1. The period of the function cos cos is

6n.

8n.

2n.

24n.

2. The eigenvalues of the matrix A
[cos 8 -sin 8
sin 8 cos are

e^±i8.

e^±2i8.

e^±3i8 .

e^±i8/2.

3. The value of sin i is

e.

1/2

1/2i

i/2

4. The value of the integral to 00) is equal to





O.

oo.

5. A rocket of proper length 40 m is observed to be 32 m long as it passes an observer. The rocket's speed relative to the observer is

0.2 c.

0.4 c.

0.6 c.

0.8 c.

6. A particle is moved from a point to by a constant force given by 6i -2j 3k, where k are orthogonal unit vectors. The work done by this force is

5 units.

0 units.

4 units.

9 units.

7. A particle moves in a plane elliptical orbit described by the positive vector r i2b sin wt jb cos wt. The angle between the velocity and acceleration at time t n/2w is

30° .

45°.

60° .

90°.

8. A spherically symmetric mass distribution of radius R is described by the density:

po/2nr r
r R

The gravitational potential due to this mass distribution at a distance r from the centre of the spherical mass is given by

GPoR^2/2r.

GpoR^2/r.

nGpo R^2/r.

0.

9. Waves in deep water travel with a phase velocity given by vp^2 where g is the acceleration due to gravity and k 2n/A is the wave number. The group velocity of the waves is

1/2 vp

vp.

vp^2.

vp/3

10. The intensities of two sound waves are 0.4 W1m2 and 10W1m2 respectively. One of 1 them is louder than the other (in decibels by

10 db

1.4 db

140 dB

14 db

11. The lattice specific heat of a metal at low temperature is proportional to

T.

T^2.

T^3.

T^4.

12. Which of the following equations is not true ill general?

dU dT dV

Cp -Cv

dU CvdT

Cv

13. For a gas at constant temperature and pressure, equilibrium corresponds to

maximum Gibbs free energy.

maximum Helmholtz energy.

maximum enthalpy.

maximum internal energy.

14. In the Michelson interferometer, the bands in the interference pattern can be shifted by displacing the mirror. If the wavelength of light used in the experiment is 546 nm, for shifting 100 bands in the interference pattern, the mirror is to be displaced by a distance of

54.6/Mm.

27.3 Mm.

546 nm.

273 nm.

15. The refractive index of diamond is 2.47 and that of window glass is 1.51. Which of the following statements is then correct?

Light travels faster in window glass by 7.72x 10^7 ms-1 .

Light travels faster in diamond by 7.72xl0^7 ms^-1.

Light travels with same speed in window glass and diamond.

Light does not travel in diamond.

16. Dispersion of electromagnetic waves

results from the fact that waves of different frequencies travel at different speeds in a medium.

refers to the phenomenon wherein a ray travels from one medium to another.

refers to the scattering of waves by particles dispersed in a medium.

accounts for the fact that the sky is blue.

17. Using Abbe's diffraction limit, the limit of resolution of a microscope d is related to the numerical aperture of the objective lens as

NA/A.

A/nA.

d A/2NA.

2NA /A.

18. The electric potential V in a region is given by V 2x 3y -z. The electric field strength is then given by

2i 3j k.

2i 3j -k.

-2i -3j k.

-2i-3j k.

19. A point charge of 6.0 nC is located at the centre of a cube, each side of which is 2 m long. The electric flux passing through each face of the cube is equal to

113 Nm^2/C.

1.13 Nm^2/C.

11.3 Nm^2/C.

0.113 Nm^2/C.

20. Two hollow charged spheres of radii R1 and R2 have equal surface charge density. If the potentials of the charged spheres on their surfaces are V1 and V2, respectively, then V1/V2 is equal to

R2/R1







21. In a uniform magnetic field, the net magnetic force on a current loop is

zero.

infinite.

attractive and finite.

repulsive and finite.

22. Which of the following statements is correct?

BJT is a voltage controlled device and FET is a current controlled device.

BJT is a current controlled device and FET is a voltage controlled device.

Both BJT and FET are voltage controlled devices.

Both BJT and FET are current controlled devices.

23. In a series LCR circuit, the voltage across the resistor leads the applied voltage by 45°. Then which of the following statements is correct?

Capacitive reactance is equal to the inductive reactance.

