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**Question 1**
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The product PV where P is pressure and V is volume has the same unit as

**Answer Details**

The unit of pressure is force per unit area, while the unit of volume is length cubed. Therefore, the product of pressure and volume is given by force times length cubed, which is equivalent to work, the amount of energy transferred when a force of one newton is applied over a distance of one meter. Therefore, the product PV has the same unit as work, which is joule (J).

**Question 2**
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Which of the following has the highest surface tension?

**Question 3**
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If the frequency of the e.m.f. source in the a.c. circuit illustrated above is \(\frac{500}{\pi}\)Hz. What is the reactance of the inductor?

**Question 4**
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A house is supplied with a 240V a.c mains. To operate a door bell rated at 8v, a transformer is used if the number of turns in the primary coil of the transformer is 900. calculate the number of turns in the secondary coil of the transformer

**Answer Details**

To calculate the number of turns in the secondary coil of the transformer, we need to use the formula: Np/Ns = Vp/Vs Where Np is the number of turns in the primary coil, Ns is the number of turns in the secondary coil, Vp is the voltage in the primary coil, and Vs is the voltage in the secondary coil. In this case, we know that the voltage in the primary coil is 240V and the voltage in the secondary coil is 8V. We also know that the number of turns in the primary coil is 900. Plugging these values into the formula, we get: 900/Ns = 240/8 Simplifying this equation, we get: 900/Ns = 30 To solve for Ns, we can multiply both sides by Ns: 900 = 30Ns Dividing both sides by 30, we get: Ns = 30 Therefore, the number of turns in the secondary coil of the transformer is 30. So, the correct option is "30".

**Question 5**
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Two capacitors C_{1} and C_{2} are connected as shown in the diagram. The capacitance C_{2} is twice C_{1} when the key is opened the energy stored up in C_{1} is W. If the key is later closed and the system is allowed to attain electrical equilibrium, the total energy stored in the system will be

**Answer Details**

When the key is open, the two capacitors are not connected and the charge on each of them is zero. The energy stored in capacitor C1 is given by the formula: W = (1/2) * C1 * V^2, where V is the voltage across capacitor C1. When the key is closed, the two capacitors are connected in parallel, and a charge Q will flow from one plate of C1 to the other plate of C2 until the voltage across both capacitors is the same. Let the voltage across both capacitors be V. Then, the charge on C1 will be Q/2, and the charge on C2 will be Q. The total energy stored in the system can be calculated as follows: W(total) = (1/2) * C1 * V^2 + (1/2) * C2 * V^2 Substituting C2 = 2C1 and Q = CV, we get: W(total) = (1/2) * C1 * V^2 + (1/2) * 2C1 * V^2 = (1/2) * 3C1 * V^2 = (3/2) * W Therefore, the total energy stored in the system when the key is closed and the system is allowed to attain electrical equilibrium is (3/2) times the energy stored in C1 when the key is open. Hence, the correct option is 3W.

**Question 6**
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The saturation vapour of a liquid depends on its

**Answer Details**

The saturation vapor pressure of a liquid depends on its temperature. When a liquid evaporates, it turns into a gas or vapor. This process of evaporation depends on the energy of the liquid molecules. The higher the temperature, the more energy the molecules have, and the more likely they are to escape from the surface of the liquid and become a gas. As the concentration of vapor molecules increases above a liquid surface, some of them may condense back into the liquid phase, and this creates an equilibrium between the liquid and vapor phases, called saturation. The saturation vapor pressure is the pressure exerted by the vapor in equilibrium with its liquid phase at a given temperature. So, as the temperature of the liquid increases, the saturation vapor pressure increases, meaning more molecules are in the gas phase. On the other hand, as the temperature decreases, the saturation vapor pressure decreases, indicating fewer molecules in the gas phase. Therefore, the saturation vapor pressure of a liquid is determined by its temperature and is independent of the volume, mass, density, or pressure of the liquid.

