1. The velocity v of a particle at time is t given by v = $at + \frac{b}{t+c}$ , where, a ,b and c are constants. The dimensions of a,b and c are respectively
a) [LT^-2, [L] and [T]
b) [L²], [T] and [LT²]
c) [LT²,[LT] and [L]
d) [L], [LT] and [T²]

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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 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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2. A car is moving along a straight road with a uniform acceleration . It passes through two points P and Q seperated by a distance with velocity 30km/h and 40km/h respectively. The velocity of the car midway between P and Q is
a) 33.3 km/h
b) 20√km/h
c) 25√2 km/h
d) 0.35 km/h

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1. The vector sum of two forces is perpendicular to their vector differences , In that case, the forces
a) are not equal to each other in magnitude
b) cannot be predicted
c) are equal to each other
d) are equal to each other in magnitude

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2. If $|\vec{A} \times \vec{B}| = \sqrt{3}\vec{A}.\vec{B}$ , then the value of $|\vec{A} + \vec{B}|$ is
a) (A² + B² + AB)^1/2
b) $\left ( A^{2} + B^{2} + AB \right )^{1/2}$
c) A+B
d) (A²+B²+√3AB)^1/2

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1. A 10N force is applied on a body produces an acceleration of 1m/s². The mass of the body is
a) 5 kg
b) 10 kg
c) 15 kg
d) 20 kg

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2. An object of mass 3 kg is at rest. If a force $\vec{F} = (6t^{2}\hat{i} + 4t\hat{j})N$ is applied on the object, then the velocity of the object at t = 3s is
a) $18\hat{i} + 3\hat{j}$
b) $18\hat{i} + 6\hat{j}$
c) $3\hat{i} + 18\hat{j}$
d) $18\hat{i} + 4\hat{j}$

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1. A bomb of mass 30 kg at rest explodes into two pieces of masses 18kg and 12kg. The velocity of 18kg mass is 6ms^-1 . The kinetic energy of the other mass is
a) 256J
b) 486J
c) 524J
d) 324J

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2. A child is swinging a awing . Minimum and maximum heights of swing from earths surface  are 0.75 m and 2m respectively. The maximum velocity of this swing is
a) 5 m/s
b) 10 m/s
c) 15 m/s
d) 20 m/s

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1. At any instant , a rolling body may be considered to be in pure rotation about an axis through the point of contact. This axis is translating forward with speed
a) equal to centre of mass
b) zero
c) twice of centre of mass
d) Data is insufficient

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2. A thin uniforn circular ring is rolling down an inclined plane of inclination 30⁰ without slipping . Its linear acceleration along the inclined plane will be
a) ​$\frac{g}{2}$
b) ​$\frac{g}{3}$
c) ​$\frac{g}{4}$
d) ​$\frac{2g}{3}$

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1. Imagine a new planet having the same density as that of earth but it is 3 times bigger than the earth in size. If the acceleration due to gravity on the surface of earth is g and that on the surface of the new planet is g, then
a) g' = 3g
b) $g' = \frac{g}{9}$
c) g' = 9g
d) g' = 27g

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2. A roller coster is designed such that riders experience weightlessness as they go around the top of a hill whose radius of curvatures is 20m. The speed of the car at the top of the hill is between
a) 14m/s and 15m/s
b) 15m/s and 16m/s
c) 16m/s and 17m/s
d) 13m/s and 14m/s

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1. One mole of an ideal gas at an initial temperature of T K does 6 R joules of work adiabatically. If the ratio of specific heats of this gas at constant pressure and a constant volume is 5/3, the final temperature of gas will be
a) ( t + 2.4)K
b) ( t - 2.4)K
c) ( t + 4)K
d) ( t - 4)K

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2. A black body at 1227⁰C emits radiations with maximum intensity at a wavelength of 5000Å. If the temperature of the body is increased by 1000⁰C, the maximum intensity will be observed at
a) 4000Å
b) 5000Å
c) 6000Å
d) 3000Å

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1. The potential energy of a simple harmonic oscillator when the particle is half way to its end point is
a) $\frac{1}{4}E$
b) $\frac{1}{2}E$
c) $\frac{2}{3}E$
d) $\frac{1}{8}E$