Capacitive reactance is greater than the inductive reactance.

Capacitive reactance is less than the inductive reactance.

The total reactance is greater than the value of pure resistance.

24. In quantum mechanics, the infinite square well potential can be considered to represent a system with

all unbound states.

all bound states.

both bound and unbound states.

neither bound nor unbound states.

25. If two operators commute, then

their eigenvalues cannot be measured.

they have the same eigenvalue.

they can have the same eigenfunction.

they are not quantum mechanical operators.

26. The value of the integral dx/sqrt(-ln is

n.

0.

sqrt(n).

oo.

27. For what value of will the following matrix be orthogonal?

1 0 0
0 a
0 a a

sqrt2

1

1/sqrt2

-sqrt2

28. The eigenvectors of the matrix A

2

are

a1 1 a2
0 0

a1 1 a2 1
1

a1= 2 a2 0
0 2

a1 1 a2 0
0 1

29. If V V x A and given that V then the vector A will be given by

-yj k.

i j -k.

5i j -2k.

-yi j 5k.

30. The value of the surface integral s xA) .is, where iy jZ k and S is the 2 surface defined by the paraboloid z with z is given by

-n.

n.

1.

-1.

31. For A 0 and .A E what are the eigenfunctions of the following differential equation y" +Ay for the boundary conditions O

C1 cos 2n-1/2

C2 sin 2n-1/2

C1 cos(nx) +C2 sin(nx)

C1 cos(2n +C2 sin(2n

32. The Fourier series of the function
t 0

in the interval t n/W can be written as

4/n E sin(nwt)/n

4/n E cos(nwt)/n

4/n E sin(nwt)/n 4/n E cos(nwt)/n.

4/n E sin(nwt)/n

33. Consider a capillary tube of radius r introduced in a liquid of density p and surface tension T. The height h of the liquid column in the capillary tube is given by

h 2T/rpg

h T/rpg

h T/2rpg

h 4T/rpg

34. How much volume of water will escape per minute from an open-top tank through an opening that is 3.0 em in diameter and 5.0 m below the water level in the tank?

<img src='./qimages/16054-34.jpg'>

4.2 m^3/min.

0.42 m^3/min.

42.0 m^3/min.

0.042 m^3/min.

35. A block of mass m tied to a string of length l hangs from the ceiling of a room such that the mass moves in a circle of radius r and the string makes an angle e with the vertical. The period of circular motion of the mass is given by

2n sqrt(l/g)

2n sqrt(l cos

2n sqrt(l/g cos

2n sqrt(l sin

36. A particle at rest is attracted towards the centre of force according to the relation F . The time required for the particle to reach the centre of force from a distance d is given by



d^2/2k

2d^2/k

oo.

37. In plane polar coordinates, which of the following relations are true? df de AA

dr/d8 d8/d8

dr/d8 d8/d8 r

dr/d8 d8/d8

dr/d8 d8/d8 8

38. A particle of mass m moves in an orbit under the influence of an attractive Coulomb force, The angular momentum of the particle is given by the constant £. The areal velocity of the particle is given by £

L/2m

2L/m

L/4m

2L/3m

39. A uniform solid sphere of mass M and radius R is fixed at a distance h above a thin infinite sheet of mass density p. With what force does the sphere attract the sheet?

2npGMR/h

4npGMR/h

2npGM

4npGM

40. Energy eigenvalues of a two-state system, which is in thermal equilibrium with a heat bath at temperature T are given by E1 and E2 (such that E2 E1 0). What is the average energy of the system for T

E2-E1/2

E2

E1+E2/2

E1

41. Consider a gas which obeys the Maxwell-Boltzman velocity distribution law. The most probable speed of a gas molecule is then given by

sqrt(ksT/m)

sqrt(ksT/2m)

sqrt(ksT/3m)

sqrt(2ksT/m)

42. A possible ideal-gas cycle operates as follows:

from an initial state V1) the gas is cooled at constant pressure to V2)

the gas is heated at constant volume to (P2 V2)

the gas expands adiabatically back to V1

The thermal efficiency of the engine is given by









where y Cp/Cv

43. An isolated system has N non-interacting particles. If each particle can exist in three states, the entropy of the system according to Boltzmann's prescription is given by

NkS ln 2.

NkS ln 3.

kS ln(3N).