**Question 7**
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Which of the following statements is not correct? Isotopes of an element have

**Question 8**
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Melting ice cools an orange drink far better than the same mass of ice-cold water because

**Answer Details**

Melting ice cools an orange drink better than the same mass of ice-cold water because ice absorbs latent heat during melting. Latent heat is the heat energy required to change the state of a substance without changing its temperature. When ice melts, it absorbs latent heat from the drink to overcome the intermolecular forces holding its particles together. This absorption of latent heat results in cooling of the drink. On the other hand, ice-cold water has already reached its melting point, and there is no further absorption of latent heat during cooling. Water has a higher specific heat than ice, which means it can absorb more heat energy without changing its temperature. However, this does not contribute to better cooling of the drink. Option (i) is incorrect because ice-cold water is actually at a lower temperature than melting ice. Option (iii) is also incorrect because while ice floats, it does not cool the air above the drink significantly. Option (v) is not entirely correct because while ice can make better thermal contact than water, it is the absorption of latent heat that makes it more effective in cooling the drink. Therefore, the correct answer is option (iv) ice absorbs latent heat during melting.

**Question 9**
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When a metal surface is irradiated, photoelectrons may be ejected from the metal. The kinetic energy of the ejected electrons depends on the

**Answer Details**

The kinetic energy of the photoelectrons ejected from a metal surface when irradiated depends on the frequency of the radiation. This is known as the photoelectric effect. When a photon of light is absorbed by a metal surface, it can transfer its energy to an electron within the metal, causing the electron to be ejected from the surface. The amount of energy transferred to the electron depends on the frequency of the photon, which is related to its wavelength. Photons with higher frequencies (shorter wavelengths) have more energy than photons with lower frequencies (longer wavelengths), and thus can transfer more energy to the ejected electron, resulting in a higher kinetic energy. Therefore, the frequency of the radiation is the key factor that determines the kinetic energy of the ejected electrons.

**Question 10**
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Calculate the refractive index of the material of the glass block shown in the diagram if YZ = 4cm

**Question 11**
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An orange fruit drops to the ground from the top of a tree 45m tall. How long does it takes to reach the ground? (g = 10ms^{-2})

**Answer Details**

To calculate the time it takes for the orange fruit to hit the ground, we can use the following formula: d = 1/2 * g * t^2 where d is the distance (in meters) the orange falls, g is the acceleration due to gravity (in meters per second squared), and t is the time (in seconds) it takes for the orange to fall. In this case, the orange falls from a height of 45m, and g is 10m/s^2. We can plug these values into the formula and solve for t: 45 = 1/2 * 10 * t^2 Simplifying the equation: t^2 = 9 t = 3 Therefore, it takes 3 seconds for the orange fruit to hit the ground. This is the answer to the problem.

**Question 12**
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A particle of charge q and mass m moving with a velocity v enters a uniform magnetic field b in the direction of the field. The force on the particle is

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A particle of charge q and mass m moving with a velocity v enters a uniform magnetic field B in the direction of the field. The force on the particle is given by the equation F = qVB sinθ, where θ is the angle between the velocity vector and the magnetic field vector. In this case, since the particle enters the field in the direction of the field, θ = 0, and sinθ = 0. Therefore, the force on the particle is zero (F = qVB sinθ = qVB(0) = 0). Option (d) is correct - the force on the particle is zero. Option (a) is incorrect because it represents the formula for the magnitude of the force on a charged particle moving perpendicular to the magnetic field. Option (b) is incorrect because it represents the formula for the acceleration of a charged particle in a magnetic field. Option (c) is incorrect because it represents the formula for the radius of the circular path followed by a charged particle moving perpendicular to the magnetic field. Therefore, the correct answer is - O.

**Question 13**
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In the arrangement illustrated above, Y and B are yellow and blue transparent light filters respectively through the filters is

**Question 14**
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At which of the following distances from the lens should a slide be placed on a slide projector if f is the focal length of the projector length?

**Question 15**
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The sound from a bell in an enclosed jar gradually faints away while the jar is being evacuated. Which of the following explains this observation?

**Answer Details**

The observation that the sound from a bell in an enclosed jar gradually faints away while the jar is being evacuated can be explained by the fact that there is no more material medium for the sound waves to propagate through. Sound waves are vibrations that propagate through a medium such as air, water, or solids. When the jar is evacuated, the air is pumped out, resulting in a decrease in pressure inside the jar. As the pressure decreases, the density of the air inside the jar decreases as well. Sound waves require a medium to travel through, and in this case, there is less and less air inside the jar, resulting in fewer particles available to transmit the sound waves. Eventually, when the jar is fully evacuated, there is no more air left inside the jar to transmit the sound waves. Therefore, the correct option is: there is no more material medium.

**Question 16**
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A fixed mass of gas of volume 600cm^{3} at a temperature of 27^{o}C is cooled at constant pressure to a temperature of 0^{o}C. What is the change in volume?

