ENTRANCE EXAMINATION, JUNE 2012
QUESTION PAPER BOOKLET
M. Se. (PHYSICS)


1. If two sides of a triangle are represented by i k and 2j then the third side is represented by

A. i-3j+2k

B. i+3j+2k

C.

D.


2. If the electric field due to a point charge Q is expressed as <img src='./qimages/1940-2.jpg'> then the divergence of this field is

<img src='./qimages/1940-2-1.jpg'>

3. Which one of the following statements is true for the matrix given below?

<img src='./qimages/1940-3.jpg'>

A. A is symmetric

B. A is hermitian

C. A is anti-symmetric

D. A is skew-Hermitian

4. Complete solution of the differential equation

<img src='./qimages/1940-4.jpg'>

is given by (where Cl and C2 are arbitrary constants)

<img src='./qimages/1940-4-1.jpg'>


5. A function varies with as shown in the figure. Which of the following represents

<img src='./qimages/1940-5.jpg'>

6. If a rigid body with N particles is constrained to be fixed at a single point, then the number of degrees of freedom is

A. 3

B. 6

C. N

D. 0

7. If a particle of mass m moves under the influence of a force obeying
<img src='./qimages/1940-7.jpg'>

then the rate of change of kinetic energy is

A. positive

B. negative

C. zero

D. can be positive or negative

8. The trajectory of a particle moving under the influence of an attractive, inverse square law force, could be

A. Elliptic

B. Parabolic

C. Hyperbolic

D. Any of the above


9. An astronaut moves in a spaceship travelling at a speed of 0.8 c is the speed of light). If the astronaut observes a photon approaching the ship from space, then the speed of this photon with respect to the observer is

A. 1.8 c

B. c

C. 0.2 c

D. 0.9 c

10. A certain weight of liquid has a volume of 100 cc at 0 degC. If the volume expansion coefficient of the liquid is 0.00112/degC, then its volume at 50°C is approximately

A. 106 cc

B. 6 cc

C. 94 cc

D. 11 cc

11. A string under tension T1 vibrates at a natural frequency, f1. If the tension of the string is increased to T2 then the natural frequency at which the string now vibrates is

<img src='./qimages/1940-11.jpg'>

12. According to the kinetic theory of gases, the root-mean-square speed of gas molecules in a mono atomic ideal gas at a temperature T is

<img src='./qimages/1940-12.jpg'>

13. If 1gm of ice at 0°C is melted and converted into water at the same temperature, then the change in entropy is, (assuming heat of fusion 79.7cal/g)

A. 0.29cal/K

B. 0cal/K

C. -79.7cal/K

D. -0.29cal/K

14. If a system is in equilibrium with entropy S at constant T and then the variation of entropy with volume (dow S/dow is given by

<img src='./qimages/1940-14.jpg'>


15. which one of the following equations does not represent a travelling wave?

<img src='./qimages/1940-15.jpg'>

16. The light and sound arising from an explosion on the sea surface were recorded by an observer in a submarine located at 1 km below the sea surface at time periods tL sub and tS sub respectively. The same event was also recorded by an observer in a helicopter, at 1 km above the sea surface, at times tL hel and tS hel respectively. Assuming that both the observers are at rest with respect to the event, which one of the following is true?

<img src='./qimages/1940-16.jpg'>

17. When the current flowing in a primary coil of a transformer increases from zero to 5A in a time of 0.01 sec, the induced emf in the secondary coil was found to be 1500 V. Then the mutual induction between the two coils is

A. 0.3H

B. 3H

C. 30H

D. 300H

18. If a charge is moving initially with a velocity of v VZ, parallel to a uniform magnetic field, Bz, the charge will then

A. accelerate along

B. oscillate back and forth around z

C. continue along z with the same speed v.

D. move in a plane perpendicular to z along a circular path.

19. A filament, assumed to be a black body, is emitting radiation at a temperature T. If the power to the filament is doubled then the temperature will

A. increase by 2 1/4

B. increase by 2 1/2

C. increase by 2.

D. increase by 4.

20. If a particle of mass M at rest explodes into two parts of masses ml and m2, then the ratio of their de Broglie wavelengths is

A. m1/m2

B. m2/m1

C. 2M/m1+m2

D. 1

21. If an electron and a proton are moving with the same kinetic energy along the same direction, when they pass through a uniform magnetic field perpendicular to the direction of their motion, which one of the following statements regarding the radii of the trajectories of these two particles in the region of the magnetic field is true?

