1. If the error in the measurement of radius of a sphere is 2%, then the error in the determination of volume of the sphere will be
a) 4%
b) 6%
c) 8%
d) 2%

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2. The ratio of the dimensions of Planks constant and that of the moment of inertia is the dimension of
a) frequency
b) velocity
c) angular momentum
d) time

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1. A man throws balls with the same speed vertically upwards one after the other at an interval of 2s. What should be the speed of the throw so that more than two balls are in the sky at any time> (Take g = 9.8 m/s²)
a) any speed less than 19.6 m/s
b) only with speed 19.6 m/s
c) more than 19.6 m/s
d) at least 9.8 m/s

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2. A particle moves along a straight line such that its displacement at any time t is given by s = 3t³+7t²+14t+5. The acceleration of the particle at t = 1 s is
a) 18 m/s²
b) 32 m/s²
c) 29m/s²
d) 24m/s²

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1. The maximum range of a gun of horizontal terrain is 16km. If g = 10 ms^-2, then muzzle velocity of a shell must be
a) 160 ms^-1
b) 200 √2 ms^-1
c) 400 ms^-1
d) 800 ms^-1

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2. A car runs at a constant speed on a circular track of radius 100m, taking 62.8s for every circular lap. The average velocity and average speed for each circular lap respectively is
a) 0,0
b) 0,10 m/s
c) 10m/s , 10m/s
d) 10m/s, 0

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1. A 0.5 kg ball moving with a speed of 12m/s strikes a hard wall at an angle of 30⁰ with the wall. It is reflected with the same speed and at the same angle. If the ball is in contact with the wall for 0.25s, the average force acting on the wall is

a) 48N
b) 24N
c) 12N
d) 96N

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2. Consider a car moving along a straight horizontal road with a speed of 72 km/h. If the coefficient of static friction between the tyres and the road is 0.5, the shortest distance in which the car can be stopped is
(Take g = 10 m/s²)
a) 30m
b) 40m
c) 72m
d) 20m

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1. A block of mass M is attached to the lower end of a vertical spring. The spring is hung from a ceiling and has force constant value k. The mass is released from rest with the spring initially unstretched . The maximum extension produced in the length of the spring will be
a) Mg/k
b) 2 Mg/k
c) 4 Mg/k
d) Mg/2k

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2. How much water a pump of 2kW can raise in one minute to a height of 10m?
[Take g = 10m/s²]
a) 1000 L
b) 1200 L
c) 100 L
d) 2000 L

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1. A thin circular ring of mass M and radius r is rotating about its axis with a constant angular velocity ω
. Four objects each of mass m, are kept gently to the opposite ends of two perpendicular diameters of the ring. The angular velocity of the ring will be
a) $\frac{(M+4m)\omega}{M}$
b) $\frac{m_{1}}{m_{2}}d$
c) d
d) $\frac{m_{2}}{m_{1}}d$

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2. A particle of mass M is revolving along a circle of radius R and another particle of mass m is revolving in a circle of radius r. If time periods of both particles are same, then the ratio of their angular velocities is
a) 1
b) $\frac{R}{r}$
c) $\frac{r}{R}$
d) $\sqrt{\frac{R}{r}}$

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1. A seconds pendulum is mounted in a rocket. Its period of oscillation decreases when the rocket
a) comes down with uniform acceleration
b) moves round the earth in a geostationary orbit
c) moves up with a uniform velocity
d) moves up with uniform acceleration

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2. The satellite of mass m is orbiting around the earth in a circular orbit with a velocity v. What will be its total energy?
a) $\frac{3}{4}mv^{2}$
b) $\frac{1}{2}mv^{2}$
c) mv²
d) $-\left ( \frac{1}{2} \right )mv^{2}$

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1. For a black body at temperature 727⁰C , its radiating power is 60 W and temperature of surrounding is 2270C . If the temperature of the black body is changed to 1227⁰C, then its radiating power will be 
a) 120 W
b) 240 W
c) 304 W
d) 320 W