**Answer Details**

We can use the combined gas law to solve this problem. The combined gas law states that the product of pressure and volume is directly proportional to the product of temperature and the number of moles of gas, assuming constant mass. Mathematically, this can be written as: P_{1}V_{1}/T_{1} = P_{2}V_{2}/T_{2} where P is pressure, V is volume, T is temperature, and the subscripts 1 and 2 refer to the initial and final states, respectively. We are told that the initial volume V_{1} is 600 cm^{3} and the initial temperature T_{1} is 27^{o}C = 300K. We also know that the pressure P remains constant throughout the process, and that the final temperature T_{2} is 0^{o}C = 273K. We can solve for the final volume V_{2}: P_{1}V_{1}/T_{1} = P_{2}V_{2}/T_{2} V_{2} = (P_{1}/P_{2}) * (T_{2}/T_{1}) * V_{1} Since the pressure is constant, we can cancel it out, and substitute in the given values: V_{2} = (273K/300K) * 600 cm^{3} = 546 cm^{3} Therefore, the change in volume is 600 cm^{3} - 546 cm^{3} = 54 cm^{3}. So, the correct answer is 54 cm^{3}.

**Question 17**
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The diagram above represents six maximum and minimum thermometer. If the temperature of the surrounding falls, which of the following correctly states how the thermometer would respond to the change in temperature?

**Question 18**
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the diagram above shows the position of a simple pendulum set in motion. At which of the positions does the pendulum have maximum kinetic energy?

**Question 20**
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In the circuit above R is a resistor whose resistance increases with increases with increase in temperature L_{1} and L_{2} are identical lamps. If the temperature of R increases

**Question 21**
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A body moving with uniform acceleration has two points(5, 15) and (20, 60) on the velocity-times graph of its motion. Calculate

**Answer Details**

Since the body is moving with uniform acceleration, the graph of its velocity vs time will be a straight line. Let the initial velocity of the body be u, and the acceleration be a. From the two given points, we can determine two equations: 1. At t = 5 s, v = 15 m/s: 15 = u + 5a 2. At t = 20 s, v = 60 m/s: 60 = u + 20a Subtracting equation 1 from equation 2, we get: 45 = 15a a = 3 m/s^2 Therefore, the acceleration of the body is 3.00 ms^-2. is the correct answer.

**Question 22**
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The graph above shows the expansion of water as the temperature increases from 0^{o}C. Which of the following deductions from the graph are true? i. Water has its maximum density at Q. ii. The volume of water is greater at 0^{o}C than at 4^{o}C. iii. The volume of water decreases uniformly when cooled from 100^{o}C. iv. When water solidifies, its volume increases

**Question 23**
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A water fall is 420m high. Calculate the difference in temperature of the water between the top and bottom of the water fall. Neglect heat loses(g = 10.0m^{-2} specific heat capacity of water = 4.20 x 10^{-3} JKg^{-1} K^{-1})

**Question 24**
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Which of the following statements above viscosity are correct? when a ball falls through a viscous liquid i. viscosity opposes the gravitational force on the ball. ii. viscosity opposes the upthrust on the ball. iii. viscosity is in the same direction as the upthrust on the ball. iv. as the ball falls faster the more viscous the liquid is

**Question 25**
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In which of the following is a stationary wave produced? i. A vibrating turning fork held near the end of a resonance tube closed at one end. ii. A string tightly stretched between two points and plucked at its middle. iii. The tuning fork vibrating in air

**Answer Details**

A stationary wave is a type of wave that appears to be standing still, even though it is made up of two waves traveling in opposite directions. Option i describes a resonance tube closed at one end and a vibrating tuning fork held near the end. In this situation, the sound wave produced by the tuning fork travels down the resonance tube and reflects off the closed end, creating a stationary wave. Option ii describes a string that is tightly stretched between two points and plucked at its middle. In this situation, the string vibrates back and forth, creating a wave that travels along the string and reflects back when it reaches the ends, creating a stationary wave. Option iii describes a tuning fork vibrating in air, which produces a sound wave that travels through the air as a longitudinal wave. This wave does not create a stationary wave since it does not reflect back and interfere with itself. Therefore, the correct answer is option i and ii only.

**Question 26**
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Two objects of masses 80kg and 50kg are separated by a distance of 0.2m. If the gravitational constant is 6.6 x 10^{-11}Nm kg, calculate the gravitational attraction between them.

