physics prelim 2005

Physics - 2005

Prelim

1. A conducting spherical shell having inner radius a and outer radius b carries a net charge Q.If a point charge q is placed at the centre of this shell, what is the surface charge density onthe outer surface ?

1) (Q - q)/(4πb2)

2) (Q + q)/(4πb2)

3) Q/(4πb2)

4) (Q + q)/(4π(b2 - a2))

2. On the T-S diagram, an isotherm is a straight line parallel to the entropy axis. What does thearea under the isotherm indicate?

1) The work done by the system

2) The change in internal energy of the system

3) The heat exchanged during the process

4) The work done on the system

3. A heat engine converts a given quantity of heat into work with maximum efficiency duringwhich one of the following processes?

1) Isobaric process

2) Isochoric process

3) Isentropic process

4) Isothermal process

4. When a wire is heated to a sufficiently high temperature, it is found to emit electrons. Theemitted electrons present in the interspace follow which one of the following distributions?

1) Maxwellian distribution

2) Boltzmann distribution

3) Lorentzian distribution

4) Exponential distribution

5. Consider the following statements in respect of van der Waals equation/van der Waalsforces :1. The values of a and b in van der Waals equation do not vary with temperature. 2. Van der Waals forces are much weaker than those arising from valence bonds and areinversely proportional to the seventh power of the distance between atoms or molecules. Which of the statements given above is/are correct?

1) 1 only

2) 2 only

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3) Both l and 2

4) Neither 1 nor 2

6. On the inversion curve, the Joule-Thomson coefficient is

1) positive

2) zero

3) negative

4) infinite

7. For a particle of mass m in a one-dimensional potential

V(x) = (1/2)kx2 + ax What is the ground state energy ? {ћ = h/(2π) and ω = (k/m)1/2}

1) ћ ω /2

2) (ћ ω /2) + ak

3) (ћ ω /2) + (a2/2k)

4) (ћ ω /2) - (a2/2k)

8. If (1) represents isothermal and (2) represents adiabatic, which of the graphs given below inrespect of an ideal gas are correct ?

1) I and II

2) II and III

3) I and III

4) I, II and III

9. An ideal gas completes a cycle consisting of two isotherms and two isochors as shown in thebelow figure. Which one of the following is correct ?

1) In the processes 1-2 and 2-3, entropy increases



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10. What is the minimum attainable pressure of an ideal gas in the process given by T = a + bV2,where a, b are constants and V is the volume of one mole of ideal gas ? (R is the universal gas constant)

1) √ab

2) R√ab

3) 2R√ab

4) √(a/b)

11. How many degrees of freedom will the gas molecules have under standard condition if ρ isthe density and P is the pressure of the gas, and V is the velocity of sound propagatingthrough if ?

1) 2 [(ρV2 / P) - 1]

2) 2 [(ρV2 / P) - 1]-1

3) [(ρV2 / P) - 1]

4) [(ρV2 / P) - 1]-1

12. What is the quantity of heat required to raise the temperature of one gram molecule throughone degree for a monatomic gas at constant volume ?

1) 0.5 R

2) 1.0 R

3) 1.5 R

4) 2.5 R

13. van der Waals equation predicts that the critical coefficient of a gas (RTc/PcVc) has the value

1) 8/3 2) 2 3) 4/3 4) 3/8

14. If the most probable speed of a gas molecule of mass m is (2kT/m)1/2, where k is Boltzmanconstant and T is the absolute temperature, then what will be the most probable value ofkinetic energy of the gas molecule ?

1) kT 2) 2kT 3) 3kT/2 4) kT/2

15. What is the relationship between pressure (p) and energy density (µ) due to diffuseradiation?

1) p = µ/3

2) p = µ

3) p = 2µ/3

4) p = µ/4

16. If heat Q is added reversibly to a system at temperature T and heat Q' is taken away from itreversibly at temperature T', then which one of the following is correct ?

1) (Q/T) - (Q'/T') = 0

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2) (Q/T) - (Q'/T') > 0

3) (Q/T) - (Q'/T') < 0

4) (Q/T) - (Q'/T') = change in internal energy of the system

17. If a solid state power supply having voltage regulation 25% has full-load voltage of 20 V,what will be its no-load voltage ?