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2. Two springs A and B have force constants K_A and K_B such that k_B = 2k_A . The four ends of the springs are stretched by the same force. If energy stored in spring A is E, then energy stored in spring B is
a) $\frac{E}{2}$
b) 2E
c) E
d) 4E

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1. A transverse wave propagating along x-axis is represented by
y (x,y) = $y \left (x,t \right )$ = $8.0 \ sin \left (0.5 \pi x - 4\pi t - \frac{\pi}{4} \right )$
where x is in metre and t is in second. The speed of the wave is
a) 4π m/s
b) 0.5 π m/s
c) $\frac{\pi}{4} \ m/s$
d) 8 m/s

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2. What is the effect of humidity on sound waves when humidity increases?
a) Speed of sound waves increases
b) Speed of sound waves decreases
c) Speed of sound waves remains same
d) Speed of sound wave becomes zero

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1. Identical charges (-q) are placed at each corners of a cube of side b, then the electrostatic potential energy of charge (+q) placed at the centre of the cube will be
a) $-\frac{4\sqrt{2}q^{2}}{\pi\varepsilon _{0}}$
b) $\frac{8\sqrt{2}q^{2}}{\pi\varepsilon _{0}b}$
c) $-\frac{4q^{2}}{\sqrt{3}\pi\varepsilon _{0}b}$
d) $\frac{8\sqrt{2}q^{2}}{4\pi\varepsilon _{0}b}$

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2. Intensity of an electric field (E) depends on distance r due to a dipole, is related as
a) E ∝ $\frac{1}{r}$
b) E ∝ $\frac{1}{r^{2}}$
c) E ∝ $\frac{1}{r^{3}}$
d) E ∝ $\frac{1}{r^{4}}$

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1. Three resistance , P,Q,R each of 2Ω an unknown resistance S form the four arms of a Wheatstones bridge circuit. When a resistance of 6Ω is connected in parallel to S the bridge gets balanced. What is the value of S?
a) 2Ω
b) 3Ω
c) 6Ω
d) 1Ω

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2. If a negligibly small current is passed through a wire of length 15m and of resistance 5Ω having uniform cross-section of 6 × 10^-7 m² , then coefficient of  resistivity of material is
a) 1 × 10^-7 Ω-m
b) 2 × 10^-7 Ω-m
c) 3 × 10^-7 Ω-m
d) 4 × 10^-7 Ω-m

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1. An electric kettle has two heating coil. When one of the coils is connected to an AC source, the water in the kettle boils in 10min. When the other coil is used the water boils in 40 min . If both the coils are connected in parallel, the time taken by the same quantity of water to boil will be
a) 25 min
b) 15 min
c) 8 min
d) 4 min

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2. Two 220V, 100W bulbs are connected first to series and then in parallel. Each time the combination is connected to a 220V AC supply line. The power drawn by the combination in each case respectively will be
a) 200W , 150W
b) 50W, 200 W
c) 50W, 100W
d) 100W, 50W

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1. A positively charged moving due east enters a region of uniform magnetic field directed vertically upwards. The particle will
a) continue to move due east
b) move in a circular orbit with its speed unchanged
c) move in a circular orbit with its speed
d) gets deflected vertically upwards

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2. At what distance from a long straight wire carrying current of 12A will the magnetic field be equal to 3×10^-5 Wb/m² ?
a) 8 × 10^-2 m
b) 12 × 10^-2 m
c) 18 × 10^-2 m
d) 24 × 10^-2 m

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1. If the magnetic dipole moment of an atom of diamagnetic material, paramagnetic material and ferromagnetic material are denoted by μ_d , μ_p and μ_f respectively , then
a) μ_d ≠ 0 and μ_f ≠ 0
b) μ_d  = 0 and μ_f ≠ 0
c) μ_d  = 0 and μ_P ≠ 0
d) μ_d ≠ 0 and μ_P = 0

