find the projection the vector a on the vector b if a=-3i+9j, b=8i-10j\n', '', 1, 'math', 'vectors'),
(1424, 'WAEC-MATH', 'WAEC-MATH-TP-18', 'WAEC-MATH-TP-18', 'Find the projection the vector a on the vector b if a=8i+4j, b=7i+3j\n', '', 1, 'math', 'vectors'),
(1425, 'WAEC-MATH', 'WAEC-MATH-TP-18', 'WAEC-MATH-TP-18', 'Find the projection the vector a on the vector b if a=-5i+2j, b=-5i+2j\n', '', 1, 'math', 'vectors'),
(1426, 'WAEC-MATH', 'WAEC-MATH-TP-18', 'WAEC-MATH-TP-18', 'Find the projection the vector a on the vector b if a=-4i+8j, b=-7i+5j\n', '', 1, 'math', 'vectors'),
(1427, 'WAEC-MATH', 'WAEC-MATH-TP-18', 'WAEC-MATH-TP-18', 'Find the projection the vector a on the vector b if a=8i+4j, b=3i+6j\n', '', 1, 'math', 'vectors'),
(1428, 'WAEC-MATH', 'WAEC-MATH-TP-18', 'WAEC-MATH-TP-18', 'Find the projection the vector a on the vector b if a=3i+5j, b=-10i-2j\n', '', 1, 'math', 'vectors'),
(1429, 'WAEC-MATH', 'WAEC-MATH-TP-18', 'WAEC-MATH-TP-18', 'Find the projection the vector a on the vector b if a=-1i-6j, b=-3i+6j\n', '', 1, 'math', 'vectors'),
(1430, 'WAEC-MATH', 'WAEC-MATH-TP-18', 'WAEC-MATH-TP-18', 'Find the projection the vector a on the vector b if a=5i+7j, b=-6i+3j\n', '', 1, 'math', 'vectors'),
(1431, 'WAEC-MATH', 'WAEC-MATH-TP-18', 'WAEC-MATH-TP-18', 'Find the projection the vector a on the vector b if a=6i-8j, b=-7i-2j\n', '', 1, 'math', 'vectors'),
(1432, 'WAEC-MATH', 'WAEC-MATH-TP-18', 'WAEC-MATH-TP-18', 'Find the projection the vector a on the vector b if a=9i-2j, b=2i-5j\n', '', 1, 'math', 'vectors'),
(1433, 'WAEC-MATH', 'WAEC-MATH-TP-18', 'WAEC-MATH-TP-18', 'Find the projection the vector a on the vector b if a=5i-8j, b=5i-9j\n', '', 1, 'math', 'vectors'),
(1434, 'WAEC-MATH', 'WAEC-MATH-TP-18', 'WAEC-MATH-TP-18', 'Find the projection the vector a on the vector b if a=-3i+3j, b=3i-4j\n', '', 1, 'math', 'vectors'),
(1435, 'WAEC-MATH', 'WAEC-MATH-TP-18', 'WAEC-MATH-TP-18', 'Find the projection the vector a on the vector b if a=8i-10j, b=3i-7j\n', '', 1, 'math', 'vectors'),
(1436, 'WAEC-MATH', 'WAEC-MATH-TP-18', 'WAEC-MATH-TP-18', 'Find the projection the vector a on the vector b if a=-4i-3j, b=-9i-3j\n', '', 1, 'math', 'vectors'),
(1437, 'WAEC-MATH', 'WAEC-MATH-TP-18', 'WAEC-MATH-TP-18', 'Find the projection the vector a on the vector b if a=5i+5j, b=9i+8j\n', '', 1, 'math', 'vectors');
INSERT INTO `practiceq` (`id`, `subject_id`, `topic_id`, `pract_id`, `question`, `answer`, `q_type`, `subject`, `sub_topic`) VALUES
(1438, 'WAEC-MATH', 'WAEC-MATH-TP-18', 'WAEC-MATH-TP-18', 'Find the projection the vector a on the vector b if a=5i-8j, b=6i-6j\n', '', 1, 'math', 'vectors'),
(1439, 'WAEC-MATH', 'WAEC-MATH-TP-18', 'WAEC-MATH-TP-18', 'Find the projection the vector a on the vector b if a=-7i+9j, b=-8i-10j\n', '', 1, 'math', 'vectors'),
(1440, 'WAEC-MATH', 'WAEC-MATH-TP-18', 'WAEC-MATH-TP-18', 'Find the projection the vector a on the vector b if a=-5i-9j, b=-8i+7j\n', '', 1, 'math', 'vectors'),
(1441, 'WAEC-MATH', 'WAEC-MATH-TP-18', 'WAEC-MATH-TP-18', 'Find the projection the vector a on the vector b if a=2i-2j, b=-4i+5j\n', '', 1, 'math', 'vectors'),
(1442, 'WAEC-MATH', 'WAEC-MATH-TP-18', 'WAEC-MATH-TP-18', 'Find the projection the vector a on the vector b if a=-10i+5j, b=9i-10j\n', '', 1, 'math', 'vectors'),
(1443, 'WAEC-MATH', 'WAEC-MATH-TP-18', 'WAEC-MATH-TP-18', 'Find the projection the vector a on the vector b if a=-6i-3j, b=-4i-6j\n', '', 1, 'math', 'vectors'),
(1444, 'WAEC-MATH', 'WAEC-MATH-TP-18', 'WAEC-MATH-TP-18', 'Find the projection the vector a on the vector b if a=9i-9j, b=-1i-10j\n', '', 1, 'math', 'vectors'),
(1445, 'WAEC-MATH', 'WAEC-MATH-TP-18', 'WAEC-MATH-TP-18', 'Find the projection the vector a on the vector b if a=2i+8j, b=8i+5j\n', '', 1, 'math', 'vectors'),
(1446, 'WAEC-MATH', 'WAEC-MATH-TP-18', 'WAEC-MATH-TP-18', 'Find the projection the vector a on the vector b if a=-3i+6j, b=3i-6j\n', '', 1, 'math', 'vectors'),
(1447, 'WAEC-MATH', 'WAEC-MATH-TP-18', 'WAEC-MATH-TP-18', 'Find the projection the vector a on the vector b if a=6i+8j, b=3i+6j\n', '', 1, 'math', 'vectors'),
(1448, 'WAEC-MATH', 'WAEC-MATH-TP-18', 'WAEC-MATH-TP-18', 'Find the projection the vector a on the vector b if a=-1i-1j, b=2i+2j\n', '', 1, 'math', 'vectors'),
(1449, 'WAEC-MATH', 'WAEC-MATH-TP-18', 'WAEC-MATH-TP-18', 'Find the direction of the vector a=-10i+9j\n', '', 1, 'math', 'vectors'),
(1450, 'WAEC-MATH', 'WAEC-MATH-TP-18', 'WAEC-MATH-TP-18', 'Find the direction of the vector a=2i+8j\n', '', 1, 'math', 'vectors'),
(1451, 'WAEC-MATH', 'WAEC-MATH-TP-18', 'WAEC-MATH-TP-18', 'Find the direction of the vector a=9i-5j\n', '', 1, 'math', 'vectors'),