1) 20 V

2) 25 V

3) 40 V

4) 50 V

18. Which one of the following elementary particles is called Baryon ?

1) Electron

2) µ-Meson

3) π-Meson

4) Neutron

19. For the neutron decay process, n → p + e + (y), where e is an electron, the particle (y) is a

1) neutrino

2) photon

3) pion

4) anti-neutrino

20. The binding energy per nucleon is largest for

1) 56Fe

2) 16O

3) 4He

4) 208Pb

21. The radius of Ge nucleus is measured to be twice the radius of 9Be4 nucleus. How manynucleons are there in the Ge nucleus?

1) 72 2) 96 3) 120 4) 144

22. A particle of mass m and energy E is incident on a potential step of height V0 (at x = 0). If E <V0, the wave function of the particle for x > 0 will be of the form

1) eikx

2) zero

3) e-kx

4) Aeikx + Be-ikx

23. If n represents the number of eigenstates of a hydrogen atom, then its discrete energy levelsare proportional to

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are proportional to

1) n

2) n2

3) 1/n

4) 1/n2

24. The eigenfunctions of hydrogen atom contain which of the following ?1. Legendre polynomials 2. Laguerre polynomials 3. Hermite polynomials Select the correct answer using the options given below :

1) 1, 2 and 3

2) 1 and 2

3) 1 only

4) 2 only

25. For a particle of m in a one-dimensional box of length l, what is the average of momentum pxfor the ground state ?

1) 0

2) h/(2l)

3) h/l

4) h/(2πl)

26. A particle constrained to move along the x-axis is described by the wve function ψ(x) = 2x; 0 < x < 1 = 0; elsewhereWhat is the probability of finding the particle within the interval (0, 0.4) ?

1) 0.85

2) 0.085

3) 0.0085

4) 0.00085

27. Consider the following statements :In order that measurable properties (such as energy, linear momentum, etc.) of a quantummechanical system by physically acceptable, it is essential that1. the corresponding eigen-function ψ(x) and its derivative (dψ(x)/dx) must be finite for allvalues of x.2. ψ(x) and (dψ(x)/dx) must be single valued for all values of x.3. ψ(x) and (dψ(x)/dx) must be continuous for all values of x.Which of the statements given above are correct?

1) 1, 2 and 3

2) 1 and 2

3) 1 and 3

4) 2 and 3

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28. For the X-ray spectrum due to transition between n = 2 and n = 1 states, for large nuclearcharge Ze, we have frequencies v0, v1, v2 for Z0 = Z0, Z1 = Z0 + 1, Z2 = Z0 + 2 respectively.Moseley's law implies which one of the following equations ?

1) v1 = (v0 + v2) / 2

2) v1 = (v0 v2) / 1/2

3) v11/2 = (v0

1/2 + v21/2) / 2

4) v1 = (v0 v2) / (v0 + v2)

29. A thermal neutron of rest mass m0 has kinetic energy given by 3kT/2, where k is theBoltzmann constant and T is the room temperature. What is the de Broglie wavelengthassociated with such a neutron ?

1) h/√(3m0kT)

2) 3hkT/(2√m0)

3) 2h/(3kT√m0)

4) 2h/√(3m0kT)

30. In the Bragg scattering of a beam of electrons each of mass m and velocity v by a nickelcrystal, the first maximum is observed at θ = 30° (θ being the angle the beam makes withthe crystal plane). What is the inter-planar distance d for the crystal?

1) h/mv

2) 2h/mv

3) h/2mv

4) mv/h

31. Two simple harmonic motions of same frequency but having a phase difference of π travel atright angles. When superimposed, what will be the nature of the resultant motion ?

1) A sine curve

2) A circle

3) An ellipse

4) A straight line

32. A cube at rest has a side of length √5m. What is the approximate volume of the cube, whenit moves with a velocity of 2 × 108 ms-1 parallel to one of its sides ?

1) 13.9 m3

2) 11.2 m3

3) 8.3 m3

4) 6.7 m3

33. For a spherical ball dropped in a long column of a viscous liquid, the speed (v) of the ball asa function of time (t) may be best represented by which one of the curves shown below inthe graph?

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1) A 2) B 3) C 4) D

34. A unit mass at position vector is moving with a velocity . What isthe angular momentum of the body about the origin ?

1) 2 units along z-axis

2) 38 units along x-axis

3) 38 units along y-axis

4) 38 units along z-axis

35. A mass m attached to a spring is oscillating in water. If the spring constant is k and restoringforce is R , which one of the following is correct ?