A. they are the same.

B. radius is greater for the electron since it has a higher velocity.

C. radius is greater for the proton since it has a higher mass.

D. radius is lower for the proton since it has the higher mass.

22. The part of the output characteristics of an n transistor, which is used while operating it as an amplifier is the

A. saturation region.

B. active region.

C. cut-off region.

D. break down region.

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

<img src='./qimages/1940-23.jpg'>

A. 0.7V and 0W

B. 5.0V and 0W

C. 0.7V and 0.7 mW

D. 5.0V and 5W


24. A source produces sound of constant frequency at 10kHz. If a person moves away from this source at twice the speed of sound, then the

A. frequency of sound sensed by the person is larger than 10 kHz.

B. frequency of sound sensed by the person is smaller than 10 kHz.

C. frequency of sound sensed by the person is equal to 10 kHz.

D. person does not hear any sound.

25. If a ray of light is travelling from a denser medium (glass) to air, and the refractive index of the denser medium is 1.5, then the Brewster angle is

A. 56°

B. 34°

C. 65°

D. 25°


26. A unit vector normal to the surface z x2 y2 at the point is given by

<img src='./qimages/1940-26.jpg'>

27. Which of the following cannot possibly be the eigen values of a real 3 x 3 matrix?

A.

B. 1-i

C.

D.

28. Two independent solutions of the differential equation <img src='./qimages/1940-28.jpg'> may be chosen to be

<img src='./qimages/1940-28-1.jpg'>

29. The area of the shaded region between the straight line and parabola as shown in the figure is given by

<img src='./qimages/1940-29.jpg'>

30. Given a the values of a and bare

A. a b

B. a b 0

C. a b 1

D. a 2.

31. If one person speaks the truth in 70% of the cases and another in 80% of the cases, then the probability that they will contradict each other in describing a single event is

A. 0.36

B. 0.38

C. 0.40

D. 0.42

32. The straight line x k touches the parabola y if k is chosen as

A. k 0

B. k

C. k

D. k any integer

33. The power series <img src='./qimages/1940-33.jpg'> converges for

A.

B.

C.

D.

34. <img src='./qimages/1940-34.jpg'> is given by

A. 0

B. 1/3

C.

D.

35. The inverse of the function y <img src='./qimages/1940-35.jpg'> is

<img src='./qimages/1940-35-1.jpg'>

36. A satellite of mass launched into a circular orbit of radius has a time period T.
If a second satellite of mass 0.75M is launched into an orbit of radius the time period of the second satellite will be given by

A. T

B. 0.65T

C. 0.75T

D. 1.54T

37. A block of mass m rests on a frictionless horizontal table and is connected to two fixed posts by springs having spring constants k and 2k. If the block is displaced from its equilibrium position, the angular frequency of vibrations is given by

<img src='./qimages/1940-37.jpg'>

38. A particle of mass m moves in a circle of radius a under the action of a central force whose potential is kmr3 0). The energy of the particle given by

A. 3/2mka3

B. 3/2mka2

C. 1/2mka3

D. 1/2mka2

39. The mutual potential energy V of two particles depends on their mutual distance as

b>0.

If the particles are in static equilibrium, then the separation is given by

A. 2a/b

B. 2b/a

C. a/b

D. b/a

40. If a body of uniform cross-sectional area A and mass density P floats in a liquid of density P0 Po) and at equilibrium displaces a volume V of the liquid, then the time period of small oscillations about the equilibrium position is

<img src='./qimages/1940-40.jpg'>

41. A particle of mass carrying a charge hangs at rest from a spring of stiffness k. If a charge is brought and held directly below at a distance of then the change in length of the spring, delta in its new equilibrium state is proportional to

<img src='./qimages/1940-41.jpg'>

42. For which of the following force fields the potential energy is not defined?

<img src='./qimages/1940-42.jpg'>

43. A uniform hollow cylinder of mass M and radius rolls from rest down an inclined plane through a distance L. If the plane makes an angle of 30° with horizontal, then the rotational kinetic energy of the cylinder when it reaches the bottom of the inclined plane is