(1452, 'WAEC-MATH', 'WAEC-MATH-TP-18', 'WAEC-MATH-TP-18', 'Find the direction of the vector a=-4i+2j\n', '', 1, 'math', 'vectors'),
(1453, 'WAEC-MATH', 'WAEC-MATH-TP-18', 'WAEC-MATH-TP-18', 'Find the direction of the vector a=2i-7j\n', '', 1, 'math', 'vectors'),
(1454, 'WAEC-MATH', 'WAEC-MATH-TP-18', 'WAEC-MATH-TP-18', 'Find the direction of the vector a=4i+5j\n', '', 1, 'math', 'vectors'),
(1455, 'WAEC-MATH', 'WAEC-MATH-TP-18', 'WAEC-MATH-TP-18', 'Find the direction of the vector a=-1i+2j\n', '', 1, 'math', 'vectors'),
(1456, 'WAEC-MATH', 'WAEC-MATH-TP-18', 'WAEC-MATH-TP-18', 'Find the direction of the vector a=-10i+6j\n', '', 1, 'math', 'vectors'),
(1457, 'WAEC-MATH', 'WAEC-MATH-TP-18', 'WAEC-MATH-TP-18', 'Find the direction of the vector a=4i-8j\n', '', 1, 'math', 'vectors'),
(1458, 'WAEC-MATH', 'WAEC-MATH-TP-18', 'WAEC-MATH-TP-18', 'Find the direction of the vector a=-3i-3j\n', '', 1, 'math', 'vectors'),
(1459, 'WAEC-MATH', 'WAEC-MATH-TP-18', 'WAEC-MATH-TP-18', 'Find the direction of the vector a=-3i+7j\n', '', 1, 'math', 'vectors'),
(1460, 'WAEC-MATH', 'WAEC-MATH-TP-18', 'WAEC-MATH-TP-18', 'Find the direction of the vector a=-7i+8j\n', '', 1, 'math', 'vectors'),
(1461, 'WAEC-MATH', 'WAEC-MATH-TP-18', 'WAEC-MATH-TP-18', 'Find the direction of the vector a=6i+7j\n', '', 1, 'math', 'vectors'),
(1462, 'WAEC-MATH', 'WAEC-MATH-TP-18', 'WAEC-MATH-TP-18', 'Find the direction of the vector a=-5i+3j\n', '', 1, 'math', 'vectors'),
(1463, 'WAEC-MATH', 'WAEC-MATH-TP-18', 'WAEC-MATH-TP-18', 'Find the direction of the vector a=2i-8j\n', '', 1, 'math', 'vectors'),
(1464, 'WAEC-MATH', 'WAEC-MATH-TP-18', 'WAEC-MATH-TP-18', 'Find the direction of the vector a=-7i+7j\n', '', 1, 'math', 'vectors'),
(1465, 'WAEC-MATH', 'WAEC-MATH-TP-18', 'WAEC-MATH-TP-18', 'Find the direction of the vector a=4i-3j\n', '', 1, 'math', 'vectors'),
(1466, 'WAEC-MATH', 'WAEC-MATH-TP-18', 'WAEC-MATH-TP-18', 'Find the direction of the vector a=-6i-5j\n', '', 1, 'math', 'vectors'),
(1467, 'WAEC-MATH', 'WAEC-MATH-TP-18', 'WAEC-MATH-TP-18', 'Find the direction of the vector a=7i-1j\n', '', 1, 'math', 'vectors'),
(1468, 'WAEC-MATH', 'WAEC-MATH-TP-18', 'WAEC-MATH-TP-18', 'Find the direction of the vector a=-7i-7j\n', '', 1, 'math', 'vectors'),
(1469, 'WAEC-MATH', 'WAEC-MATH-TP-18', 'WAEC-MATH-TP-18', 'Find the direction of the vector a=-8i-2j\n', '', 1, 'math', 'vectors'),
(1470, 'WAEC-MATH', 'WAEC-MATH-TP-18', 'WAEC-MATH-TP-18', 'Find the direction of the vector a=-1i-3j\n', '', 1, 'math', 'vectors'),
(1471, 'WAEC-MATH', 'WAEC-MATH-TP-18', 'WAEC-MATH-TP-18', 'Find the direction of the vector a=-10i+9j\n', '', 1, 'math', 'vectors'),
(1472, 'WAEC-MATH', 'WAEC-MATH-TP-18', 'WAEC-MATH-TP-18', 'Find the direction of the vector a=-4i+2j\n', '', 1, 'math', 'vectors'),
(1473, 'WAEC-MATH', 'WAEC-MATH-TP-18', 'WAEC-MATH-TP-18', 'Find the direction of the vector a=2i-9j\n', '', 1, 'math', 'vectors'),
(1474, 'WAEC-MATH', 'WAEC-MATH-TP-18', 'WAEC-MATH-TP-18', 'Find the direction of the vector a=7i-6j\n', '', 1, 'math', 'vectors'),
(1475, 'WAEC-MATH', 'WAEC-MATH-TP-18', 'WAEC-MATH-TP-18', 'Find the direction of the vector a=3i+8j\n', '', 1, 'math', 'vectors'),
(1476, 'WAEC-MATH', 'WAEC-MATH-TP-18', 'WAEC-MATH-TP-18', 'Find the direction of the vector a=8i+5j\n', '', 1, 'math', 'vectors'),
(1477, 'WAEC-MATH', 'WAEC-MATH-TP-18', 'WAEC-MATH-TP-18', 'Find the direction of the vector a=5i+5j\n', '', 1, 'math', 'vectors'),
(1478, 'WAEC-MATH', 'WAEC-MATH-TP-18', 'WAEC-MATH-TP-18', 'Find the direction of the vector a=-1i+8j\n', '', 1, 'math', 'vectors'),
(1479, 'WAEC-MATH', 'WAEC-MATH-TP-18', 'WAEC-MATH-TP-18', 'Find the direction of the vector a=-10i-5j\n', '', 1, 'math', 'vectors'),
(1480, 'WAEC-MATH', 'WAEC-MATH-TP-18', 'WAEC-MATH-TP-18', 'Find the direction of the vector a=5i-8j\n', '', 1, 'math', 'vectors'),
(1481, 'WAEC-MATH', 'WAEC-MATH-TP-18', 'WAEC-MATH-TP-18', 'Find the direction of the vector a=-9i-7j\n', '', 1, 'math', 'vectors'),
(1482, 'WAEC-MATH', 'WAEC-MATH-TP-18', 'WAEC-MATH-TP-18', 'Find the direction of the vector a=8i+4j\n', '', 1, 'math', 'vectors'),
(1483, 'WAEC-MATH', 'WAEC-MATH-TP-18', 'WAEC-MATH-TP-18', 'Find the direction of the vector a=2i-5j\n', '', 1, 'math', 'vectors'),
(1484, 'WAEC-MATH', 'WAEC-MATH-TP-18', 'WAEC-MATH-TP-18', 'Find the direction of the vector a=2i+3j\n', '', 1, 'math', 'vectors'),
(1485, 'WAEC-MATH', 'WAEC-MATH-TP-18', 'WAEC-MATH-TP-18', 'Find the direction of the vector a=-6i+7j\n', '', 1, 'math', 'vectors'),
(1486, 'WAEC-MATH', 'WAEC-MATH-TP-18', 'WAEC-MATH-TP-18', 'Find the direction of the vector a=-6i-5j\n', '', 1, 'math', 'vectors'),
(1487, 'WAEC-MATH', 'WAEC-MATH-TP-18', 'WAEC-MATH-TP-18', 'Find the direction of the vector a=8i+7j\n', '', 1, 'math', 'vectors'),