1)

2)

3)

4)

36. A uniform spring of spring constant k is cust into two pieces whose lengths are in the ratio 1 :2. What is the ratio of frequencies of oscillations in the vertical direction when mass m eachis suspended from the smaller and the larger pieces of the spring?

1) 1/√2

2) √2

3) 1/2

4) 2

37. Which one of the following statements is correct ?Binding energy of a nucleus is maximum when it contains

1) even number of protons and even number of neutrons

2) odd number of protons and odd number of neutrons

3) odd number of protons and even number of neutrons

4) even number of protons and odd number of neutrons

38. A projectile is projected with a speed u making an angle 2θ with the horizontal. What is thespeed when its direction of motion makes an angle θ with the horizontal ?

1) (u cos 2θ)/2

2) u cos θ

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3) u (2 cos θ - sec θ)

4) u (cos θ - sec θ)

39. After cutting off a circular portion of radius R/2 from the centre of a uniform circular disc ofradius R, the moment of inertia about an axis passing through its centre and perpendicularto its plane becomes I. What is the moment of inertia of the original disc about the same axis?

1) 2I

2) 4I

3) (8/7) I

4) (16/15) I

40. If two bodies of mass M and 4M are attached to the two ends of a spring of spring constants, what is the period of oscillation?

1) 4π√(M/(5s))

2) 4π√(5s/M)

3) 2π√(5M/s)

4) 2π√(5M/(2s))

41. Which one of the following statements is correct ?

1) Gravitational force has an inverse-square dependence on distance, whereas electro-magnetic, weak and strong forces are the short range forces

2) Gravitational and electromagnetic forces have the inverse-square dependence ondistance, whereas weak and strong forces are the short range forces

3) Gravitational electromagnetic and weak forces have the inverse-square dependence ondistance, whereas strong force is the short range force

4) Gravitational, electromagnetic, weak and strong forces have the inverse-squaredependence on distance

42. If the radius of earth were to decrease by 1%, its mass remaining the same, what would bethe approximate change in acceleration due to gravity ?

1) Decrease by 2%

2) Increase by 2%

3) Decrease by 1%

4) Increase by 1%

43. A gun shoots three times as high when its angle of elevation is α as when it is β. What is theratio of the horizontal distances travelled respectively in the two cases ?

1) 1 : 3

2) 1 : 1

3) 2 : 1

4) 3 : 5 : 1

44. A block B is resting on a horizontal plate in the x-y plane and the coefficient of friction

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between the black and the plate is µ. The plate begins to move in the x-direction and itsvelocity is v = bt2, t being time and b being a constant. At what time will the block start slidingon the plate ?

1) µb/g

2) µgb/2

3) µg/b

4) µg/2b

45. A body of mass M moves under the action of a central force with potential V (R) = AR3 (A >0). For what kinetic energy will the orbit be a circle of radius r about the origin ?

1) 3AMr3/2

2) 3AMr/2

3) 3AMr4/2

4) 3AMr3

46. Moment of inertia of a uniform disc of mass m about an axis x = a is mk2, where k is theradius of gyration. What is its moment of inertia about an axis x = a + b ?

1) mk2 + m (a + b)2

2) mk2 + m ((a + b)2/2)

3) mk2 + m (b2/2)

4) mk2 + mb2

47. A charge q is placed symmetrically with respect to three faces of equal area as shown in thefigure given below. What is the total electric flux through the faces ?

1) q/ε0

2) q/(2ε0)

3) q/(3ε0)

4) zero

48. Two parallel plate capacitors of capacitances C and 2C are connected in parallel andcharged to a potential difference V. The battery is then disconnected and the region betweenthe plates of the capacitor of capacitance C is completely filled with a material of dielectricconstant K. What is the potential difference across the capacitors now?

1) (3V)/(K + 2)

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2) (2V)/(K + 3)

3) KV

4) V/K

49. In an a.c. circuit with the combination of L and C, which one of the following represents thevariation of frequency (f) with reactance (X) ?

1)

2)

3)

4)

50. Which one of the following statements is correct ?A material while superconducting behaves like

1) a diamagnet

2) a paramagnet

3) a ferromagnet

4) an antiferromagnet

51. Dielectric constant of mica is 6. What is the velocity of light in this medium approximately ?

1) 1.2 × 107m/s

2) 5.0 × 107m/s

3) 1.2 × 108 m/s

4) 3.0 × 108 m/s

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52. In a series resonant circuit, L = 1H, C = 0.25 µf and the quality factor is 100. What is therange of FWHM (Full Width at Half Maximum) of the resonant circuit ?