3kS ln(N).

44. Two identical sound sources A and B are kept 1 m apart under water and emit sound waves of frequency 3500 Hz and are in phase with each other. A microphone is placed on a line parallel to AB at a distance of 1 km from AB. At what distance should the microphone be positioned to capture the maximum sound intensity?

466 m and 1664 m

466 m

1664 m

1065 m

(Speed of sound in water 1500

45. Consider the superposition of two waves given by y1 A sin(kx and y2 3A sin(kx wt). The amplitudes of the resultant standing wave and traveling wave, respectively, are

4A, 0.

A,3A

0,4A

2A,2A

46. A whistle of frequency 540 Hz rotates in a horizontal circle of radius 2 m at an angular speed of 15.0 rad/s. The maximum and minimum frequencies heard by a listener, standing a long distance away at rest from the centre of the circle are respectively

594 Hz and 495 Hz.

540 Hz and 540 Hz.

565.7 Hz and 516.5 Hz.

500 Hz and 450 Hz.

(Speed of sound 330

47. An open organ pipe is closed suddenly. As a result, the frequency of the second overtone of the closed pipe becomes higher by 100 vibrations/sec than that of the first overtone of the original pipe. The fundamental frequency of the open pipe is

100 Hz.

200 Hz.

250 Hz.

150 Hz.

48. Monochromatic light of wavelength 600 nm is incident on two slits of spacing 0.15 mm and the resulting intensity pattern is observed on a screen 1.5 m away. The location of the first maximum is at

<img src='./qimages/16054-48.jpg'>

6 mm.

12 mm.

3 mm.

1.5 mm.

49. Consider Newton's rings experiment in transmission observed using 589 nm wavelength light. The space between the glass plate and plano-convex lens of radius of curvature 10 m is filled with a liquid. If the radius of the third bright ring is 3.65 lYUll, the refractive index of the liquid is

1.52.

1.01.

1.33.

2.11.

50. Consider a beam of light from a discharge tube falling onto a diffraction grating at normal incidence. If the maxima of spectral lines of wavelength A1 6563 A° and A2 4102 A° coincide in the direction the diffraction grating constant is

5 X m.

5 x m.

5 x m.

1 x m.

51. In photographing the Sun's spectrum, it was found that the yellow spectral line 5890 in the spectra obtained from the left and right edges of the sun is displaced by 0.08 A°. The linear velocity of rotation of the solar disk is

0.3 x m/s.

3 x 10^8 m/s.

2 m/s.

2 x 10^3 m/s.

52. A beam of light passing through a calcite quarter wave plate and a quartz quarter wave plate placed after it suffers a phase shift. The ratio of the thickness of the two plates in terms of their respective refractive indices is



no/ne.





53. Consider an object placed at a fixed distance D from a screen. Real images are formed on the screen for two positions of a lens, separated by a distance d. The ratio between the sizes of the two images is given by



.





54. A parallel plate capacitor of plate area 0.2 m2 and plate spacing of 1 cm is charged to 1000 V and is then disconnected from the battery. The plates are pulled apart to twice the initial plate spacing. The work required in this process is

17.7 X J.

8.85 X J.

5.9 X J.

4.43 X J.

55. If R is the radius of a thin spherical shell and is the surface charge density of the shell, then the values of the electric field at a distance r from the centre of the shell for r Rand r R are given respectively by

r^2O/EoR^2;0

R^2O/EoR^2;0

EoR^2/Eor^2

R^2O/Eor^2 everywhere.

56. Which of the following statements is true?

An electrostatic field is irrotational.

An electrostatic field is solenoidal.

An electrostatic field has to be both irrotational and solenoidal.

An electrostatic field is neither irrotational nor solenoidal.

57. An electric dipole with P1 zP1 is located at the origin of a Cartesian coordinate system. A second dipole of dipole moment P2 zP2 is located on the axis at a distance r from the origin. What is the force between the two dipoles?

-P1P2/Eor^3

-3P1P2/2nEor^4

-2P1P2/nEor^4

-P1P2/2nEor^2

58. A capacitor consisting of two plane parallel plates separated by a distance d is immersed vertically in a dielectric fluid of dielectric constant K and density p. Let b be the width and a be the length of the plates and x be the height of the fluid in the capacitor. Then the capacitance of the capacitor (in Gaussian units) is

<img src='./qimages/16054-58.jpg'>

a].

b/4nd[(Kx

b/4nd[(Ka

ax].