(1488, 'WAEC-MATH', 'WAEC-MATH-TP-18', 'WAEC-MATH-TP-18', 'Find the direction of the vector a=-1i+4j\n', '', 1, 'math', 'vectors'),
(1489, 'WAEC-MATH', 'WAEC-MATH-TP-18', 'WAEC-MATH-TP-18', 'Find the direction of the vector a=6i-6j\n', '', 1, 'math', 'vectors'),
(1490, 'WAEC-MATH', 'WAEC-MATH-TP-18', 'WAEC-MATH-TP-18', 'Find the direction of the vector a=6i-10j\n', '', 1, 'math', 'vectors'),
(1491, 'WAEC-MATH', 'WAEC-MATH-TP-18', 'WAEC-MATH-TP-18', 'Find the direction of the vector a=-10i-9j\n', '', 1, 'math', 'vectors'),
(1492, 'WAEC-MATH', 'WAEC-MATH-TP-18', 'WAEC-MATH-TP-18', 'Find the direction of the vector a=-7i+5j\n', '', 1, 'math', 'vectors'),
(1493, 'WAEC-MATH', 'WAEC-MATH-TP-18', 'WAEC-MATH-TP-18', 'Find the direction of the vector a=9i-1j\n', '', 1, 'math', 'vectors'),
(1494, 'WAEC-MATH', 'WAEC-MATH-TP-18', 'WAEC-MATH-TP-18', 'Find the direction of the vector a=-2i-9j\n', '', 1, 'math', 'vectors'),
(1495, 'WAEC-MATH', 'WAEC-MATH-TP-18', 'WAEC-MATH-TP-18', 'Find the direction of the vector a=8i-2j\n', '', 1, 'math', 'vectors'),
(1496, 'WAEC-MATH', 'WAEC-MATH-TP-18', 'WAEC-MATH-TP-18', 'Find the direction of the vector a=9i+5j\n', '', 1, 'math', 'vectors'),
(1497, 'WAEC-MATH', 'WAEC-MATH-TP-18', 'WAEC-MATH-TP-18', 'Find the direction of the vector a=7i+3j\n', '', 1, 'math', 'vectors'),
(1498, 'WAEC-MATH', 'WAEC-MATH-TP-18', 'WAEC-MATH-TP-18', 'If a=4i+3j, find -10a\n', '', 1, 'math', 'vectors'),
(1499, 'WAEC-MATH', 'WAEC-MATH-TP-18', 'WAEC-MATH-TP-18', 'If a=7i-3j, find 4a\n', '', 1, 'math', 'vectors'),
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(1501, 'WAEC-MATH', 'WAEC-MATH-TP-18', 'WAEC-MATH-TP-18', 'If a=-4i-1j, find 9a\n', '', 1, 'math', 'vectors'),
(1502, 'WAEC-MATH', 'WAEC-MATH-TP-18', 'WAEC-MATH-TP-18', 'If a=-6i-9j, find -4a\n', '', 1, 'math', 'vectors'),
(1503, 'WAEC-MATH', 'WAEC-MATH-TP-18', 'WAEC-MATH-TP-18', 'If a=-3i+6j, find 7a\n', '', 1, 'math', 'vectors'),
(1504, 'WAEC-MATH', 'WAEC-MATH-TP-18', 'WAEC-MATH-TP-18', 'If a=-10i-1j, find 6a\n', '', 1, 'math', 'vectors'),
(1505, 'WAEC-MATH', 'WAEC-MATH-TP-18', 'WAEC-MATH-TP-18', 'If a=-4i-4j, find -9a\n', '', 1, 'math', 'vectors'),
(1506, 'WAEC-MATH', 'WAEC-MATH-TP-18', 'WAEC-MATH-TP-18', 'If a=-3i+7j, find 8a\n', '', 1, 'math', 'vectors'),
(1507, 'WAEC-MATH', 'WAEC-MATH-TP-18', 'WAEC-MATH-TP-18', 'If a=4i-10j, find -6a\n', '', 1, 'math', 'vectors'),
(1508, 'WAEC-MATH', 'WAEC-MATH-TP-18', 'WAEC-MATH-TP-18', 'If a=2i-5j, find 8a\n', '', 1, 'math', 'vectors'),
(1509, 'WAEC-MATH', 'WAEC-MATH-TP-18', 'WAEC-MATH-TP-18', 'If a=-10i+8j, find -9a\n', '', 1, 'math', 'vectors'),
(1510, 'WAEC-MATH', 'WAEC-MATH-TP-18', 'WAEC-MATH-TP-18', 'If a=7i+3j, find 4a\n', '', 1, 'math', 'vectors'),
(1511, 'WAEC-MATH', 'WAEC-MATH-TP-18', 'WAEC-MATH-TP-18', 'If a=-4i-5j, find 6a\n', '', 1, 'math', 'vectors'),
(1512, 'WAEC-MATH', 'WAEC-MATH-TP-18', 'WAEC-MATH-TP-18', 'If a=6i+5j, find -9a\n', '', 1, 'math', 'vectors'),
(1513, 'WAEC-MATH', 'WAEC-MATH-TP-18', 'WAEC-MATH-TP-18', 'If a=8i+7j, find -2a\n', '', 1, 'math', 'vectors'),
(1514, 'WAEC-MATH', 'WAEC-MATH-TP-18', 'WAEC-MATH-TP-18', 'If a=5i-7j, find 2a\n', '', 1, 'math', 'vectors'),
(1515, 'WAEC-MATH', 'WAEC-MATH-TP-18', 'WAEC-MATH-TP-18', 'If a=-6i-3j, find -8a\n', '', 1, 'math', 'vectors'),
(1516, 'WAEC-MATH', 'WAEC-MATH-TP-18', 'WAEC-MATH-TP-18', 'If a=-1i+7j, find 2a\n', '', 1, 'math', 'vectors'),
(1517, 'WAEC-MATH', 'WAEC-MATH-TP-18', 'WAEC-MATH-TP-18', 'If a=9i-5j, find -6a\n', '', 1, 'math', 'vectors'),
(1518, 'WAEC-MATH', 'WAEC-MATH-TP-18', 'WAEC-MATH-TP-18', 'If a=-9i-8j, find -5a\n', '', 1, 'math', 'vectors'),
(1519, 'WAEC-MATH', 'WAEC-MATH-TP-18', 'WAEC-MATH-TP-18', 'If a=9i+5j, find 7a\n', '', 1, 'math', 'vectors'),
(1520, 'WAEC-MATH', 'WAEC-MATH-TP-18', 'WAEC-MATH-TP-18', 'If a=-1i+2j, find 7a\n', '', 1, 'math', 'vectors'),
(1521, 'WAEC-MATH', 'WAEC-MATH-TP-18', 'WAEC-MATH-TP-18', 'If a=3i-10j, find -10a\n', '', 1, 'math', 'vectors'),
(1522, 'WAEC-MATH', 'WAEC-MATH-TP-18', 'WAEC-MATH-TP-18', 'If a=4i+6j, find 2a\n', '', 1, 'math', 'vectors'),
(1523, 'WAEC-MATH', 'WAEC-MATH-TP-18', 'WAEC-MATH-TP-18', 'If a=7i-2j, find -4a\n', '', 1, 'math', 'vectors'),
(1524, 'WAEC-MATH', 'WAEC-MATH-TP-18', 'WAEC-MATH-TP-18', 'If a=-8i+6j, find 8a\n', '', 1, 'math', 'vectors'),
(1525, 'WAEC-MATH', 'WAEC-MATH-TP-18', 'WAEC-MATH-TP-18', 'If a=-5i+7j, find -2a\n', '', 1, 'math', 'vectors'),
(1526, 'WAEC-MATH', 'WAEC-MATH-TP-18', 'WAEC-MATH-TP-18', 'If a=-6i+3j, find -6a\n', '', 1, 'math', 'vectors'),
(1527, 'WAEC-MATH', 'WAEC-MATH-TP-18', 'WAEC-MATH-TP-18', 'If a=6i+2j, find -6a\n', '', 1, 'math', 'vectors'),
(1528, 'WAEC-MATH', 'WAEC-MATH-TP-18', 'WAEC-MATH-TP-18', 'If a=-1i+3j, find 8a\n', '', 1, 'math', 'vectors'),