1) (1990 - 2010) rad / s

2) (1980 - 2020) rad /s

3) (1995 - 2005) rad / s

4) (1900 - 2010) rad / s

53. What is the kinetic energy gained by an electron due to acceleration through a potentialdifference of 1 V?

1) 1 eV

2) 1 joule

3) 5 Nm

4) 10 Nm

54. Charge is distributed uniformly throughout a long non-conducting cylinder of radius R. Whichone of the following graphs best represents the magnitude of the resulting electric field E asa function of r, the distance from the axis of the cylinder ?

1)

2)

3)


4)

55. A loop of diameter d is rotated in a uniform electric field until the position of maximum electricflux is found. The flux in this position is measured to be Ф. What is the electric field strength?

1) 4Ф/πd2

2) 2Ф/πd2

3) Ф/πd2

4) πФd2/4

56. A power supply P1 delivers 20 V d.c. with a ripple of 1.0 V r.m.s. while the power supply P2delivers 50 V d.c. with a ripple of 2.0 mV r.m.s. Which one of the following is correct ?

1) P1 performs better than P2

2) P2 performs better than P1

3) Both P1 and P2 perform equally and similarly

4) Comparison between P1 and P2 is not possible

57. If the ratio of the concentration of electrons to that of holes in a semiconductor is 7/5 and theratio of the currents is 7/4, then what is the ratio of their drift velocities ?

1) 4/7 2) 5/8 3) 4/5 4) 5/4

58. In the figure below, Ec, Eg and Ev represent the conduction bandwidth, the band gap and thevalence of a semiconductor respectively. If the lattice constant of this semiconductor isdecreased, then which one of the following is correct ?

1) Ec, Ev and Eg increase

2) Ec, Ev and Eg decrease

3) Ec and Ev and increase but Eg decrease

4) Ec and Ev and decrease but Eg increase


59. The circuit given below has two oppositely connected ideal diodes in parallel. What is thecurrent flowing in the circuit ?

1) 1.33 A

2) 1.71 A

3) 2.00 A

4) 2.31 A

60. A Zener diode has a breakdown voltage of 9.1 V with a maximum power dissipation of 364mW. What is the maximum current that the diode can withstand ?

1) 0.04 A

2) 0.4 A

3) 4.0 A

4) 40 A

61. Which one of the following gives the output F for the logic diagram shown below ?

1)

2)

3)

4)

62. The number of bits that a digital computer can process in parallel at a time is called

1) Byte

2) Binary digit

3) Word length

4) PACE

63. If the memory chip size is 256 × 1 bits, what is the number of chips required to make up 1kbyte of memory ?

1) 32 chips

2) 64 chips

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4) 256 chips

64. Given below are four types of read only memories used in microcomputers : 1. EPROM2. PROM3. ROM 4. EAROMWhich one of the following is the correct sequence in terms of maximum to minimum easefor storing program in them ?

1) 2 - 3 - 1 - 4

2) 4 - 1 - 2 - 3

3) 3 - 2 - 1 - 4

4) 4 - 1 - 3 - 2

65. A radioactive nucleus has a half-life of 100 years. If the number of nuclei at t = 0 is N0, whatwill be the number of nuclei which have decayed in 300 years ?

1) 7 N0 / 8

2) N0 / 2

3) 3 N0 / 4

4) N0 / 8

66. A beam of atoms splits into 4 components in the Stern-Gerlach experiment with a weakmagnetic field. What is the total angular momentum quantum number j for these atoms ?

1) 3/2 2) 1/2 3) 3 4) 4

Directions for question 67 to 72 :The following consist of two statements : one labelled as the ‘Assertion (A)’ and theother as ‘Reason (R)’. You are to examine these two statements carefully and selectthe answers to these items using the options given below :

(a) Both A and R are individually true, and R is the correct explanation of A (b) Both A and R are individually true but R is not the correct explanation of A (c) A is true but R is false (d) A is false but R is true

67. Assertion (A) : Energy is released when two light elements combine to form a heavierelement. Reason (R) : Binding energy per nucleon decreases with mass number in the region oflarge mass numbers.

1) a 2) b 3) c 4) d

68. Assertion (A) : A disc rolls down on inclined plane faster than a ring of same outer radius,material and thickness. Reason (R) : Radius of gyration of disc is greater than that of ring.