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2. A beaker full of hot water is kept in a room. It it cools from 80⁰C and 75⁰C in t₁, minutes , from 75⁰C to 70⁰C, t₂ minutes and from 70⁰C to 65⁰C to in t₃ minutes then
a) t₁ = t₂ = t₃
b) t₁ < t₂  = t₃
c) t₁ < t₂ < t₃
d) t₁ > t₂ > t₃

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1. A particle moving along the X-axis executes simple harmonic motion, then the force acting on it is given by
a) -Akx
b) A cos Kx
c) A exp(-Kx)
d) Akx

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2. A body executes SHM with an amplitude a. At what displacements from the mean position is the potential energy of the body is one-fourth of its total energy?
a) ​$\frac{a}{4}$
b) ​$\frac{a}{2}$
c) ​$\frac{3a}{4}$
d) Some other fraction of a

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1. Which of the following equation represents a wave?
a) y = a sinωt
b) y = a cos kx
c) y = a sin(ωt - bx+c)
d) y = a sin(ωt - kx)

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2. Two sources are at a finite distance apart. They emit sounds of wavelength λ. An observer situated between them on line joining approaches one source with speed u. Then the number of beats heard/s by observer will be
a) $\frac{2u}{\lambda}$
b) $\frac{u}{\lambda}$
c) $\frac{u}{2\lambda}$
d) $\frac{u}{\lambda}$

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1. A charge q is placed at the corner of a cube of side a. The electric flux through the cube is
a) $\frac{q}{\varepsilon_{0}}$
b) $\frac{q}{3\varepsilon_{0}}$
c) $\frac{q}{6\varepsilon_{0}}$
d) $\frac{q}{8\varepsilon_{0}}$

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2. A charge q is placed at the centre of the line joining two exactly equal positive charges Q. The system of three charges will be in equilibrium , if q is equal to
a) $\frac{-Q}{4}$
b) +Q
c) -Q
d) $\frac{Q}{2}$

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1. You are given several identical resistances each of value R = 10Ω and each capable of carrying a maximum current of one ampere. It is required to make a suitable combination of these resistances of 5Ω which can carry a current of 4A. The minimum number of resistances of the type R that will required for this job is
a) 4
b) 10
c) 8
d) 20

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2. There are  three copper wires of length and cross - sessional area (L,A), (2L, (1/2)A), ((1/2)L,2A) . In which case is the resistance minimum?
a) It is the same in all three cases
b) Wire of cross-sessional area 2A
c) Wire of cross-sessional area A
d) Wire of cross-sessional area $\frac{1}{2}A$

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1. Direct current is passed through a copper sulphate solution using platinum electrodes. The elements liberated at the electrodes are
a) copper at anode and sulphur at cathode
b) sulphur at anode and copper at cathode
c) oxygen at anode and copper at cathode
d) copper at anode and oxygen at cathode

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2. A current of 2A, passing through a conductor produces 80J of heat in 10s. The resistance of the conductor in ohm is
a) 0.5
b) 2
c) 4
d) 20

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1. Tesla is the unit of
a) magnetic flux
b) magnetic field
c) magnetic induction
d) magnetic moment

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2. A charged particle of charge q and mass m enters perpendicularly in a magnetic field $\vec{B}$. Kinetic energy of the particle is E, then frequency of rotation is
a) $\frac{qB}{m\pi}$
b) $\frac{qB}{2\pi m}$
c) $\frac{qBE}{2\pi m}$
d) $\frac{qB}{2\pi E}$

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1. Due to the earths magnetic field , charged cosmic ray particles
a) can never rach the poles
b) can never reach the equator
c) require less kinetic energy to reach the equator than the poles
d) require greater kinetic energy to reach the equator, than the poles

