1. The theory of relativity was given by French scientists, Albert Einstein.
a) True
b) False

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2. Computers are based on_________
a) digital computer
b) digital logic
c) android
d) none of these

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1. The relative density of a material of a body is found by weighing it first in air and then in water. If the weight of the body in air is W₁ = 8.00 ± 0.05 N and weight in water W₂ = 6.00 ± 0.05 N, then the relative density ρ_r = W₁/(W₁ - W₂) with the maximum permissible error is
a) 4.00 ± 0.62%
b) 4.00 ± 0.82%
c) 4.00 ± 3.2%
d) 4.00 ± 5.62%

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2. Young modulus of steel is 1.9 x 10¹¹ N/M². When expressed in CGS units of dynes/cm² , it will be equal to (1N = 10⁵ dyne, 1,² = 10<>sup>4 cm²)
a) 1.9 x 10¹⁰
b) 1.9 x 10¹¹
c) 1.9 x 10¹²
d) 1.9 x 10¹³

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1. A ball is thrown from the top of a tower in vertically upward direction. Velocity at a point h metre below the point of projection is twice of the velocity at a point h metre above the point of projection. Find the maximum height reached by the ball above of top of tower.
a) 2h
b) 3h
c) (5/3)h
d) (4/3)h

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2. Two trains 121 m and 99 m in length are running in opposite directions with velocites 40 km/h and 32 km/h. They will completely cross each other in 10 s.
a) True
b) False

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1. A bullet is to be fired with a speed of 2000 ms^-1 to hit a target 200 m away on a level ground. If g=10 ms^-1, the gum should be aimed
a) Directly at the target
b) 5 sm below the target
c) 5 cm above the target
d) 2 cm above the target

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2. For a paricle performing uniform circular motion, choose the correct statements (s) from the following:
a) Magnitude of particle velocity(speed)
b) Particle velocity remains directed perpendicular to radius vector
c) Direction of acceleration keeps changing as particle moves
d) Angular momentum is constant in magnitude but direction keeps changing.

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1. A 20 kg block is initially at rest. A 75 N force is required to set the block in motion.After the motion, a force of 60 N is applied to keep the block mving with constant speed. The coefficient of sliding friction is
a) 0.6
b) 0.52
c) 0.44
d) 0.35

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2. A circular road of radius 1000m has banking angle 450 . The maximum safe speed (in ms^-1) of a car having a mass 2000 kg will be, if the coefficient of friction between tyre and road is 0.5
a) 172
b) 124
c) 99
d) 86

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1. A block of mass m has initial velocity u having direction towards +x axis. The block stops after covering a distance S causing similar extension in the string of constant K holding it. It μ is the kinetic friction between the block and the surface on which it was moving, the distance S is given by

a) $\frac{1}{K}\mu^{2}m^{2}g^{2}$
b) $\frac{1}{K}\left (mKu^{2} - \mu^{2}m^{2}g^{2} \right )^{1/2}$
c) $\frac{1}{K}\left (\mu^{2}m^{2}g^{2} + mKu^{2} + \mu mg \right )^{1/2}$
d) $\frac{-\mu mg + \sqrt{\mu^{2}m^{2}g} + mu^{2}k}{k}$

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2. A block of mass 10 kg is moving in x-direction with a constant speed of 10 m/s. It is subjected to a retarding force F = 0.1 x joule/metre during its travel from x = 20 m to x =30 m. Its final K.E. will be
a) 475 J
b) 450 J
c) 275 J
d) 250 J

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1. A body A of mass M while falling vertically downwards under gravity breaks into two parts; a body B of mass 1/3 M and a body C of mass 2/3 M. The centre of mass of bodies B and C taken together shifts compared to that of body A towards
a) Body B
b) Body C
c) Does not shift
d) Depends on height of breaking

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2. Two persons of masses 55 kg and 65 kg respectively, are at the opposite ends of a boat. The length of the boat is 3.0 m and weighs 100 kg. The 55 kg man walks up to the 65 kg man and sits with him. If the boat is in still water the centre of mass of the system shifts by:
a) 3.0 m
b) 2.3 m
c) Zero
d) 0. 75m