1) a 2) b 3) c 4) d


69. Assertion (A) : The energy eigenvalue of the lowest energy state of a simple harmonicoscillator is called zero-point energy.Reason (R) : Energy of this state is zero.

1) a 2) b 3) c 4) d

70. Assertion (A) : In quantum mechanics, a particle with total energy E can tunnel through apotential barrier of height V0 greater than E, which is classically impenetrable due to kineticenergy becoming negative inside the barrier. Reason (R) : Wave particle duality in quantum mechanics allows the particle to havenegative kinetic energy.

1) a 2) b 3) c 4) d

71. Assertion (A) : It is possible to obtain Newton's rings with transmitted light. Reason (R) : Phase change of π is introduced in any one beam of the transmitted light.

1) a 2) b 3) c 4) d

72. Assertion (A) : In almost all measuring optical instruments, Ramsden eyepiece is used.Reason (R) : A cross wire or a scale can be fitted at the position of the image formed by theobjective.

1) a 2) b 3) c 4) d

73. A spring oscillating in water is acted upon by an external force B cos ω t. With the passage oftime, the frequency of the spring tends to be

1) greater than ω2) less than ω3) equal to ω4) decreasing exponentially

74. Reference frame A is moving with a velocity VA with respect to earth and reference fram B ismoving with a velocity VB with respect to reference frame A. If MA and MB are the masses ofa body in A and B respectively and c is the speed of light, then what is the value of MA/MB ?

1) √(1 – V2B/c2)

2) [1 – ((VA – VB)2/c2)]-1/2

3) √(1 – (VA – VB)2/c2)

4) (1 – V2B/c2)-1/2

75. A particle of rest mass (10m)/3 decays at rest into rwo mesons of mass m each. What is thevelocity of each meson in terms of the velocity of light c ?

1) 3c/10

2) 3c/5

3) 2c/5

4) 4c/5


76. A cube has density ρ 0 when at rest. What is the density of the cube when it moves withvelocity v (close to c) parallel to one of its sides ?

1) ρ0 (1 - v2/c2)1/2

2) ρ0 (1 - v2/c2)-1/2

3) ρ0 (1 - v2/c2)-1

4) ρ0 (1 - v2/c2)

77. Which one of the following represents relativistic version of Newton's Second Law of motionwith rest mass m0 and speed v ?

1) F = m0 (dv/dt)(1 - v2/c2)-3/2

2) F = m0 (dv/dt)(1 - v2/c2)3/2

3) F = m0 (dv/dt)(1 - v2/c2)-1/2

4) F = m0 (dv/dt)(1 - v2/c2)

78. A source of sound approaches an observer and then recedes from it. Ratio of frequencies ofsound as the source approaches and as the source recedes is 6 : 5 What is the speed atwhich the source is moving ?(Velocity of sound = 330 m s-1)

1) 24 m s-1

2) 27 m s-1

3) 30 m s-1

4) 33 m s-1

79. A light ray is travelling through a ring of an optical fibre which is made of four differentglasses (shown above) but each part has the same geometrical thickness, if their refractiveindices are (i) 1.51, (ii) 1.52, (iii) 1.53, (iv) 1.54 respectively, light ray will take the maximumtime in crossing which part ?

1) Part No. 1

2) Part No. 2

3) Part No. 3

4) Part No. 4

80. A convex lens of optical glass (µ = 1.42) is immersed in a liquid (µ = 1.49) inside a glass cell.How does the lens-liquid combination act ?


1) As a converging lens

2) As a diverging lens

3) As a piano-parallel lens

4) As a piano-convex lens

81. Let FR and FV be the focal length corresponding to red and violet colours respectively for acombination of lenses. For removal of chromatic aberration, which one of the followingconditions holds good ?

1) (FR/FV) = 1

2) (FR/FV) = 2

3) (FR/FV) > 1, but not equal to 2

4) (FR/FV) < 1

82. If the refractive index of the material of a prism is cot (A/2) and vertex angle of the prism is A,what is the angle of minimum deviation ?