**Question 27**
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a tap supplies water at 26^{o}C while another supplies water at 82^{o}C. If a man wishes to bathe with water at 40^{o}C the ratio of hot mass of hot water to that of cold water required is

**Question 28**
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A ball is projected horizontally from the top of a hill with a velocity of 20m^{-1}. If it reaches the ground 4 seconds later, what is the height of the hill? (g = 10ms^{-2})

**Answer Details**

We can solve this problem using the kinematic equations of motion. Since the ball is projected horizontally, its initial vertical velocity is zero. We can use the following equation to find the height of the hill: h = (1/2)gt^2 Where h is the height of the hill, g is the acceleration due to gravity, and t is the time taken for the ball to reach the ground. In this case, g = 10ms^-2 and t = 4s. Plugging these values into the equation, we get: h = (1/2)(10)(4)^2 = 80m Therefore, the height of the hill is 80 meters. This is option (C). To summarize, the ball is projected horizontally with a velocity of 20m/s, which means its initial vertical velocity is zero. Using the kinematic equation for displacement, we can find the height of the hill. The ball takes 4 seconds to reach the ground, so we substitute this value along with the acceleration due to gravity into the equation. The resulting answer is 80 meters, which is the height of the hill.

**Question 29**
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An induction coil is generally used to

**Answer Details**

An induction coil is generally used to produce a large output voltage. An induction coil is a type of transformer that uses a magnetic field to convert a low voltage (input voltage) to a high voltage (output voltage). The coil works on the principle of electromagnetic induction, where a changing magnetic field induces an electric current in a nearby conductor. In an induction coil, the primary coil is connected to a source of electrical energy, and the secondary coil is connected to the load. When an electric current flows through the primary coil, it creates a changing magnetic field that induces an electric current in the secondary coil, resulting in a large output voltage. The ratio of the number of turns in the primary coil to the number of turns in the secondary coil determines the voltage transformation ratio.

**Question 30**
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An electron charge 1.6 x 10^{-19}C is accelerated in vacuum from rest at zero volt towards a plate at 40k V. Calculate the kinetic energy of the electron

**Answer Details**

The work done in accelerating the electron is given by W = qV where q is the charge of the electron and V is the potential difference. The potential difference is given as 40 kV, which is equivalent to 40 x 10^3 V. Therefore, the work done in accelerating the electron is: W = (1.6 x 10^-19 C) x (40 x 10^3 V) = 6.4 x 10^-15 J This work done is equal to the kinetic energy gained by the electron since it started from rest. Therefore, the kinetic energy of the electron is: K.E = 6.4 x 10^-15 J Hence, the correct option is: 3.2 x 10^-15 J.

**Question 31**
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A wire, 20m long is heated from a temperature of 5oC to 55oC. If the change in length is 0.020m, calculate the linear expansivity of the wire

**Answer Details**

Linear expansivity is a measure of how much a material changes in length when its temperature changes. It is denoted by the Greek letter alpha (α) and is expressed in units of K^{-1}. The formula for linear expansivity is: α = ΔL / (L_i * ΔT) Where: ΔL = change in length L_i = initial length ΔT = change in temperature Using the values given in the question, we have: ΔL = 0.020 m L_i = 20 m ΔT = (55 - 5) = 50 K Substituting these values into the formula, we get: α = 0.020 / (20 * 50) = 2.0 x 10^{-5} K^{-1} Therefore, the linear expansivity of the wire is 2.0 x 10^{-5} K^{-1}. Answer choice (C) is the correct answer.

**Question 32**
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The unit of stress is

**Answer Details**

The unit of stress is Nm^{-2} (Newtons per square meter), also known as Pascal (Pa). Stress is defined as force per unit area and is a measure of the internal forces acting on a material. When a force is applied to a material, it creates internal forces that tend to resist the deformation or change in shape. Stress is the measure of these internal forces per unit area. The unit Nm represents work or energy, while N represents force, and Nm^{2} does not have a physical meaning.

**Question 34**
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The work function of a metal is 4.65ev and the metal is illuminated with a radiation of 6.86ev. What is the kinetic energy of the electrons ejected from the surface of the metal?