(1529, 'WAEC-MATH', 'WAEC-MATH-TP-18', 'WAEC-MATH-TP-18', 'If a=-1i+4j, find 3a\n', '', 1, 'math', 'vectors'),
(1530, 'WAEC-MATH', 'WAEC-MATH-TP-18', 'WAEC-MATH-TP-18', 'If a=9i-10j, find -7a\n', '', 1, 'math', 'vectors'),
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(1612, 'WAEC-MATH', 'WAEC-MATH-TP-18', 'WAEC-MATH-TP-18', 'Calculate the cross product of the vectors a=-10i-1j, b=9i-8j\n', '', 1, 'math', 'vectors'),
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(1614, 'WAEC-MATH', 'WAEC-MATH-TP-18', 'WAEC-MATH-TP-18', 'Calculate the cross product of the vectors a=-1i-2j, b=-3i-10j\n', '', 1, 'math', 'vectors'),
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(1618, 'WAEC-MATH', 'WAEC-MATH-TP-18', 'WAEC-MATH-TP-18', 'Calculate the cross product of the vectors a=-8i-10j, b=-6i-8j\n', '', 1, 'math', 'vectors'),
(1619, 'WAEC-MATH', 'WAEC-MATH-TP-18', 'WAEC-MATH-TP-18', 'Calculate the cross product of the vectors a=7i+6j, b=-5i-2j\n', '', 1, 'math', 'vectors'),
(1620, 'WAEC-MATH', 'WAEC-MATH-TP-18', 'WAEC-MATH-TP-18', 'Calculate the cross product of the vectors a=-2i+9j, b=-10i-8j\n', '', 1, 'math', 'vectors'),
(1621, 'WAEC-MATH', 'WAEC-MATH-TP-18', 'WAEC-MATH-TP-18', 'Calculate the cross product of the vectors a=-6i-10j, b=6i-4j\n', '', 1, 'math', 'vectors'),
(1622, 'WAEC-MATH', 'WAEC-MATH-TP-18', 'WAEC-MATH-TP-18', 'Calculate the cross product of the vectors a=-6i+5j, b=6i-4j\n', '', 1, 'math', 'vectors'),
(1623, 'WAEC-MATH', 'WAEC-MATH-TP-18', 'WAEC-MATH-TP-18', 'Calculate the cross product of the vectors a=9i-1j, b=6i+8j\n', '', 1, 'math', 'vectors'),
(1624, 'WAEC-MATH', 'WAEC-MATH-TP-18', 'WAEC-MATH-TP-18', 'Calculate the cross product of the vectors a=-4i+4j, b=5i+4j\n', '', 1, 'math', 'vectors'),
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(1652, 'WAEC-MATH', 'WAEC-MATH-TP-18', 'WAEC-MATH-TP-18', 'If a=-10i-5j, b=-1i-9j, find -2a+5b\n', '', 1, 'math', 'vectors'),
(1653, 'WAEC-MATH', 'WAEC-MATH-TP-18', 'WAEC-MATH-TP-18', 'If a=-8i-8j, b=4i-4j, find -3a+5b\n', '', 1, 'math', 'vectors'),
(1654, 'WAEC-MATH', 'WAEC-MATH-TP-18', 'WAEC-MATH-TP-18', 'If a=-2i-5j, b=-3i+4j, find 3a+10b\n', '', 1, 'math', 'vectors'),
(1655, 'WAEC-MATH', 'WAEC-MATH-TP-18', 'WAEC-MATH-TP-18', 'If a=-6i+5j, b=-9i+3j, find 3a-2b\n', '', 1, 'math', 'vectors'),
(1656, 'WAEC-MATH', 'WAEC-MATH-TP-18', 'WAEC-MATH-TP-18', 'If a=-5i-5j, b=-4i-10j, find -9a-4b\n', '', 1, 'math', 'vectors'),
(1657, 'WAEC-MATH', 'WAEC-MATH-TP-18', 'WAEC-MATH-TP-18', 'If a=6i+2j, b=-7i-1j, find -2a-2b\n', '', 1, 'math', 'vectors'),
(1658, 'WAEC-MATH', 'WAEC-MATH-TP-18', 'WAEC-MATH-TP-18', 'If a=-3i-4j, b=-5i+6j, find -6a-4b\n', '', 1, 'math', 'vectors'),
(1659, 'WAEC-MATH', 'WAEC-MATH-TP-18', 'WAEC-MATH-TP-18', 'If a=9i-10j, b=2i+7j, find 2a-7b\n', '', 1, 'math', 'vectors'),
(1660, 'WAEC-MATH', 'WAEC-MATH-TP-18', 'WAEC-MATH-TP-18', 'If a=3i+4j, b=8i-5j, find 6a+10b\n', '', 1, 'math', 'vectors'),
(1661, 'WAEC-MATH', 'WAEC-MATH-TP-18', 'WAEC-MATH-TP-18', 'If a=4i-10j, b=-5i+6j, find -6a+8b\n', '', 1, 'math', 'vectors'),
(1662, 'WAEC-MATH', 'WAEC-MATH-TP-18', 'WAEC-MATH-TP-18', 'If a=8i-2j, b=7i+7j, find -6a-9b\n', '', 1, 'math', 'vectors'),
(1663, 'WAEC-MATH', 'WAEC-MATH-TP-18', 'WAEC-MATH-TP-18', 'If a=-3i+9j, b=6i-7j, find 4a-8b\n', '', 1, 'math', 'vectors'),
(1664, 'WAEC-MATH', 'WAEC-MATH-TP-18', 'WAEC-MATH-TP-18', 'If a=-10i-9j, b=7i-5j, find -4a-7b\n', '', 1, 'math', 'vectors'),
(1665, 'WAEC-MATH', 'WAEC-MATH-TP-18', 'WAEC-MATH-TP-18', 'If a=-10i-10j, b=-10i+5j, find 5a+7b\n', '', 1, 'math', 'vectors'),
(1666, 'WAEC-MATH', 'WAEC-MATH-TP-18', 'WAEC-MATH-TP-18', 'If a=-1i-4j, b=-1i+7j, find -2a-9b\n', '', 1, 'math', 'vectors'),
(1667, 'WAEC-MATH', 'WAEC-MATH-TP-18', 'WAEC-MATH-TP-18', 'If a=-2i-10j, b=6i+3j, find -3a-6b\n', '', 1, 'math', 'vectors'),
(1668, 'WAEC-MATH', 'WAEC-MATH-TP-18', 'WAEC-MATH-TP-18', 'If a=8i-7j, b=-7i+2j, find -5a-3b\n', '', 1, 'math', 'vectors'),
(1669, 'WAEC-MATH', 'WAEC-MATH-TP-18', 'WAEC-MATH-TP-18', 'If a=-8i-8j, b=-6i-9j, find -9a-3b\n', '', 1, 'math', 'vectors'),
(1670, 'WAEC-MATH', 'WAEC-MATH-TP-18', 'WAEC-MATH-TP-18', 'If a=7i+4j, b=2i+9j, find 2a-9b\n', '', 1, 'math', 'vectors'),
(1671, 'WAEC-MATH', 'WAEC-MATH-TP-18', 'WAEC-MATH-TP-18', 'If a=-2i+4j, b=-8i+9j, find 3a-9b\n', '', 1, 'math', 'vectors'),
(1672, 'WAEC-MATH', 'WAEC-MATH-TP-18', 'WAEC-MATH-TP-18', 'If a=4i+7j, b=5i+6j, find -3a+5b\n', '', 1, 'math', 'vectors'),
(1673, 'WAEC-MATH', 'WAEC-MATH-TP-18', 'WAEC-MATH-TP-18', 'If a=-1i-8j, b=-10i-1j, find -9a+1b\n', '', 1, 'math', 'vectors'),
(1674, 'WAEC-MATH', 'WAEC-MATH-TP-18', 'WAEC-MATH-TP-18', 'If a=-7i-6j, b=-5i-1j, find -10a-6b\n', '', 1, 'math', 'vectors'),
