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MH SET 2020: 27 December, Paper II, Physics

  • Date: 27 December 2020
  • Paper code: JUN32220
  • Series: A
  • Language: Bilingual
  • 28 pages
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Test Booklet Code & Serial No.
                                                                                                                      A
                                                     PHYSICAL SCIENCE
Signature and Name of Invigilator                                                                  Seat No.
1. (Signature) .........................................                                                    (In figures as in Admit Card)
      (Name) ................................................                     Seat No. ..............................................................
2. (Signature) .........................................                                                    (In words)

      (Name) ................................................                       OMR Sheet No.

JUN - 32220                                                                                           (To be filled by the Candidate)
Time Allowed : 2 Hours]                                                                                [Maximum Marks : 200
Number of Pages in this Booklet : 28                                                    Number of Questions in this Booklet : 100
                      Instructions for the Candidates
1.         Write your Seat No. and OMR Sheet No. in the space provided             1.
           on the top of this page.
2.         This paper consists of 100 objective type questions. Each question
           will carry two marks. All questions of Paper II will be compulsory.     2.
3.         At the commencement of examination, the question booklet
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           (C) and (D). You have to darken the circle as indicated below on        4.                       (A), (B), (C)   (D)
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2
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JUN - 32220/II—A
                                               Physical Science
                                                            Paper II
Time Allowed : 120 Minutes]                          [Maximum Marks : 200
Note : This Paper contains Hundred (100) multiple choice questions. Each question
       carrying Two (2) marks. Attempt All questions.
1.   Unit vector perpendicular to                                     3.   A particle passes through a medium

     A      2iˆ             ˆj     kˆ and B    3iˆ   4 ˆj    kˆ            and is deflected by a small angle

     is :                                                                     0 upon each collision within the
                                                                           medium with equal probability in
                 3iˆ             5 ˆj 11kˆ                                 any direction. The mean square
     (A)
                                 155
                                                                           angular scattering after N such
            iˆ         ˆj         2kˆ                                      collision,   2   is :
     (B)
                            6
                                                                           (A) 0
            4iˆ             ˆj 5kˆ
     (C)                                                                   (B) N 02
                            42

                                                                                   2
            iˆ         2 ˆj 4 kˆ                                                   0
     (D)                                                                   (C)
                         21                                                      N

2.   If S is a closed surface enclosing a                                  (D) N2 02
     volume V and n̂ is the unit vector
                                                                      4.   When a complex number Z is
     normal to the surface and r is the
                                                                           multiplied by i, the resulting vector
     position vector, then the value of the
                                                                           iz, in the z plane, is obtained by
     integral                     nˆ dS is :
                                                                           rotating the vector z through :
                            S

     (A) V                                                                 (A)

     (B) 2V                                                                (B) – /2

     (C) 0                                                                 (C) 3 /2

     (D) 3V                                                                (D)   /2
                                                                  3                                      [P.T.O.
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                                        z2                                          a     b
5.   The residue of the function                      8.   The matrices A =                   and
                                   z2        a2                                      b    a
     at z = ia is :
                                                                 c        d
                                                           B=                 , for some values of
           ia                                                     d       c
     (A)
            2
                                                           a, b, c, d :
     (B) –a2

     (C) ia                                                (A) have no commutation relation
     (D)
                                                                between them
6.   If y = ezt is a solution of y – 5y
     + ky = 0, then k is equal to :                        (B) Commute for all values of a, b,
     (A) 1
                                                                c, d
     (B) 4

     (C) 5                                                 (C) Commute if and only if a, b, c,

     (D) 6                                                      d are real numbers
7.   Solution of the differential equation
                                                           (D) Anticommute for all values of
       dy
     x    + y = x4 with the boundary
       dx                                                       a, b, c, d
     condition that y = 1 at x = 1 is :
     (A) y = 5x4 – 4                                  9.   For any operator A, i (A+ – A) is :

                x4     4x                                  (A) Hermitian
     (B) y
                5      5
                                                           (B) Anti-Hermitian
                4 x4    1
     (C) y
                 5      5x
                                                           (C) Unitary
                 4
                x      4
     (D) y
                5      5x                                  (D) Orthogonal

                                                  4
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10. The complex Fourier transform of
                                                 12.
    e–|x| is :

                2
    (A)
            1       n2

                1
    (B)
            1       n2

                4
    (C)
            1       n2                                 A mass of 1 kg is connected to a