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2. A bar magnet having a magnetic moment of 2 × 10⁴ JT^-1 is free to rotate in a horizontal plane. A horizontal magnetic field B = 6 × 10^-4 T exists in the space. The work done in taking the magnet slowly from a direction parallel to the field to a direction 60⁰ from the field is
a) 0.6J
b) 12J
c) 6J
d) 2J

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1. An inductor may store energy in
a) its electric field
b) its coils
c) its magnetic field
d) Both in electric and magnetic field

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2. What is the self-inductance of a coil which produces 5 V when the current changes from 3 A to 2 A in one millisecond?
a) 5000H
b) 5 mH
c) 50 H
d) 5H

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1. Power dissipated in an L-C-R circuit series circuit connected to an AC source of emf ε is
a) $\frac{\varepsilon^{2}R}{\left [R^{2} + \left ( L\omega - \frac{1}{C \omega} \right ) \right ]^{2}}$
b) $\frac{\varepsilon^{2}\sqrt{R^{2} + \left (L\omega - \frac{1}{C\omega} \right )^{2}}}{R}$
c) $\frac{\varepsilon^{2}\left [ R^{2} + \left (L\omega + \frac{1}{C\omega} \right )\right ]}{R}$
d) $\frac{\epsilon^{2}R}{\sqrt{R^{2}+ \left (L\omega - \frac{1}{C\omega} \right )^{2}}}$

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2. The time constant of C-R circuit is
a) $\frac{1}{CR}$
b) $\frac{C}{R}$
c) CR
d) $\frac{R}{C}$

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1. A body is located on a wall. Its image of equal size is to be obtained on a parallel wall with the help of a convex lens. The lens is placed at a distance d ahead of second wall, then the required focal length will be
a) $only \frac{d}{4}$
b) $only \frac{d}{2}$
c) more than  $\frac{d}{4}$  but less than  $\frac{d}{2}$ 
d) less than  $\frac{d}{4}$ 

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2. Electromagnetic radiation of frequency v frequency, velocity v and wavelength  λ , in air, enters a glass slab of refractive index μ ; The frequency, wavelength and velocity of light in the glass slab will be, respectively
a) $\frac{v}{\mu} , \frac{\lambda}{\mu}, v$
b) $v , \lambda, \frac{v}{\mu}$
c) $v, \frac{\lambda}{\mu}, \frac{v}{\mu}$
d) $\frac{v}{\mu}, \frac{\lambda}{\mu}, \frac{v}{\mu}$

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1. Ultraviolet radiation of 6.2 eV falls on an aluminium surface. KE of fastest electron emitted is (work function = 4.2 eV)
a) 3.2 × 10^-21 J
b) 3.2 × 10^-19 J
c) 7 × 10^-25 J
d) 9 × 10^-32 J

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2. The figure shows a plot of photocurrent versus anode potential for a photo sensitive surface for three different radiations . Which one of the following is a correct statement?

a) Curves a and b represent incident radiations of different frequencies and different intensities
b) Curves a and b represent incident radiations of same frequency but of different intensities
c) Curves b and c represent incident radiations of diifferent frequencies and different intensities
d) Curves b and c represent incident radiations of same frequency having same intensity

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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. When hydrogen atom is in its first excited level, its radius is
a) four times, its ground state radius
b) twice, its ground state radius
c) same as its ground state radius
d) half of its ground state radius

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1. The count rate of a Geiger Muller counter for the radiation of a radioactive material of half-life 30 min decreases to 5 s^-1 after 2h. The initial count rate was
a) 20 s^-1 
b) 25 s^-1 
c) 80 s^-1 
d) 625 s^-1 

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2. An element A decays into element C by a two step process
A → B + ₂He⁴
B → C + 2e^-
Then
a) A and C are isotopes
b) A and C are isobars
c) A and B are isotopes
d) A and B are isobars

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1. In bcc structure of lattice constant a, the minimum distance between atoms is
a) $\frac{\sqrt{3}a}{2}$
b) $\sqrt{2}a$
c) $\frac{a}{\sqrt{2}}$
d) $\frac{a}{2}$

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2. Sodium has body centered packing, If the distance between two nearest atoms is 3.7Å, then the lattice parameter is
a) 4.3Å
b) 3.9Å
c) 4.3Å
d) 4.8Å

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