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QUESTION: 1

For vectors the vector product

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QUESTION: 2

A particle of mass m carrying charge q is moving in a circle in a magnetic field B. According to the Bohr’s model, the energy of the particle in the n^{th} level is _____.

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QUESTION: 3

A conducting slab of copper PQRS is kept on the xy plane in a uniform magnetic field along xaxis as indicated in the figure. A steady current I flows through the cross- section of the slab along the y- axis. The direction of the electric field inside the slab, arising due to the applied magnetic field is along the

Solution:

QUESTION: 4

A collimated beam of light of diameter 1 mm is propagating along the x- axis. The beam is to be expanded 10 mm using a combination of two convex lenses. A lens of focal length of 50 mm and another lens with focal length F are to be kept at a distance d between them. The values of F and d respectively, are

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QUESTION: 5

Octal equivalent of decimal number 478_{10} is

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QUESTION: 6

A spherical ball of ice has radius R_{0} and is rotating with an angular speed w about an axis passing through its centre. At time t = 0, it starts acquiring mass because the moisture around it starts to freeze on it uniformly. As a result its radius increases as R(t) = R_{0} + αt, where a is a constant.

The curve which best describes its angular speed with time is

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QUESTION: 7

In a photoelectric effect experiment, ultraviolet light of wavelength 320 nm falls on the photocathode with work function of 2.1 eV. The stopping potential should be close to

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QUESTION: 8

In 1- dimension, an ensemble of N classical particles has energy of the form The average internal energy of the system at temperature T is ___ .

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QUESTION: 9

In an ideal operational amplifier depicted below, the potential at node A is

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QUESTION: 10

To operate a npn transistor in active region, its emitter- base and collector- base junction respectively, should be

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QUESTION: 11

The value of

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QUESTION: 12

In a parallel plate capacitor the distance between the plates is 10 cm. Two dielectric slabs of thick- ness 5 cm each and dielectric constants K_{1}= 2 and K_{2} = 4 respectively, are inserted between the plates. A potential of 100 V is applied across the capacitor as shown in the figure. The value of the net bound surface charge density at the interface of the two dielectrics is

Solution:

QUESTION: 13

The electric fields of two light sources with nearby frequencies ω_{1} and ω_{2}, and wave vectors k_{1} and k_{2}, are expressed as respectively. The interference pattern on the screen is photographed at t = t_{0}; denote For this pattern

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QUESTION: 14

A solid metallic cube of heat capacity S is at temperature 300 K. It is brought in contact with a reservoir at 600 K. If the heat transfer takes place only between the reservoir and the cube, the entropy change of the reservoir after reaching the thermal equilibrium is ____

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QUESTION: 15

If the surface integral of the field over the closed surface of an arbitrary unit sphere is to be zero, then the relationship between α, β and γ is

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QUESTION: 16

The moment of inertia of a disc about one of its diameters is IM. The mass per unit area of the disc is proportional to the distance from its centre. If the radius of the disc is R and its mass is M, the value of I_{M} is _______

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QUESTION: 17

The rigid uniform horizontal wire PQ of mass M, pivoted at P, carries a constant current I. It rotates with a constant angular speed in a uniform vertical magnetic field B. If the current were switched off, the angular acceleration of the wire, in terms of B, M and I would be

Solution:

QUESTION: 18

Two points N and S are located in the northern and southern hemisphere, respectively, on the same longitude. Projectiles P and Q are fired from N and S, respectively, towards each other.Which of the following option is correct for the projectiles as they approach the equator ?

Solution:

QUESTION: 19

Two particles A and B of mass m and one particle C of mass are kept on the x axis in thr order ABC, Particle A is given a velocity vi . Consequently there are two collisions, both of which are completely inelastic. If the net energy loss because of these collisions is 7/8 of the initial energy,, the value of M is (ignore frictional losses)

Solution:

QUESTION: 20

The line integral of a vector field where r^{2} = x^{2} + y^{2}, is taken around a square (see figure) of side unit length and centered at (x0, y0) with the value of the integral is L, then

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QUESTION: 21

Diamond lattice can be considered as a combination of two f_{cc} lattices displaced along the body diagonal by one quarter of its length. There are eight atoms per unit cell. The packing fraction of the diamond structure is

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QUESTION: 22

Thermal neutrons (energy = 300 k_{B} = 0.025 eV) are sometimes used for structural determination of materials. The typical lattice spacing of a material for which these can be used is

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QUESTION: 23

What is the maximum height above the dashed line attained by the water stream coming out at B from a thin tube of the water tank assembly shown in the figure? Assume h = 10 m, L = 2m, and θ = 30^{o}.

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QUESTION: 24

A steady current in a straight conducting wire produces a surface charge on it. Let E_{out} and E_{in} be the magnitudes of the electric fields just outside and just inside the wire, respectively. W hich of the following statements is true for these fields ?

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QUESTION: 25

A small charged spherical shell of radius 0.01 m is at a potential of 30 V. The electrostatic energy of the shell is

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QUESTION: 26

At an instant shown, three point masses m, 2m and 3m rest on a horizontal surface, and are at the vertices of an equilateral triangle of unit side length. Assuming that G is the gravitational constant, the magnitude and direction of the torque on the mass 3m, about the point O, at that instant is

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QUESTION: 27

A sine wave of 5V amplitude is applied at the input of the circuit shown in the figure. which of the following waveforms represents the output most closely?

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QUESTION: 28

1011 binary have been applied at X_{3} X_{2} X_{1} X_{0} input in the shown logic circuit made of XOR gates. The binary output Y_{3} Y_{2} Y_{1} Y_{0} of the circuit will be

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QUESTION: 29

A ring of radius R carries a linear charge density l. It is rotating with angular speed w. The magnetic field at its center is

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QUESTION: 30

A stationary source (see figure below) emits sound waves of frequency f towards a wall. If an observer moving with speed u in a direction perpendicular to the wall, measures a frequency f’ = 9/8 f at the instant shown, then u is related to the speed of sound V_{s} as

Solution:

QUESTION: 31

A real gas has specific volume v at temperature T. Its coefficient of volume expansion and isothermal compressibility are a and kT, respectively. Its molar specific heat at constant pressure C_{p} and molar specific heat at constant volume C_{v} are related as

Solution:

QUESTION: 32

Two frames, O and O’, are in relative motion as shown. O’ is moving with speed c/2, where c is the speed of light. In frame O, two separate events occur at (x_{1}, t_{1}) and (x_{2}, t_{2}). In frame O’, these events occur simultaneously. The value of (x_{2} - x_{1})(t_{2} - t_{1}) is

Solution:

QUESTION: 33

White light is incident on a grating G_{1} with groove density 600 lines/mm and width 50 mm. A small portion of the diffracted light is incident on another grating G_{2} with groove density 1800 lines/mm and width 15 mm. The resolving power of the combined system is

Solution:

QUESTION: 34

Four particles of mass m each are inside a two dimensional square box of side L. If each state obtained from the solution of the Schrodinger equation is occupied by only one particle, the minimum energy of the system in units of h^{2}/mL^{2} is

Solution:

QUESTION: 35

At atmospheric pressure (= 105 Pa), aluminium melts at 550 K. As it melts, its density decreases from 3 x 10^{3} kg/m^{3} to 2.9 x 10^{3} kg/m^{3}. Latent heat of fusion of aluminium is 24 x 10^{3} J/kg. The melting point of aluminium at a pressure of 10^{7} Pa is closest to

Solution:

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