1) π - 2A

2) π - A

3) (π/2) - 2A

4) (π/2) - A

83. Light takes 4.5 × 10-10 s to travel 10 cm in a transparent medium. What is the optical pathlength covered by it ?

1) 11.5 cm

2) 13.5 cm

3) 15.5 cm

4) 17.5 cm

84. Which one of the following statements is correct ? A zone plate is used as a convex lens to focus light of wavelength λ. The focal length is

1) independent of λ in the visible region

2) proportional of λ in the visible region

3) inversely proportional to λ and is more for violet rays than for red rays

4) proportional to λ-1/2 and is more for violet rays than for red rays

85. A circularly polarised beam of light passes through a quarter wave plate. The emergingbeam is

1) plane polarised

2) circularly polarised

3) elliptically polarised

4) partially polarised

86. When an unpolarised light beam passes through a double refracting medium, it splits up into


two beams called ordinary ray and extraordinary ray. Consider the following statements : 1. Intensities of the both rays are equal. 2. Refractive index of the ordinary ray remains constant. 3. Refractive index of the extraordinary ray does not remain constant. 4. Both the rays are unpolarised. Which of the statements given above are correct ?

1) 1, 2 and 3

2) 1 and 4

3) 2 and 3

4) 3 and 4

87. Which one of the following statements is correct ?Optically active substances are responsible for

1) the rotation of the plane of polarisation of polarised light

2) producing polarised light

3) producing bifringence

4) converting ordinary light into polarised light

88. The coefficient of thermal conductivity of a gas is proportional to

1) T2

2) T

3) 1/T

4) √T

89. If the mean kinetic energy of a smoke particle executing Brownian motion in air is Esmokeand the mean kinetic energy of an air molecule is Eair, then which one of the following iscorrect?

1) Esmoke > Eair

2) Esmoke = Eair

3) Esmoke < Eair

4) No relation between Esmoke and Eair can be established

90. The equation of state of a gas is given as P (V - b) = nRT where b is a constant, n is the number of moles and R is the universal gas constant. When 2moles of this gas undergo reversible isothermal expansion from volume V to volume 2V,what is the work done by the gas ?

1) 2RT ln [(V - b)/(2V - b)]

2) 2RT ln [(2V - b)/(V - b)]

3) 2RT ln [(V - b)/(2V)]

4) 2RT ln [(2V)/(V - b)]

91. Consider the following statements : 18/26 ias.edooni.com

Some of the important results of Andrews' experiment are that1. there exists a temperature called critical temperature, above which a gas cannot beliquefied however great the applied pressure is. 2. oxygen, nitrogen and hydrogen are permanent gases and they cannot be liquefied. Which of the statements given above is/are correct ?

1) 1 only

2) 2 only

3) Both 1 and 2

4) Neither 1 nor 2

92. The plots of Maxwell's distribution function (dN/dc) versus speed (c) for a given sample of agas at three different temperatures T1, T2 and T3 respectively are shown in the belowdiagram. If the areas on the c-axis under three curves I, II and III be denoted by AI, AII andAIII respectively, then which one of the following is correct ?

1) AI > AII > AIII

2) AI = AII = AIII

3) AI < AII < AIII

4) AII < AI < AIII

93. A quarter wave plate is placed over a shiny coin. A plane polariser is placed on top of thequarter wave plate such that the transmission axis of the polariser is at 45° to the fast axis ofthe quarter wave plate. How does the shiny coin appear now ?

1) Dark

2) Shiny as before

3) Shinier than before

4) Coloured

94. What is the ground state energy of positronium ? (The ground state energy of hydrogen is -13.6 eV)

1) -3.4 eV

2) -6.8 eV

3) -13.6 eV

4) -27.2 eV


95. Match List-I (Different Types of Laser) with List-II (Active Medium) and select the correctanswer using the options given below the lists :

List-I

(Different Types of Laser) List-II

(Active Medium)

A Ruby Laser 1 Liquid laser

B He-Ne Laser 2 Solid state laser

C Dye Laser 3 Gas laser

D Injection Laser 4 Junction semiconductor laser

1) A-2 B-1 C-3 D-4

2) A-4 B-3 C-1 D-2

3) A-2 B-3 C-1 D-4

4) A-4 B-1 C-3 D-2

96. A soap film of thickness d and refractive index µ is illuminated by white light incident at anangle i. The light refracted at an angle θ is examined by a spectroscope, and twoconsecutive bright bands are seen corresponding to wafelengths λ 1 and λ 2. The pathdifference 2µD cos θ is given by

1) (λ1 - λ2)/(λ1 λ2)

2) (λ1 + λ2)/(λ1 λ2)

3) (λ1 λ2)/(λ1 + λ2)

4) (λ1 λ2)/(λ1 - λ2)

97. In a diffraction grating, slit width is e and ruling separation is d. If second-order spectrum isto be avoided, one should choose

1) e = d/2

2) e = 2d

3) e = √2d

4) e = d

98. A diffraction grating has N lines and grating element is (e + d). For wavelength λ, what is themaximum resolving power possible?