(1675, 'WAEC-MATH', 'WAEC-MATH-TP-18', 'WAEC-MATH-TP-18', 'If a=2i-4j, b=-6i+2j, find -6a-2b\n', '', 1, 'math', 'vectors'),
(1676, 'WAEC-MATH', 'WAEC-MATH-TP-18', 'WAEC-MATH-TP-18', 'If a=6i+3j, b=-1i+8j, find -5a+1b\n', '', 1, 'math', 'vectors'),
(1677, 'WAEC-MATH', 'WAEC-MATH-TP-18', 'WAEC-MATH-TP-18', 'If a=6i-8j, b=-8i+3j, find -7a-5b\n', '', 1, 'math', 'vectors'),
(1678, 'WAEC-MATH', 'WAEC-MATH-TP-18', 'WAEC-MATH-TP-18', 'If a=-9i-6j, b=8i-8j, find -2a+4b\n', '', 1, 'math', 'vectors'),
(1679, 'WAEC-MATH', 'WAEC-MATH-TP-18', 'WAEC-MATH-TP-18', 'If a=6i-7j, b=-10i-4j, find 6a+5b\n', '', 1, 'math', 'vectors'),
(1680, 'WAEC-MATH', 'WAEC-MATH-TP-18', 'WAEC-MATH-TP-18', 'If a=7i-10j, b=-7i+7j, find -4a+9b\n', '', 1, 'math', 'vectors'),
(1681, 'WAEC-MATH', 'WAEC-MATH-TP-18', 'WAEC-MATH-TP-18', 'If a=-8i-9j, b=4i-2j, find -4a-6b\n', '', 1, 'math', 'vectors'),
(1682, 'WAEC-MATH', 'WAEC-MATH-TP-18', 'WAEC-MATH-TP-18', 'If a=-4i+9j, b=6i-8j, find -4a+5b\n', '', 1, 'math', 'vectors'),
(1683, 'WAEC-MATH', 'WAEC-MATH-TP-18', 'WAEC-MATH-TP-18', 'If a=-10i-2j, b=-7i+7j, find -6a+9b\n', '', 1, 'math', 'vectors'),
(1684, 'WAEC-MATH', 'WAEC-MATH-TP-18', 'WAEC-MATH-TP-18', 'If a=4i-7j, b=-6i+9j, find -2a+3b\n', '', 1, 'math', 'vectors'),
(1685, 'WAEC-MATH', 'WAEC-MATH-TP-18', 'WAEC-MATH-TP-18', 'If a=-1i-10j, b=8i+3j, find -4a+9b\n', '', 1, 'math', 'vectors'),
(1686, 'WAEC-MATH', 'WAEC-MATH-TP-18', 'WAEC-MATH-TP-18', 'If a=-7i-6j, b=-6i+8j, find 4a-5b\n', '', 1, 'math', 'vectors'),
(1687, 'WAEC-MATH', 'WAEC-MATH-TP-18', 'WAEC-MATH-TP-18', 'If a=6i-2j, b=8i-4j, find 8a+8b\n', '', 1, 'math', 'vectors'),
(1688, 'WAEC-MATH', 'WAEC-MATH-TP-18', 'WAEC-MATH-TP-18', 'If a=-1i+9j, b=-1i-8j, find -9a+9b\n', '', 1, 'math', 'vectors'),
(1689, 'WAEC-MATH', 'WAEC-MATH-TP-18', 'WAEC-MATH-TP-18', 'If a=-9i-8j, b=-3i-2j, find -6a-8b\n', '', 1, 'math', 'vectors'),
(1690, 'WAEC-MATH', 'WAEC-MATH-TP-18', 'WAEC-MATH-TP-18', 'If a=-7i-9j, b=3i-1j, find -2a-7b\n', '', 1, 'math', 'vectors'),
(1691, 'WAEC-MATH', 'WAEC-MATH-TP-18', 'WAEC-MATH-TP-18', 'If a=-7i+3j, b=-4i+4j, find 9a-6b\n', '', 1, 'math', 'vectors'),
(1692, 'WAEC-MATH', 'WAEC-MATH-TP-18', 'WAEC-MATH-TP-18', 'If a=-3i-5j, b=4i-3j, find -9a+10b\n', '', 1, 'math', 'vectors'),
(1693, 'WAEC-MATH', 'WAEC-MATH-TP-18', 'WAEC-MATH-TP-18', 'If a=8i-2j, b=8i+7j, find 8a-3b\n', '', 1, 'math', 'vectors'),
(1694, 'WAEC-MATH', 'WAEC-MATH-TP-18', 'WAEC-MATH-TP-18', 'If a=-7i+6j, b=-3i-8j, find 7a-3b\n', '', 1, 'math', 'vectors'),
(1695, 'WAEC-MATH', 'WAEC-MATH-TP-18', 'WAEC-MATH-TP-18', '', '', 1, 'math', 'vectors'),
(1696, 'WAEC-MATH', 'WAEC-MATH-TP-21', 'WAEC-MATH-TP-21', 'Calculate the length of an arc, which subtend an angle of <latex>65^{circ}</latex> at the centre of a circle of radius <latex>43cm</latex>\n', '', 1, 'math', 'arc'),
(1697, 'WAEC-MATH', 'WAEC-MATH-TP-21', 'WAEC-MATH-TP-21', 'Calculate the length of an arc, which subtend an angle of <latex>144^{circ}</latex> at the centre of a circle of radius <latex>16cm</latex>\n', '', 1, 'math', 'arc'),
(1698, 'WAEC-MATH', 'WAEC-MATH-TP-21', 'WAEC-MATH-TP-21', 'Calculate the length of an arc, which subtend an angle of <latex>56^{circ}</latex> at the centre of a circle of radius <latex>29cm</latex>\n', '', 1, 'math', 'arc'),
(1699, 'WAEC-MATH', 'WAEC-MATH-TP-21', 'WAEC-MATH-TP-21', 'Calculate the length of an arc, which subtend an angle of <latex>136^{circ}</latex> at the centre of a circle of radius <latex>19cm</latex>\n', '', 1, 'math', 'arc'),
(1700, 'WAEC-MATH', 'WAEC-MATH-TP-21', 'WAEC-MATH-TP-21', 'Calculate the length of an arc, which subtend an angle of <latex>116^{circ}</latex> at the centre of a circle of radius <latex>37cm</latex>\n', '', 1, 'math', 'arc'),
(1701, 'WAEC-MATH', 'WAEC-MATH-TP-21', 'WAEC-MATH-TP-21', 'Calculate the length of an arc, which subtend an angle of <latex>82^{circ}</latex> at the centre of a circle of radius <latex>49cm</latex>\n', '', 1, 'math', 'arc'),
(1702, 'WAEC-MATH', 'WAEC-MATH-TP-21', 'WAEC-MATH-TP-21', 'Calculate the length of an arc, which subtend an angle of <latex>170^{circ}</latex> at the centre of a circle of radius <latex>35cm</latex>\n', '', 1, 'math', 'arc'),
(1703, 'WAEC-MATH', 'WAEC-MATH-TP-21', 'WAEC-MATH-TP-21', 'Calculate the length of an arc, which subtend an angle of <latex>34^{circ}</latex> at the centre of a circle of radius <latex>12cm</latex>\n', '', 1, 'math', 'arc'),
(1704, 'WAEC-MATH', 'WAEC-MATH-TP-21', 'WAEC-MATH-TP-21', 'Calculate the length of an arc, which subtend an angle of <latex>176^{circ}</latex> at the centre of a circle of radius <latex>17cm</latex>\n', '', 1, 'math', 'arc'),
(1705, 'WAEC-MATH', 'WAEC-MATH-TP-21', 'WAEC-MATH-TP-21', 'Calculate the length of an arc, which subtend an angle of <latex>67^{circ}</latex> at the centre of a circle of radius <latex>33cm</latex>\n', '', 1, 'math', 'arc'),