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1. Suppose the gravitational force varies inversely as the nth power of the distance. Then the time period of a planet in circular orbit of radius R around the sun will be proportional to
a) R^-n
b) Rⁿ
c) R^(n-1)/2
d) R^(n+1)/2

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2. Two particles of equal mass `m` go around a circle of radius R under the action of their mutual gravitationsl attraction. The speed of each particle with respect to their centre of mass is
a) √(Gm/R)
b) √(Gm/4R)
c) √(Gm/3R)
d) √(Gm/2R)

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1. The volume of an air bubble becomes three times as it rises from the bottom of a lake to its surface. Assuming atmospheric pressure to be 75 cm of mercury and density of water to be 1/10 of the density of mercury, the depth of the lake is
a) 5 m
b) 10 m
c) 15 m
d) 20 m

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2. A rings is cut from a platinum tube 8.5 cm internal and 8.7 cm external diameter. It is supported horizontally from the pan of a balance, so that it comes in contacts with the water in a glass vessel . If an extra 3.103 g.f. is required to pull it away from water, the surface tension of water is
a) 72 dyn/cm
b) 70.80 dyn/cm
c) 63.35 dyn/cm
d) 60 dyn/cm

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1. In a surface tension experiment with a capillary tube water rises upto 0.1 m. If the same experiment is repeated on an artificial satellite, which is revolving around the earth, water will rise in the capillary tube upto a height of
a) 0.1 m
b) M
c) M/2
d) M

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2. The workdone by pressure in forcing 1 m³ of water through a pipe if the pressure difference across the pipe is 10⁴ Pa, is
a) 10⁵ J
b) 10⁴ J
c) 10³ J
d) 10² J

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1. An ideal gas is expanded such that PT² = a constant. The coefficient of volume expansion of the gas is
a) 1/T
b) 2/T
c) 3/T
d) 4/T

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2. The value of specific heat of a solid or liquid is ____________but________for gases.
a) Unique ; not so
b) Not so ; unique
c) Both a and b
d) None of these

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1. In the relation dQ = dU + dW, the quantity which remains the same for all process is
a) dQ
b) dW
c) dU
d) all of the above

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2. If ΔU and ΔW represents the increases in internal energy and work done by the system respectively in a thermodynamical process, which of the following is true?
a) ΔU = -ΔW, in a adiabatic process
b) ΔU = -ΔW, in a thermal process
c) ΔU ≠ -ΔW, in a adiabatic process
d) ΔU = ΔW, in a adiabatic process

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1. The specific heat at constant volume for the monoatomic argon is 0.075 kxal/kg-K,whereas its gram molecular specific heat is C_v = 2.98 cal/mol/K. The mass of the argon atom is (Avogadros number = 6.02 x 10²³ molecules/mol)
a) 6.60 x 10^-23g
b) 3.30 x 10^-23g
c) 2.20 x 10^-23g
d) 13.20 x 10²³ g

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2. Five moles of hydrogen gas are heated from 30⁰C to 60⁰C at constant pressure. Heat given to the gas is (given R = 2 cal/mol degree)
a) 750 cal
b) 630 cal
c) 1050 cal
d) 1470 cal

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1. A particle executing harmonic motion is having velocities v₁ and v₂ at distance is x₁ and x₂ from the equilibrium position. The amplitude of the motion is
a) $\sqrt{\frac{v_{1}^{2} x_{2} - v_{2}^{2} x_{1}}{v_{1}^{2} + v_{2}^{2}}}$
b) $\sqrt{\frac{v_{1}^{2}x_{1}x^{2} - v_{2}^{2} x_{2}^{2}}{v_{1}^{2} + v_{2}^{2}}}$
c) $\sqrt{\frac{v_{1}^{2}x_{2}^{2} - v_{2}^{2}x_{1}^{2}}{v_{1}^{2} - v_{2}^{2}}}$
d) $\sqrt{\frac{v_{1}^{2}x_{2}^{2} + v_{2}^{2} x_{1}^{2}}{v_{1}^{2} + v_{2}^{2}}}$