1) N (e + d)/λ2) (e + d)/(Nλ)

3) (e + d)N2/λ4) (e + d - λ)2N/λ2

99. The core of an optical fibre has refractive index 1.6 and its cladding has refractive index 1.5.What is the approximate numerical aperture of the optical fibre ?

1) 0.31 2) 0.56 3) 0.68 4) 0.88

100. Match List-I (Phase Difference between Two Similar Superimposed Waves having MutuallyPerpendicular States of Polarisation and Propagating through the Same Axis) with List-II


(Results) and select the correct answer using the options given below the lists :

List-I (Phase Difference between Two Similar Superimposed Waves

having Mutually Perpendicular States of Polarisation andPropagating through the Same Axis)

List-II(Result)

A θ = π 1 Linearlypolarisedlight

B θ = π/2 2

Leftcircularlypolarisedlight

C θ = 2π/3 3

Rightcircularlypolarisedlight

D θ = 3π/2 4 Ellipticallypolarisedlight

1) A-1 B-3 C-4 D-2

2) A-4 B-2 C-1 D-3

3) A-1 B-2 C-4 D-3

4) A-4 B-3 C-1 D-2

101. Match List-I (Optical Instrument) with List-II (Characteristics of the Instrument) and selectthe correct answer using the options given below the lists :

List-I

(OpticalInstrument)

List-II

(Characteristics of the Instrument)

A Huygens eye-piece

1 Analysis of elliptically polarised light

B Optical fibre 2 Chromatic and spherical aberrations are reduced to a minimum

C Babinet'scompensator

3 Production of circularly polarised light

D Quarter waveplate

4 Refractive index is maximum at the axis and decreasestowards the periphery

1) A-2 B-4 C-1 D-3

2) A-3 B-4 C-1 D-2

3) A-2 B-1 C-4 D-3

4) A-3 B-1 C-4 D-2

102. Two light waves having their intensities in the ratio 16 : 9 interfere to produce interferencepattern. What is the ratio of maximum intensity to minimum intensity in this pattern ?

1) 4 : 321/26 ias.edooni.com

2) 25 : 7

3) 625 : 49

4) 49 : 1

103. Consider the following statements :The continuous X-rays spectrum is the result of 1. inverse photo-electric emission. 2. decrease in the kinetic energy of the incident electrons on the target atom. 3. annihilation of the mass of the incident electron. Which of the statements given above are correct ?

1) 1, 2 and 3

2) 1 and 2

3) 2 and 3

4) 1 and 3

104. A µ-meson which is about 200 times as heavy as an electron is captured by a proton toform a hydrogen-like atom. What is the radius of the first Bohr orbit ? (The radius of firstBohr orbit for normal hydrogen atom is 0.5 Å)

1) 100 Å

2) 0.25 Å

3) 0.025 Å

4) 0.0025 Å

105. Match List-I with List-II and select the correct answer using the options given below the lists:

List-I List-II

A Goudsmit and Uhlenbeck 1 Antisymmetric state

B Moseley's plot 2 Space quantization

C Pauli exclusion 3 Bohr's theory

D Stern-Gerlach 4 Electron spin

1) A-1 B-3 C-4 D-2

2) A-4 B-3 C-1 D-2

3) A-1 B-2 C-4 D-3

4) A-4 B-2 C-1 D-3

106. For what value of g is the function x + gy, an eigenfunction of Lz with eigenvalue - ћ, whereћ, where ћ = (h/2π), h being the Planck's constant ?

1) g = 1

2) g = -1

3) g = i

4) g = -i


107. The frequency of the radiation emitted by a hydrogen atom for the transition between n = 2and n = 1 states is v0. What is the frequency of the radiation emitted by the hydrogen atomfor transition between n = 4 and n = 1 states ?

1) 3v0/2

2) 2v0

3) 4v0

4) 5v0/4

108. The maximum energy of deuterons coming out of a cyclotron accelerator is 20 MeV. Whatis the maximum energy of protons that can be obtained from the accelerator ?