(1706, 'WAEC-MATH', 'WAEC-MATH-TP-21', 'WAEC-MATH-TP-21', 'Calculate the length of an arc, which subtend an angle of <latex>19^{circ}</latex> at the centre of a circle of radius <latex>21cm</latex>\n', '', 1, 'math', 'arc'),
(1707, 'WAEC-MATH', 'WAEC-MATH-TP-21', 'WAEC-MATH-TP-21', 'Calculate the length of an arc, which subtend an angle of <latex>71^{circ}</latex> at the centre of a circle of radius <latex>33cm</latex>\n', '', 1, 'math', 'arc'),
(1708, 'WAEC-MATH', 'WAEC-MATH-TP-21', 'WAEC-MATH-TP-21', 'Calculate the length of an arc, which subtend an angle of <latex>44^{circ}</latex> at the centre of a circle of radius <latex>48cm</latex>\n', '', 1, 'math', 'arc'),
(1709, 'WAEC-MATH', 'WAEC-MATH-TP-21', 'WAEC-MATH-TP-21', 'Calculate the length of an arc, which subtend an angle of <latex>92^{circ}</latex> at the centre of a circle of radius <latex>13cm</latex>\n', '', 1, 'math', 'arc'),
(1710, 'WAEC-MATH', 'WAEC-MATH-TP-21', 'WAEC-MATH-TP-21', 'Calculate the length of an arc, which subtend an angle of <latex>170^{circ}</latex> at the centre of a circle of radius <latex>39cm</latex>\n', '', 1, 'math', 'arc'),
(1711, 'WAEC-MATH', 'WAEC-MATH-TP-21', 'WAEC-MATH-TP-21', 'Calculate the length of an arc, which subtend an angle of <latex>84^{circ}</latex> at the centre of a circle of radius <latex>36cm</latex>\n', '', 1, 'math', 'arc'),
(1712, 'WAEC-MATH', 'WAEC-MATH-TP-21', 'WAEC-MATH-TP-21', 'Calculate the length of an arc, which subtend an angle of <latex>170^{circ}</latex> at the centre of a circle of radius <latex>35cm</latex>\n', '', 1, 'math', 'arc'),
(1713, 'WAEC-MATH', 'WAEC-MATH-TP-21', 'WAEC-MATH-TP-21', 'Calculate the length of an arc, which subtend an angle of <latex>171^{circ}</latex> at the centre of a circle of radius <latex>14cm</latex>\n', '', 1, 'math', 'arc'),
(1714, 'WAEC-MATH', 'WAEC-MATH-TP-21', 'WAEC-MATH-TP-21', 'Calculate the length of an arc, which subtend an angle of <latex>28^{circ}</latex> at the centre of a circle of radius <latex>20cm</latex>\n', '', 1, 'math', 'arc'),
(1715, 'WAEC-MATH', 'WAEC-MATH-TP-21', 'WAEC-MATH-TP-21', 'Calculate the length of an arc, which subtend an angle of <latex>34^{circ}</latex> at the centre of a circle of radius <latex>26cm</latex>\n', '', 1, 'math', 'arc'),
(1716, 'WAEC-MATH', 'WAEC-MATH-TP-21', 'WAEC-MATH-TP-21', 'Calculate the length of an arc, which subtend an angle of <latex>78^{circ}</latex> at the centre of a circle of radius <latex>30cm</latex>\n', '', 1, 'math', 'arc'),
(1717, 'WAEC-MATH', 'WAEC-MATH-TP-21', 'WAEC-MATH-TP-21', 'Calculate the length of an arc, which subtend an angle of <latex>100^{circ}</latex> at the centre of a circle of radius <latex>32cm</latex>\n', '', 1, 'math', 'arc'),
(1718, 'WAEC-MATH', 'WAEC-MATH-TP-21', 'WAEC-MATH-TP-21', 'Calculate the length of an arc, which subtend an angle of <latex>66^{circ}</latex> at the centre of a circle of radius <latex>46cm</latex>\n', '', 1, 'math', 'arc'),
(1719, 'WAEC-MATH', 'WAEC-MATH-TP-21', 'WAEC-MATH-TP-21', 'Calculate the length of an arc, which subtend an angle of <latex>147^{circ}</latex> at the centre of a circle of radius <latex>48cm</latex>\n', '', 1, 'math', 'arc'),
(1720, 'WAEC-MATH', 'WAEC-MATH-TP-21', 'WAEC-MATH-TP-21', 'Calculate the length of an arc, which subtend an angle of <latex>44^{circ}</latex> at the centre of a circle of radius <latex>14cm</latex>\n', '', 1, 'math', 'arc'),
(1721, 'WAEC-MATH', 'WAEC-MATH-TP-21', 'WAEC-MATH-TP-21', 'Calculate the length of an arc, which subtend an angle of <latex>175^{circ}</latex> at the centre of a circle of radius <latex>32cm</latex>\n', '', 1, 'math', 'arc'),
(1722, 'WAEC-MATH', 'WAEC-MATH-TP-21', 'WAEC-MATH-TP-21', 'Calculate the length of an arc, which subtend an angle of <latex>37^{circ}</latex> at the centre of a circle of radius <latex>31cm</latex>\n', '', 1, 'math', 'arc'),
(1723, 'WAEC-MATH', 'WAEC-MATH-TP-21', 'WAEC-MATH-TP-21', 'Calculate the length of an arc, which subtend an angle of <latex>73^{circ}</latex> at the centre of a circle of radius <latex>40cm</latex>\n', '', 1, 'math', 'arc'),
(1724, 'WAEC-MATH', 'WAEC-MATH-TP-21', 'WAEC-MATH-TP-21', 'Calculate the length of an arc, which subtend an angle of <latex>69^{circ}</latex> at the centre of a circle of radius <latex>30cm</latex>\n', '', 1, 'math', 'arc'),
(1725, 'WAEC-MATH', 'WAEC-MATH-TP-21', 'WAEC-MATH-TP-21', 'Calculate the length of an arc, which subtend an angle of <latex>105^{circ}</latex> at the centre of a circle of radius <latex>19cm</latex>\n', '', 1, 'math', 'arc'),