                                                       spring at one end using a massless,
    (D)
            1       n2
                                                       rigid string. Initially the spring is
11. A mouse of mass m jumps on a freely
                                                       in unstretched state. If the mass falls
    rotating disc of moment of inertia I
                                                       through a distance h before stopping
    and radius R. If       0 and   are the
                                                       (now the spring is in stretched
    angular velocities of the disc before
                                                       condition), then the distance h is
    and after mouse jumps, then the
                                                       given as :
    ratio       / 0 is :

    (A) I/mR2                                          (A) 0.196 m


    (B) I/I – mR2                                      (B) 1.96 m


    (C) I/I + mR2                                      (C) 0.14 m

    (D) (I – mR2)/I                                    (D) 1.4 m

                                             5                                        [P.T.O.
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13. The mutual potential energy V of                  15. The number of degrees of freedom
    two particles is function of their
                                                          for an astronaut constrained to move
    mutual distance r, given as :
                                                          on surface of a spherical spaceship
                  a       b
     V r                    , a > 0, b > 0
                 r2       r
                                                          freely moving in space, is :
    If the particles are in static
                                                          (A) 5
    equilibrium, then the separation (r)
    is :                                                  (B) 6

    (A) 2b/a
                                                          (C) 4
    (B) b/2a
                                                          (D) 3
    (C) a/b
                                                      16. A particle falls vertically under the
    (D) 2a/b
                                                          action of gravity and a frictional
14. A particle of mass m moves in an
    ellipitical orbit under the action of                 force obtainable from dissipation
    inverse square central force. If         is                             1 2
                                                          function G(v) =     kv , k is constant.
                                                                            2
    the ratio of maximum angular
                                                          The Lagrange’s equation of motion
    velocity to the minimum angular
    velocity, then the eccentricity of the                is :

    ellipse is given as :
                                                          (A) my     ky     mg   0
    (A)     /(     + 1)
                                                          (B) my     ky     mg   0
    (B) (        + 1)/
                                                          (C) my     ky     mg   0
    (C) (        – 1)/

    (D) (        – 1)/(     + 1)                          (D) my     mg     0

                                                  6
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17. Suppose a system has holonomic and           19. A frame of reference S is rotating
    conservative part, and also some                 with constant angular velocity
    part of forces acting on the system              with respect to a stationary frame
    are not conservative. Let the typical
                                                     of reference S. Both the frames of
    non-conservative force acting on jth
                                                     reference have common origin. The
    particle is denoted as Q i . The
                                                     time derivative of vector A in S
    Hamilton’s equations of motion
                                                     is :
    modify to :
                                                            dA
                H          H                         (A)              A
    (A) qi         , pi          Qi                         dt
                pi         qi
                                                            dA             dA
                H           H                        (B)              A+
    (B) qi         , pi           Qi                        dt             dt
                pi         qi
                                                            dA                 dA
                H          H                         (C)                  A+
                   , pi          Qi                         dt                 dt
    (C) qi      pi         qi
                                                            dA   dA
                                                     (D)
                H           H                               dt   dt
    (D) qi         , pi           Qi
                pi         qi
                                                 20. A particle as observed in certain
18. A rigid body, whose two of the                   frame of reference has a total energy
    principal moments of inertia are
                                                     of 13 GeV and a momentum of
    equal and the third is zero, is called
                                                     5 GeV/c. Its rest mass is :
    as :
                                                     (A) 12 GeV/c2
    (A) Asymmetrical top

    (B) Rotor                                        (B) 12 MeV/c2

    (C) Spherical top                                (C) 1.2 MeV/c2

    (D) Symmetrical top                              (D) 1.2 GeV/c2

                                             7                                      [P.T.O.
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21. Current I is flowing through an                      23. The SI unit of magnetic dipole
    infinitely long wire placed along the
                                                             moment is .................................. .
    x-axis. The Cartessian coordinates of
    the points A and B are A(2, 1, 4)                        (A) Cm
    and B(–6, 1, 4). The ratio of
    magnitudes of B at point A to that                       (B) Cm 2

    at point B is ............................ .
                                                             (C) Cm/s
        1
    (A)
        3
                                                             (D) Cm2/s
    (B) 3

    (C) 1                                                24. A solid sphere of radius R with its

    (D) µ 0 I                                                center at origin has a volume charge

22. A charged particle is released from                      density                A r , where A is a
    rest in a region where both uniform
                                                             constant. The magnitude of electric
    constant electric field and uniform
    constant magnetic field are present.                     field, E , at r < R, varies with r

    If these fields are perpendicular to
                                                             as ................... .
    each other, then the trajectory of the                                      1
                                                             (A) E         r    2
    particle is a .............................. .
                                                                            1
    (A) Straight line
                                                             (B) E         r2
    (B) Circle                                                              3
                                                             (C) E         r2
    (C) Cycloid

    (D) Circular helix                                       (D) E         r 2

                                                     8
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25. Three point charges q, q and –2q are                    27. What is the magnitude of the
                                                                Poynting vector at the surface of a
    located at (0, –1, 1), (0, 1, 1) and
                                                                long cylindrical wire of radius R,
    (0,    0,    –1)     respectively.            The
                                                                length L, carrying current I, when
    magnitude of electric dipole moment                         its ends are kept at a potential

    of this charge distribution is :                            difference V ?