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2. If a diamagnetic substance is brought near the north or the south pole of a bar magnet, it is
a) repelled by the both poles
b) repelled by the north pole and attracted by the south pole
c) attracted by the north pole and repelled by the south pole
d) attracted by both the poles

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1. If N is the number of turns in a coil, the value of self-inductance varies as
a) N⁰
b) N
c) N²
d) N^-2

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2. A conducting circular loop is placed in a uniform magnetic field 0.04 T with its plane perpendicular to the magnetic field . The radius of the loop starts shrinking at 2 mms^-1. The induced emf in the loop when the radius is 2 cm is
a) 3.2π μ V
b) 4.8 π μ V
c) 0.8 π μ V
d) 1.6 π μ V

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1. For a series LCR-circuit, the power loss at resonance is
a) $\frac{V^{2}}{\omega L - \frac{1}{\omega C}}$
b) i²Cω
c) i²R
d) $\frac{V^{2}}{\omega C}$

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2. Ozone layer blocks the radiation of wave length
a) less than 3 x 10^-7 m
b) equal to 3 x 10^-7 m
c) more than 3 x 10^-7 m
d) All of the above

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1. Pick out the longest wavelength from the following types of radiations.
a) Blue light
b) Gamma rays
c) X-rays
d) Red light

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2. A microscope is focussed on a mark on a piece of paper  and then a slab of glass of thickness 3 cm and refractive index 1.5 is placed over the mark. How should the microscope be moved to get the mark in focus again?
a) 1 cm upward
b) 4.5 cm downward
c) 1 cm downward
d) 2 cm upward

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1. Which of the following is not the property of cathode rays?
a) It produces heating effect
b) It does not deflect in electric field
c) Its casts shadow
d) It produces fluorescence

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2. A photosensitive metallic surface has work function, h v₀. If photons of energy 2hv₀ fall on this surface, the electrons come out with a maximum velocity of 4 x 10⁶ m/s. When the photon energy is increased to 5hv₀, then maximum velocity of photoelectrons will be
a) 2 x 10⁶ m/s
b) 2 x 10⁷ m/s
c) 8 x 10⁵ m/s
d) 8 x 10⁶ m/s

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1. In the Bohrs model of a hyydrogen atom , the centripetal force is furnished by the coulomb attraction between the proton and the electron. If a₀ is the radius of the ground state orbit, m is the mass and e is the charge on the electron,  ε₀ is the vacuum permittivity , the speed of the electron is
a) zero
b) $\frac{e}{\sqrt{\varepsilon_{0}a_{0} m}}$
c) $\frac{e}{\sqrt{4\pi \varepsilon_{0}a_{o}m}}$
d) $\frac{\sqrt{4\pi \varepsilon_{0}a_{o}m}}{e}$

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2. The energy of ground electronic state of hydrogen atom is -13.6 eV. The energy of the first excited state will be
a) -54.4 eV
b) -27.2eV
c) -6.8 eV
d) -3.4 eV

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1. If in a nuclear fusion process, the mass of the fusing nuclei be m₁ and m₂ and the mass of the resultant nucleus be m₃, then
a) m₃ = m₁ + m₂
b) m₃ = |m₁ - m₂ |
c) m₃ < (m₁+m₁)
d) m₃ > (m₁+m₂)

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2. A nuclear reaction given by
_ZX^A → _Z+1Y^A + _-1e⁰ + $\bar{v}$  represents
a) fusion of protons during synthesis of heavier elements
b) fission reaction
c) β-decay
d) γ-decay

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1. The current gain for a transistor working as common base amplifier is 0.96. If the emitter current is 7.2mA, then the base current is
a) 0.29mA
b) 0.35mA
c) 0.39mA
d) 0.43mA

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2. A transistor is operated in common - emitter configuration at V_c = 2VOlt such that a change in the base current from 100 μA to 200 μA produces a change in the collector current from 5 mA to 10mA. The current gain is
a) 75
b) 100
c) 150
d) 50

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