(1726, 'WAEC-MATH', 'WAEC-MATH-TP-21', 'WAEC-MATH-TP-21', 'What is the angle subtend at the center of a circle by an arc, with length <latex>9.58cm</latex> and diameter <latex>18cm</latex>\n', '', 1, 'math', 'arc'),
(1727, 'WAEC-MATH', 'WAEC-MATH-TP-21', 'WAEC-MATH-TP-21', 'What is the angle subtend at the center of a circle by an arc, with length <latex>8.45cm</latex> and diameter <latex>19cm</latex>\n', '', 1, 'math', 'arc'),
(1728, 'WAEC-MATH', 'WAEC-MATH-TP-21', 'WAEC-MATH-TP-21', 'What is the angle subtend at the center of a circle by an arc, with length <latex>13.82cm</latex> and diameter <latex>11cm</latex>\n', '', 1, 'math', 'arc'),
(1729, 'WAEC-MATH', 'WAEC-MATH-TP-21', 'WAEC-MATH-TP-21', 'What is the angle subtend at the center of a circle by an arc, with length <latex>11.51cm</latex> and diameter <latex>44cm</latex>\n', '', 1, 'math', 'arc'),
(1730, 'WAEC-MATH', 'WAEC-MATH-TP-21', 'WAEC-MATH-TP-21', 'What is the angle subtend at the center of a circle by an arc, with length <latex>55.51cm</latex> and diameter <latex>37cm</latex>\n', '', 1, 'math', 'arc'),
(1731, 'WAEC-MATH', 'WAEC-MATH-TP-21', 'WAEC-MATH-TP-21', 'What is the angle subtend at the center of a circle by an arc, with length <latex>1.83cm</latex> and diameter <latex>21cm</latex>\n', '', 1, 'math', 'arc'),
(1732, 'WAEC-MATH', 'WAEC-MATH-TP-21', 'WAEC-MATH-TP-21', 'What is the angle subtend at the center of a circle by an arc, with length <latex>60.29cm</latex> and diameter <latex>48cm</latex>\n', '', 1, 'math', 'arc'),
(1733, 'WAEC-MATH', 'WAEC-MATH-TP-21', 'WAEC-MATH-TP-21', 'What is the angle subtend at the center of a circle by an arc, with length <latex>2.27cm</latex> and diameter <latex>20cm</latex>\n', '', 1, 'math', 'arc'),
(1734, 'WAEC-MATH', 'WAEC-MATH-TP-21', 'WAEC-MATH-TP-21', 'What is the angle subtend at the center of a circle by an arc, with length <latex>26.06cm</latex> and diameter <latex>36cm</latex>\n', '', 1, 'math', 'arc'),
(1735, 'WAEC-MATH', 'WAEC-MATH-TP-21', 'WAEC-MATH-TP-21', 'What is the angle subtend at the center of a circle by an arc, with length <latex>39.01cm</latex> and diameter <latex>43cm</latex>\n', '', 1, 'math', 'arc'),
(1736, 'WAEC-MATH', 'WAEC-MATH-TP-21', 'WAEC-MATH-TP-21', 'What is the angle subtend at the center of a circle by an arc, with length <latex>48.5cm</latex> and diameter <latex>40cm</latex>\n', '', 1, 'math', 'arc'),
(1737, 'WAEC-MATH', 'WAEC-MATH-TP-21', 'WAEC-MATH-TP-21', 'What is the angle subtend at the center of a circle by an arc, with length <latex>12.75cm</latex> and diameter <latex>43cm</latex>\n', '', 1, 'math', 'arc'),
(1738, 'WAEC-MATH', 'WAEC-MATH-TP-21', 'WAEC-MATH-TP-21', 'What is the angle subtend at the center of a circle by an arc, with length <latex>14.29cm</latex> and diameter <latex>39cm</latex>\n', '', 1, 'math', 'arc'),
(1739, 'WAEC-MATH', 'WAEC-MATH-TP-21', 'WAEC-MATH-TP-21', 'What is the angle subtend at the center of a circle by an arc, with length <latex>39.48cm</latex> and diameter <latex>31cm</latex>\n', '', 1, 'math', 'arc'),
(1740, 'WAEC-MATH', 'WAEC-MATH-TP-21', 'WAEC-MATH-TP-21', 'What is the angle subtend at the center of a circle by an arc, with length <latex>16.65cm</latex> and diameter <latex>23cm</latex>\n', '', 1, 'math', 'arc'),
(1741, 'WAEC-MATH', 'WAEC-MATH-TP-21', 'WAEC-MATH-TP-21', 'What is the angle subtend at the center of a circle by an arc, with length <latex>7.03cm</latex> and diameter <latex>13cm</latex>\n', '', 1, 'math', 'arc'),
(1742, 'WAEC-MATH', 'WAEC-MATH-TP-21', 'WAEC-MATH-TP-21', 'What is the angle subtend at the center of a circle by an arc, with length <latex>29.66cm</latex> and diameter <latex>20cm</latex>\n', '', 1, 'math', 'arc'),
(1743, 'WAEC-MATH', 'WAEC-MATH-TP-21', 'WAEC-MATH-TP-21', 'What is the angle subtend at the center of a circle by an arc, with length <latex>4.58cm</latex> and diameter <latex>35cm</latex>\n', '', 1, 'math', 'arc'),
(1744, 'WAEC-MATH', 'WAEC-MATH-TP-21', 'WAEC-MATH-TP-21', 'What is the angle subtend at the center of a circle by an arc, with length <latex>8.44cm</latex> and diameter <latex>11cm</latex>\n', '', 1, 'math', 'arc'),
(1745, 'WAEC-MATH', 'WAEC-MATH-TP-21', 'WAEC-MATH-TP-21', 'What is the angle subtend at the center of a circle by an arc, with length <latex>7.82cm</latex> and diameter <latex>13cm</latex>\n', '', 1, 'math', 'arc'),
(1746, 'WAEC-MATH', 'WAEC-MATH-TP-21', 'WAEC-MATH-TP-21', 'What is the angle subtend at the center of a circle by an arc, with length <latex>22.71cm</latex> and diameter <latex>42cm</latex>\n', '', 1, 'math', 'arc'),
(1747, 'WAEC-MATH', 'WAEC-MATH-TP-21', 'WAEC-MATH-TP-21', 'What is the angle subtend at the center of a circle by an arc, with length <latex>15.91cm</latex> and diameter <latex>24cm</latex>\n', '', 1, 'math', 'arc'),