A. mgL/2

B. mgL

C. mgL/4

D. mgL/8

44. If S1,S2 and S12 denote the surface tensions of a liquid drop, its supporting liquid and the interface between them, respectively, then the liquid drop will spread over the surface of the supporting liquid when

A. S1 S12 S2

B. S2 S1 +S12

C. S2 S11 +S12

D. S1 S2 S12

45. A solid block which is 2m in side and having a thickness of 0.25m is compressed across its thickness. If its Young's modulus is 20 x 106 N/m2 then the force required to compress the solid by 0.01m in length across its thickness is

A. 2 x 105N

B. 8 x 105N

C. 1 x 105N

D. 12.5 x 105N

46. Consider a long thin wire of cross sectional area with Young' s modulus tension mass per unit length M and density p. In such a system, which of the following statements regarding the speeds of transverse and longitudinal waves will be true?

A. The speeds are equal if the fractional increase in its length is 1.

B. The speeds are equal if the fractional increase in its length is 1/2.

C. The speeds are equal if the fractional increase in its length is 2.

D. The speeds can never be equal.

47. The surface tension, sigma, of a liquid of density delta, which rises to a height h in a capillary of a diameter D is

<img src='./qimages/1940-47.jpg'>

48. If the equilibrium state of the vapour near and above the critical point is described by the Van der Waal equation of state RT, where v V/n is the molar volume, which one of the following statements about the the critical values of (molar) volume, pressure and temperature at the critical point is true?

<img src='./qimages/1940-48.jpg'>

49. If W is the work done on a system in a reversible process and b..F is the change in its free energy, then

A. W >delta F

B. W delta F

C. W delta F

D. W not equal to delta F


50. In an infinitesimal adiabatic process, the work done

A. is a perfect differential.

B. is not a perfect differential.

C. is zero.

D. depends on the temperature.

51. The outer surface of a brass sheet at 100°C is kept in contact with the outer surface of a steel sheet at 0°C. If the thickness and cross-sectional areas of both the sheets are equal and the ratio of their thermal conductivities is then the temperature of the
interface at equilibrium is

A. 66.7°C

B. 50°C

C. 33°C

D. 100°C

52. A refrigerator is operated between two reservoirs maintained at 250K and 300K respectively. If its coefficient of performance is one-third that of a Carnot engine and it absorbs 500J from the low temperature reservoir, then the heat lost to the high temperature reservoir is

A. 800J

B. 1500J

C. 600J

D. 155J

53. If a metal rod is heated at one end and immersed in ice (at at the other end, then the mass of ice that melts in a given time, is

A. directly proportional to the length of the rod and inversely proportional to the area of cross-section.

B. directly proportional to the area of cross-section and inversely proportional to thermal conductivity of the rod.

C. directly proportional to both the length and thermal conductivity of the rod.

D. directly proportional to the thermal conductivity of the rod and inversely proportional to its length.


54. Two waves are described by y1 asin(4piet) and y2 acos(4piet). The phase difference between these two waves is

A. pie

B. 0

C. 2pie

D. pie/2

55. The fraction of kinetic energy in the total energy of a simple harmonic oscillator, when its displacement is half of its amplitude, is given by

A. 0

B. 0.5

C. 1

D. 0.75

56. Which one of the following statements about sound waves is true?

A. sound waves cannot be polarized.

B. sound waves can only be circularly polarized.

C. sound waves can only be plane polarized.

D. sound waves can be plane polarized or circularly polarized.

57. If surface waves in a lake have a phase velocity given by v a root lamda/2pie, where a is constant, then their group velocity is

A. v

B. 2v

C. v/2

D. v/a

58. If a dipole p situated at the origin is pointing in the +z-direction, then the force on a point charge q at is

<img src='./qimages/1940-58.jpg'>

59. Wires of equal resistance 10 ohm are joined together in the form of two pyramids with a common base, as shown in the figure. If current enters through A and leaves through then the resistance between the two points A and B is

<img src='./qimages/1940-59.jpg'>

A. 5ohm

B. 10ohm

C. 20ohm

D. 40ohm

60. The resonance frequency of an LCR circuit was found to be 1200 Hz. If another capacitor of equal value is connected in parallel to the existing one in the circuit, then the new resonance frequency is