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2. Each of the two strings of length 51.6cm and 49.1cm are tensioned seperately by 20N force. Mass per unit of both the strings is same and equal to 1 g/m. When both the strings vibrate simultaneously, the number of beats is
a) 7
b) 8
c) 3
d) 5

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1. Four simple harmonic motions : x₁ = 8sinωt ; x₂ = 6 sin &omegat + π/2) ; x₃ = 4 sin (ωt+π) and x₄ = 2 sin(ωt+3π/2) are superimposed on each other. The resulting amplitude and its phase difference with x₁ are respectively
a) 20 tan^-1(1/2)
b) 4√2 , π/2
c) 20 tan^-1(2)
d) 4√2 . π/4

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2. A train is moving with a constant speed along a circular track. The engine of the train emits a sound of frequency f. the frequency heard by the guard at the rear end of the train
a) is less than f
b) is greater than f
c) is equal to f
d) may be greater than , less than or equal to f depending on factors like speed of train and radius of circular track

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1. A vector perpendicular to $\hat{i} + \hat{j} + \hat{k}$ is
a) $\hat{i} - \hat{j} + \hat{k}$
b) $\hat{i} - \hat{j} - \hat{k}$
c) $-\hat{i} - \hat{j} - \hat{k}$
d) $3\hat{i} + 2\hat{j} - 5\hat{k}$

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2. The resultant of two vectors $\vec{A}$ and $\vec{B}$ is perpendicular to the vector $\vec{A}$ and its magnitude is equal to half of the magnitude of vector $\vec{B}$. The angle between $\vec{A}$ and $\vec{B}$ is

a) 120⁰
b) 150⁰
c) 135⁰
d) None of these

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1. The first ball of mass m moving with a velocity u collides head on with the second ball of mass m at rest. If the coefficient of restitution is e, then the ratio of the velocities of the first and the second ball after the collision is
a) $\frac{1-e}{1+e}$
b) $\frac{1+e}{1-e}$
c) $\frac{1+e}{2}$
d) $\frac{1-e}{2}$

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2. A ball is dropped from a height of 45 m from the ground. The coefficient of restitution between the ball and the ground is 2/3. What is the distance travelled by the ball in 4th second of its motion. Assume negligible time is spent in rebounding . Let g = 10 m s².
a) 5 m
b) 20 m
c) 15 m
d) 10 m

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1. A disc of radius 0.2 m is rolling with slipping on a flat horizontal surface, as shown in Figure. The instantaneous centre of rotation is (the lowest contact point O and centre of disc is C)

a) zero
b) 0.1 m above O on line OC
c) 0.2 m below O on line OC
d) 0.2 m above O on line OC

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2. A disc of radius R rolls on a horizontal ground with linear acceleration a nad angular acceleration α as shown in Figure. The magnitude of acceleration of point P as shown in the figure at an instant when its linear velocity is v and angular velocity is ω will be

a) $\sqrt{(a+r\alpha)^{2}+(r\omega ^{2})^{2}}$
b) $\frac{ar}{R}$
c) $\sqrt{r^{2}\alpha ^{2} + r^{^{2}}\omega^{4}}$
d) rα

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1. A hollow cylindrical container floats in water with half its length immersed. A liquid of specific gravity σ is slowly poured into the container until the levels of the liquid inside the container and of water outside are the same. It is observed that the container is submerged to two-thirds its length. Then the value of σ is
a) $\frac{1}{2}$
b) $\frac{1}{3}$
c) $\frac{1}{4}$
d) $\frac{1}{3}$

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2. In a horizontal pipeline of uniform cross section the pressure falls by 8 N/m² between two points separated by 1 km. If oil of density 800 kg/m³ flows through the pipe, find the change in KE per kg of oil at these points.
a) 10^-2 J/kg
b) 10^-3 J/kg
c) 10^-4 J/kg
d) 10^-1 J/kg

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