**Answer Details**

The kinetic energy of the ejected electrons can be calculated using the equation: Kinetic energy of electron = Energy of incident radiation - Work function of the metal Substituting the given values, we have: Kinetic energy of electron = 6.86ev - 4.65ev Kinetic energy of electron = 2.21ev Therefore, the kinetic energy of the electrons ejected from the surface of the metal is 2.21ev. Hence, the correct option is (b) 2.21ev.

**Question 35**
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What type of motion does the skin of a talking drum perform when its being struck with the drum stick?

**Answer Details**

The skin of a talking drum performs a vibratory motion when it is being struck with the drum stick. When the drum is struck, the skin vibrates back and forth, producing sound waves that travel through the air. The skin moves in a series of up-and-down motions that are perpendicular to the surface of the drum. The shape of the drum, and the tension of the skin, determine the frequency of the vibration and the pitch of the resulting sound. The player can vary the pitch by squeezing the drum under their arm or by applying pressure to the skin with their non-dominant hand. Therefore, the correct option is vibratory.

**Question 36**
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A body moves with a constant speed but has an acceleration. this process if it

**Answer Details**

A body that moves with a constant speed but has an acceleration is moving in a circular path. Acceleration is the rate at which the velocity of an object changes. When an object moves in a circular path, it is constantly changing direction, even if it is moving at a constant speed. This means that its velocity is changing, and therefore, it has an acceleration. The direction of the acceleration is always towards the center of the circular path, and its magnitude is given by the formula a = v^2/r, where a is the acceleration, v is the speed of the object, and r is the radius of the circular path. Therefore, the correct option is: moves in a circle.

**Question 37**
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The half-life of a radioactive substance is 2 seconds. Calculate the decay constant

**Question 38**
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The boiling point of a liquid depends on the following except the

**Question 39**
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Two mirrors are inclined as shown in the diagram. A ray of light RO strikes the arrangement at O and emerges along PO. The emergent ray has been deviated through

**Question 40**
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Which of the following remains unchanged as light travels from one medium to the other? i. speed. ii. wavelength. iii. frequency.

**Question 41**
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A 90W immersion heater is used to supply energy for 5 minutes. The energy supplied is used to completely melt 160g of a solid at its melting point. Calculate the specific latent heat of the solid.

**Answer Details**

To calculate the specific latent heat of the solid, we need to use the formula: Q = mL where Q is the amount of energy supplied by the immersion heater, m is the mass of the solid, and L is the specific latent heat of the solid. First, we need to calculate the amount of energy supplied by the immersion heater. We know that the heater has a power output of 90W and it is used for 5 minutes, so the total energy supplied is: Q = Pt = 90W x 5min x 60s/min = 27,000 J Next, we can use this value of Q and the mass of the solid, which is 160g, to calculate the specific latent heat L: L = Q/m = 27,000 J / 160g = 168.75 Jg^{-1} Therefore, the specific latent heat of the solid is 168.75 Jg^{-1}. Option (D) 168.75 Jg^{-1} is the correct answer.

**Question 42**
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plane as 63cm of HG while a ground observer records a reading of 75cm of Hg with his barometer. assuming that the density of air is constant, calculate the height of the plane above the ground. (Take the relative densities of air and mecury as 0.00136 and 13.6 respectively

**Answer Details**

To solve this problem, we can use the formula: h = (ρm/ρa) * (P0 - P) where: h = height of the plane above the ground ρm = density of mercury (13.6 g/cm^3) ρa = density of air (0.00136 g/cm^3) P0 = atmospheric pressure at ground level (75 cm of Hg) P = atmospheric pressure at the height of the plane (63 cm of Hg) First, we need to convert the units of the densities from g/cm^3 to kg/m^3 to be consistent with the units of the atmospheric pressure in meters of mercury (m of Hg): ρm = 13.6 * 1000 kg/m^3 = 13600 kg/m^3 ρa = 0.00136 * 1000 kg/m^3 = 1.36 kg/m^3 Now, we can plug in the values and solve for h: h = (13600/1.36) * (75 - 63) h = 10000 * 12 h = 120000 meters Therefore, the height of the plane above the ground is 120,000 meters. Note: This answer seems unreasonable as it is much higher than the typical cruising altitude of commercial airplanes. This may be due to a mistake in the given information or in the calculations.

**Question 43**
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Which of the following are true of plane-polarised right? i. Plane polarisation of light is the formation of hydrogen bubbles on the particle of light. ii. Plane components. iii. A plane polarised light vibrates in one plane. iv. Polarisation of light is characteristic of transverse vibration

**Question 45**
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