                                                                (A) zero
    (A) zero
                                                                              VI
    (B) q                                                       (B)
                                                                      2 R2     2 RL

    (C) 2q                                                             VI
                                                                (C)
                                                                       R 2L
    (D) 4q
                                                                     VI
26. The electrostatic potential is given                        (D) 2 RL

    by     = k(x2 + y2 + z2), where k is                    28. Velocity of light in air is 3 × 108
                                                                m/s. Velocity of light in a medium
    a constant. The volume charge
                                                                having relative permittivity 3 and
    density giving rise to the above                            relative permeability 2 is .......... .

    potential is ............................ .                        3
                                                                (A)      × 108 m/s
                                                                       2
    (A) 6       0 k
                                                                       3
                                                                (B)      × 108 m/s
    (B) –6       0 k                                                  4

                                                                (C)          8
                                                                       2 × 10 m/s
    (C) 2       0 k
                                                                       3
    (D) –2                                                      (D)      × 108 m/s
                 0 k                                                  2

                                                        9                                       [P.T.O.
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29. Which of the following volume                           31. Out of the following particles, all
    charge densities J r generates the
                                                                having the same kinetic energy,
    magnetic                      vector   potential
                                                                which has the longest wavelength ?
    A r           y2 xˆ      x2 ˆy ?
                                                                (A) An    -particle
          2
    (A)           ( xˆ     yˆ )
              0                                                 (B) An electron
              2
    (B)           ( xˆ     ˆy)                                  (C) A proton
              0

          2                                                     (D) A neutron
    (C)           ( x xˆ      y ˆy)
              0
                                                            32. If quantum mechanical operators of
              2
    (D)           ( x xˆ      y ˆy)                             two observables of a system do not
              0

30. A square wave guide with perfect                            commute, then :
    conductor boundaries is of cross-
                                                                (A) the total energy of the system
    sectional area l2. The wave guide is
    placed in vacuum. The minimum                                   must be negative

    frequency of the electromagnetic
                                                                (B) the parity of the wave function
    waves that can propagate through
                                                                    of the system must be odd
    this wave guide is ................... .

          c                                                     (C) the observables corresponding
    (A)
          l
                                                                    to these operators must be time-
          2c
    (B)                                                             independent
           l
            c                                                   (D) it is impossible to know the
    (C)
           l
                                                                    precise values of the observables
                 c
    (D)       2                                                     simultaneously
                l
                                                       10
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                                                               35. Given 10 > and 11 > are the ground
33. Given the operators  = i xpy                  ypx
                                                                   and first excited state for a one-
    and B̂ = ypz                 zpy the commutator                dimensional harmonic oscillator, the
        ˆ B
        A, ˆ       is :                                            uncertainty in position         x for a
                                                                   particle in the state given by
    (A)            xpz       px z
                                                                    1
                                                                         (10 > + 11 >) is :
    (B)            xpz       px z                                    2

    (C)        xpz         px z                                     Given xˆ             aˆ   aˆ
                                                                                   2m               !
    (D)        xpz         px z

34. A particle in one-dimension is                                 (A) "x
                                                                                  2m !
    moving              under       the     potential
    described by :
                                                                   (B) "x
                                                                                  m !
                           for      x   0

  V x          V0          for      0   x   a, V0   0                             2
                                                                   (C) "x
               0           for      x   a                                         m !

    The minimum depth of the potential                                            4
                                                                   (D) "x
    for at least one bound state is :                                             m !