A. 2400Hz

B. 1697Hz

C. 849Hz

D. 600Hz

61. If a 2MeV alpha particle (2He4) incident on 47Ag107 nucleus is scattered at then the impact parameter is (e2/4pieE0 1.44 MeV fm)

A. 3.38 X 10-15m

B. 47 x 10-5m

C. 6.78 x 10-15m

D. 0m

62. The electron in a Hydrogen atom in its ground state gets elevated to the highest permissible excited state, by absorbing an energy equal to 12.1 eV. The change in the angular momentum of the electron is

A. h/pie

B. 2h/pie

C. 3h/pie

D. h/2pie

63. Photons with energies pw and qw are incident one after another on a metal having work function where p and q are integers. The ratio of respective maximum velocities is

<img src='./qimages/1940-63.jpg'>

64. Separate Compton effect experiments are carried out using visible light and X -rays. If the scattered radiation is observed at the same scattering angle, then

A. the X-rays have greater shift in wavelength and greater change in photon energy.

B. the two radiations have the same shift in wavelength and X-rays have a greater change in photon energy.

C. the two radiations have the same shift in wavelength and visible light has greater change in photon energy

D. the two radiations have the same shift in wavelength and the same change in photon energy.

65. Which of the following represents the first excited state wave function of a massive particle confined to move in a one-dimensional box of length L (the x-axis represents the space co-ordinate and the y-axis represents the shape of the wave-function, in each figure.).

<img src='./qimages/1940-65.jpg'>

66. When a beam of 100 eV electrons is incident on a crystal at an angle a first order Bragg reflection occurs, then the lattice spacing is

A. 13.2x10-15m

B. 13.2xl0-13m

C. 14.2xl0-14m

D. 1.32x10-15m

67. If a particle of mass 1.67x10-27 kg is confined to move in a box of length 10-14m and infinite depth, the minimum kinetic energy of the particle would be

A. 0.21 MeV

B. 0.33 MeV

C. 0.21 eV

D. 3.3 eV

68. The current IL flowing in the circuit is <img src='./qimages/1940-68.jpg'>

A. 1mA

B. 1.5 mA

C. 0.5 mA

D. 3mA

69. If the binary number 01101010 is converted into the hexadecimal system, then it is written as

A. 6AH

B. 106H

C. 610H

D. 2EH

70. The minimum current required to achieve Zener action in the diode shown in the circuit is 0.5mA and the maximum power it can withstand is 1W. The input voltage range over which this diode can regulate the output voltage is

<img src='./qimages/1940-70.jpg'>

A. 9.95V-20V

B. 10V-100V

C. 10.05V-20V

D. 10.7V-20.7V

71. A 1 mewF capacitor is connected in series with a 1 kohm, resistance and an AC source as shown in the figure. If V1 is the magnitude of the output voltage when a 10kHz AC signal of certain amplitude is applied at the input and V2 is the magnitude of the output voltage when a 1Hz AC signal of the same amplitude is applied, then the ratio of V1 to V2 is approximately

<img src='./qimages/1940-71.jpg'>

A. 100/2pie

B. 1000/2pie

C. 2pie/100

D. 2pie/1000

72. If light passes through a glass slab of 1cm thickness and refractive index 1.5 at an angle of 45° with respect to the normal to the slab, then it deviates from the original path by

A. 1cm

B. 1.06cm

C. 0.6cm

D. 0.53cm

73. The output of light from a laser source of 1mW power passing through two crossed polarizers is zero. If another polarizer is introduced between these two at an angle of 45° with respect to the optic axis of one of them, the output power at the detector is

A. 0mW

B. 0.5mW

C. 0.75mW

D. 0.25mW

74. If the output from a 1V source is attenuated by 2 dB, then the measured voltage will be

A. 0.5V

B. 0.1V

C. 0.01V

D. 0.001V


75. If the actual wavelength of light emitted from a luminous body is 6000 but is measured to be 6030 then its relative velocity with respect to the observer is

A. 1x106 m/sec

B. 1.5x106 m/sec

C. 3x106 m/sec

D. 6x106 m/sec