1) 10 MeV

2) 20 MeV

3) 30 MeV

4) 40 MeV

109. Which one of the following relations describes the variation of refractive index (µ) of anoptical substance with wavelength (λ) of light ? (Neglect higher order terms)

1) µ = A + B λ2

2) µ = A + B λ-1

3) µ = A + B λ-2

4) µ = A + B λ

110. Which one of the following circuits is electrically equivalent to the circuit given below ?

1)

2)


3)

4)

111. In a Hall effect experiment, what happens to Hall voltage if the applied magnetic field isdoubled, keeping the Ohmic current density unchanged ?

1) It increases 4 times

2) It becomes half

3) It remains unchanged

4) It increases 2 times

112. A circular loop of resistance R and encompassing an area A is subjected to a magnetic fieldB0 e-bt perpendicular to its plane, B0 and b being constants, and t is the time. What is theinduced current at time t = 0?

1) B0bA/R

2) B0bR/A

3) B0bR/b

4) B0bR/2A

113. What is the Poynting vector at the surface of a long cylindrical wire of radius R, length Lcarrying a current I, when its ends are kept at a potential difference of V?

1) zero

2) VI/(2πR2 + 2πRL)

3) VI/(πR2L)

4) VI/(2πRL)

114. Black-body radiation behaves like a perfect gas of adiabatic exponent (γ) equal to

1) 1/2 2) 1/3 3) 1 4) 4/3

115. If the value of van der Waals constant b for a real gas is 32 cm3/mole, then what is theapproximate volume of one molecule of the gas ? (Avogadro constant = 6.02 × 1023)

1) 5.2 × 10-23 cm3

2) 3.9 × 10-23 cm3

3) 2.6 × 10-23 cm3

4) 1.3 × 10-23 cm3


116. What is the value of current passing through the branch AB in the electric circuit given below?

1) 8/7 A

2) 2/3 A

3) 3/2 A

4) 3/7 A

117. Which one of the following graphs represents the variation of magnetic flux density (B) withdistance (r) from a long straight conductor carrying current ?

1)

2)

3)

4)

118. What is the approximate peak value of an alternating current producing four times the heatproduced per second by a steady current of 2.0 A in a resistor ?


1) 2.8 A

2) 4.0 A

3) 5.6 A

4) 8.0 A

119. Which one of the following statements is correct ?If in the Wheatstone bridge, the battery and galvanometer are interchanged, the conditionfor balance

1) is not disturbed

2) is disturbed

3) depends on internal resistance of the battery

4) depends of the values of resistances in the bridge

120. Consider a rhombus ABCD with B = 120°. A charge q placed at corner A prodces field Eand potential V at the corner D. If we now add charges -2q and +q at the corners B and Crespectively, what will be magnitudes of the field and potential at D respectively ?

1) E and 0

2) 0 and V

3) √(2) E and V/2

4) E/√(2) and V/√2


Answer Key

1) 2 2) 1 3) 3 4) 2 5) 2 6) 2 7) 1 8) 4 9) 3 10) 3

11) 1 12) 1 13) 1 14) 4 15) 1 16) 1 17) 2 18) 4 19) 4 20) 1

21) 1 22) 3 23) 4 24) 2 25) 2 26) 2 27) 1 28) 3 29) 1 30) 3

31) 1 32) 3 33) 2 34) 1 35) 4 36) 1 37) 1 38) 3 39) 3 40) 1

41) 2 42) 2 43) 2 44) 4 45) 1 46) 4 47) 2 48) 1 49) 4 50) 1

51) 3 52) 1 53) 1 54) 1 55) 1 56) 2 57) 4 58) 3 59) 3 60) 1

61) 1 62) 3 63) 1 64) 2 65) 1 66) 3 67) 1 68) 1 69) 3 70) 1

71) 1 72) 1 73) 3 74) 1 75) 4 76) 2 77) 1 78) 3 79) 4 80) 2

81) 1 82) 1 83) 2 84) 3 85) 1 86) 3 87) 1 88) 4 89) 2 90) 2

91) 1 92) 2 93) 4 94) 2 95) 3 96) 4 97) 4 98) 1 99) 2 100) 1

101) 4 102) 4 103) 1 104) 4 105) 2 106) 1 107) 4 108) 1 109) 3 110) 1

111) 4 112) 1 113) 4 114) 4 115) 4 116) 1 117) 3 118) 2 119) 1 120) 1

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physics prelim 2005

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