(1748, 'WAEC-MATH', 'WAEC-MATH-TP-21', 'WAEC-MATH-TP-21', 'What is the angle subtend at the center of a circle by an arc, with length <latex>5.67cm</latex> and diameter <latex>13cm</latex>\n', '', 1, 'math', 'arc'),
(1749, 'WAEC-MATH', 'WAEC-MATH-TP-21', 'WAEC-MATH-TP-21', 'What is the angle subtend at the center of a circle by an arc, with length <latex>66.41cm</latex> and diameter <latex>47cm</latex>\n', '', 1, 'math', 'arc'),
(1750, 'WAEC-MATH', 'WAEC-MATH-TP-21', 'WAEC-MATH-TP-21', 'What is the angle subtend at the center of a circle by an arc, with length <latex>29.66cm</latex> and diameter <latex>25cm</latex>\n', '', 1, 'math', 'arc'),
(1751, 'WAEC-MATH', 'WAEC-MATH-TP-21', 'WAEC-MATH-TP-21', 'What is the angle subtend at the center of a circle by an arc, with length <latex>37.07cm</latex> and diameter <latex>34cm</latex>\n', '', 1, 'math', 'arc'),
(1752, 'WAEC-MATH', 'WAEC-MATH-TP-21', 'WAEC-MATH-TP-21', 'What is the angle subtend at the center of a circle by an arc, with length <latex>43.76cm</latex> and diameter <latex>29cm</latex>\n', '', 1, 'math', 'arc'),
(1753, 'WAEC-MATH', 'WAEC-MATH-TP-21', 'WAEC-MATH-TP-21', 'What is the angle subtend at the center of a circle by an arc, with length <latex>12.56cm</latex> and diameter <latex>10cm</latex>\n', '', 1, 'math', 'arc'),
(1754, 'WAEC-MATH', 'WAEC-MATH-TP-21', 'WAEC-MATH-TP-21', 'What is the angle subtend at the center of a circle by an arc, with length <latex>21.38cm</latex> and diameter <latex>43cm</latex>\n', '', 1, 'math', 'arc'),
(1755, 'WAEC-MATH', 'WAEC-MATH-TP-21', 'WAEC-MATH-TP-21', 'What is the angle subtend at the center of a circle by an arc, with length <latex>34.54cm</latex> and diameter <latex>45cm</latex>\n', '', 1, 'math', 'arc'),
(1756, 'WAEC-MATH', 'WAEC-MATH-TP-21', 'WAEC-MATH-TP-21', 'Find the angle subtend at the center of a circle by an arc, with length <latex>80.1cm</latex> if a arc with length <latex>80.1cm</latex> subtend an angle of <latex>164^{circ}</latex> at the centre of a circle \n', '', 1, 'math', 'arc'),
(1757, 'WAEC-MATH', 'WAEC-MATH-TP-21', 'WAEC-MATH-TP-21', 'Find the angle subtend at the center of a circle by an arc, with length <latex>28.17cm</latex> if a arc with length <latex>28.17cm</latex> subtend an angle of <latex>95^{circ}</latex> at the centre of a circle \n', '', 1, 'math', 'arc'),
(1758, 'WAEC-MATH', 'WAEC-MATH-TP-21', 'WAEC-MATH-TP-21', 'Find the angle subtend at the center of a circle by an arc, with length <latex>136.62cm</latex> if a arc with length <latex>136.62cm</latex> subtend an angle of <latex>178^{circ}</latex> at the centre of a circle \n', '', 1, 'math', 'arc'),
(1759, 'WAEC-MATH', 'WAEC-MATH-TP-21', 'WAEC-MATH-TP-21', 'Find the angle subtend at the center of a circle by an arc, with length <latex>52.19cm</latex> if a arc with length <latex>52.19cm</latex> subtend an angle of <latex>88^{circ}</latex> at the centre of a circle \n', '', 1, 'math', 'arc'),
(1760, 'WAEC-MATH', 'WAEC-MATH-TP-21', 'WAEC-MATH-TP-21', 'Find the angle subtend at the center of a circle by an arc, with length <latex>92.66cm</latex> if a arc with length <latex>92.66cm</latex> subtend an angle of <latex>166^{circ}</latex> at the centre of a circle \n', '', 1, 'math', 'arc'),
(1761, 'WAEC-MATH', 'WAEC-MATH-TP-21', 'WAEC-MATH-TP-21', 'Find the angle subtend at the center of a circle by an arc, with length <latex>8.79cm</latex> if a arc with length <latex>8.79cm</latex> subtend an angle of <latex>24^{circ}</latex> at the centre of a circle \n', '', 1, 'math', 'arc'),
(1762, 'WAEC-MATH', 'WAEC-MATH-TP-21', 'WAEC-MATH-TP-21', 'Find the angle subtend at the center of a circle by an arc, with length <latex>50.68cm</latex> if a arc with length <latex>50.68cm</latex> subtend an angle of <latex>83^{circ}</latex> at the centre of a circle \n', '', 1, 'math', 'arc'),
(1763, 'WAEC-MATH', 'WAEC-MATH-TP-21', 'WAEC-MATH-TP-21', 'Find the angle subtend at the center of a circle by an arc, with length <latex>63.79cm</latex> if a arc with length <latex>63.79cm</latex> subtend an angle of <latex>159^{circ}</latex> at the centre of a circle \n', '', 1, 'math', 'arc'),
(1764, 'WAEC-MATH', 'WAEC-MATH-TP-21', 'WAEC-MATH-TP-21', 'Find the angle subtend at the center of a circle by an arc, with length <latex>19.54cm</latex> if a arc with length <latex>19.54cm</latex> subtend an angle of <latex>28^{circ}</latex> at the centre of a circle \n', '', 1, 'math', 'arc'),
(1765, 'WAEC-MATH', 'WAEC-MATH-TP-21', 'WAEC-MATH-TP-21', 'Find the angle subtend at the center of a circle by an arc, with length <latex>36.01cm</latex> if a arc with length <latex>36.01cm</latex> subtend an angle of <latex>43^{circ}</latex> at the centre of a circle \n', '', 1, 'math', 'arc');