59. A circular loop of wire of radius R lies in the xy-plane with its centre at the origin. The loop carries a steady current I in the clockwise direction. The magnetic field at any point on the z-axis in the free space is of the form B where k is the unit vector in the z-direction. Then which equation does B satisfy?



Integral dzB(z) MoI

Integral dzB(z) 00

Integral dzB(z) MoI

60. A magnet, initially stationary, is pushed closer to a loop and then stopped. Which of the following graphs closely represent the variation of the current I in the galvanometer detecting the current as a function of time

<img src='./qimages/16054-60.jpg'>

61. Which of the following statements is TRUE?

Electrical forces do no work.

Magnetic forces do no work.

Mechanical forces do no work.

Gravitational forces do no work.

62. A segment of wire is bent into an arc of radius R and it subtends an angle 0 as shown in the figure. Point P is at the centre of the circular segment. The wire carries current I. The magnitude of the magnetic field at P is given by

<img src='./qimages/16054-62.jpg'>

MoI/28R

MoI8/(2n)^2R

MoI8/4nR

MoI8/4nR^2

63. A cylindrical wire of permeability 11 carries a steady current I. If the radius of the wire is what is the value of the magnetic field B inside the wire?

<img src='./qimages/16054-63.jpg'>

MoIEo/4nr

MoIEo/r

MoIEo/2nr

MoIEo/2r

64. Consider an L circuit with L 30 mH, R 10 ohm and V 12 V. What is the current at t 0.001

0.82 A

0.12 A

0.34 A

0.40 A

65. Consider the circuit shown below. What is current I that is flowing through the 10 kD resistor?

<img src='./qimages/16054-65.jpg'>

1.2 mA

1.0 mA

0.4 mA

0.24 mA

66. The Thevenin's voltage across the open terminals A and B in the circuit shown is 6 V. The Thevenin's resistance across the open terminals A and B is

<img src='./qimages/16054-66.jpg'>

20 k.ohm

10 k.ohm

90 k.ohm

18.75 k.ohm

67. Diodes D1 and D2 shown in the circuit are practical silicon diodes. The voltage drop across the diode D2 and the power dissipated by this diode are, respectively,

<img src='./qimages/16054-67.jpg'>

VD2 0.72 V and PD2 0 W.

VD2 5.0 V and PD2 0W.

VD2 0.7 V and PD2 0.7 mW.

VD2 5.0 V and PD2 5W.

68. The minimum value of base current required to saturate the transistor shown in the figure below is

<img src='./qimages/16054-68.jpg'>

0.2 mA.

10 mA

1.2 mA

0.12 mA

69. Commutator of two Hermitian operators is always

Hermitian.

Anti-Hermitian.

Unitary.

Anti-Unitary.

70. A charged harmonic oscillator of mass charge e and frequency w is placed in an electric field E. The ground state energy of the oscillator changes due to the electric field by an amount

e^2E^2/4mw^2

e^2E^2/2mw^2

e^2E^2/3mw^2



71. The uncertainty product for the ground state of a simple harmonic oscillator is

equal to h.

equal to h/2.

greater than h/2.

less than h/2.

72. Which of the following statements is wrong?

The eigenfunctions of a Hermitian operator belonging to different eigenvalues are orthogonal.

The eigenfunctions of a Hermitian operator form a complete set of states.

The Hamiltonian of a simple harmonic oscillator is Hermitian.

The eigenvalues of a Hermitian operator are always positive integers.

73. A particle moves in a one-dimensional box of length 2 nm. It is given that the energy difference between the second and third excited states is E. The length of the box is now doubled. Then which of the following statements is true?

E increases by 4 times.

E increases by 16 times.

E decreases by 4 times.

E decreases by 8 times.

74. The energy radiated by a hydrogen atom as a result of a trasition from n 2 to n 1 state is E. If the magnitude of the charges of the proton and electron are doubled, the energy radiated a result of the same transition will be

(a)2E.

(b)4E.

(c)8E.

(d)16E.

75. Crystals exhibit Bragg's diffraction of visible light if the lattice constant of the crystals is of the order of

1 nm.

50 nm.

250 nm.

500 nm.