               2    2                                          36. A muonic atom is formed by a muon
    (A)                                                            (µ –) and a proton. The longest
           2ma2
                                                                   wavelength of spectral line (in
               2    2
    (B)                                                            Balmer series) of such an atom is
           8ma2
                                                                   approximately (h = 6.6 × 10–34 Js)
               2   2
                                                                   (A) 20.5 Å
    (C)            2
           ma                                                      (B) 2.05 Å

           2 2         2                                           (C) 205 Å
    (D)
           ma2                                                     (D) 10.25 Å
                                                          11                                       [P.T.O.
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37. A particle in a one-dimensional              39. In    the   Born       approximation,
    infinite potential well of width L is            scattering amplitude f( ) for Yukawa
    acted on by a perturbation                                              #e       r
                                                     potential V(r) =                    is given by
    H = b(L – x)           0   x   L                                             r
          = 0              otherwise                                         $      2 2
                                                                                     k
                                                     (Given data : b = 2k sin , E =     )
    First order correction to the first                                      2      2m
    excited state is :                                           2m#
           bL                                        (A)     2   2
                                                                       b2
    (A)
            2
           bL                                                    2m#
    (B)                                              (B)     2   2          3
               2                                                       b2
    (C) 2bL
                                                                 2m#
    (D) bL                                                                  2
                                                     (C)     2   2
                                                                       b2
38. Minimum energy of a collection of
    six non-interacting electrons of spin                        2m#
    1                                                (D)     2    2
       and mass m, placed in a one-                                    b2
    2
    dimensional infinite potential well          40. Which one of the following given
    of width L is :                                  below represents the bound state

           3 2     2                                                                            d2
    (A)                                              eigen function of the operator
            mL2                                                                                 dx2
                                                     in the region 0        x            with eigen
           14 2        2
    (B)                                              value –4 ?
               mL2
                2 2
                                                     (A) A0 e2x
           7
    (C)                                              (B) A0 e–2x
            mL2
                                                     (C) A0 cosh 2x
           91 2        2
    (D)                                              (D) A0 sinh 2x
               mL2
                                            12
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41. Density and specific heat at constant        43. A three-dimensional classical

    volume are :                                     Harmonic Oscillator is in thermal
    (A) both intensive variables                     equilibrium with a heat reservoir at
    (B) both extensive variables
                                                     temperature T. Its average total
    (C) intensive      and    extensive
                                                     energy would be :
          variables respectively
    (D) extensive      and    intensive              (A) 6 kBT

          variables respectively
                                                     (B) 3/2 kBT
42. A capacitor of capacitance C farads
    is charged from a battery of emf V               (C) kBT

    volts. Out of the work done by the               (D) 3 kBT
                        1
    battery an amount CV2 is stored
                        2
                                                 44. A system at temperature 30 K is so
    in the capacitor and the rest is

    released to the surroundings. If the             large that its temperature does

    process is carried at temperature T              not change if 107 J of heat is added.

    the change in the entropy of the                 The factor by which the number
    universe would be :                              of accessible states increase is
          CV 2                                       (kB = 1.3807 × 10–23 JK–1)
    (A)
           8T

        CV 2                                         (A) 2.4 ×1014
    (B)
         T                                                          14
                                                     (B) e2.4 ×10
        CV 2
    (C)
         2T                                          (C) 107
          CV 2
    (D)                                              (D) 30 × 107
           4T
                                            13                                     [P.T.O.
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                                               47. The number of distinct ways in
45. Consider a system with only two
                                                   which 7 identical Fermions can be
    energy levels with energies E0 = 0             distributed in 3 energy levels is :

    and E1 = 1.3806 × 10–23 J. The                        7!
                                                   (A)
                                                         4!3!
    level E0 has degeneracy 2 and the              (B) 37

    level E1 has degeneracy 3. The                 (C) 0
                                                   (D) 210
    partition function at T = 1 K is
                                               48. One block at temperature T1 and
    (KB = 1.3806 × 10–23 JK–1) :                   another            identical             block    at
                                                   temperature T 2 are placed in
    (A) z = 2e0 + 3e–1                             thermal contact and come to an
                                                   equilibrium, the system being
    (B) z = 6e–3                                   isolated from surroundings. If the
                                                   heat capacities at constant volume
    (C) z = 6(e0 + e–1)
                                                   C depend on temperature as C = aT,
                                                   the entropy change of the system
    (D) z = 6e–1
                                                   would be :
46. Fermi level in a solid is a direct                                               1/2
                                                                 T12       T22
                                                   (A) a 2             2         !
                                                                                           T1   T2
    measure of :

                                                            T1        T2
    (A) Electronic current                         (B) a
                                                                 2
                                                                                 2
    (B) Temperature of solid                                     T1        T2
                                                   (C) a ln           4T1 T2
    (C) Resistivity of solid
                                                             2T1 T2
    (D) Chemical potential of electrons            (D) a ln T     T
                                                                  1        2


                                          14
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49. An ideal gas at temperature T                 51. In a critically damped series LCR

    expands in an isothermal process                  circuit :

    from volume V1 to volume V2. The                  (A) R2 = 4L/C
    work done in the process is :
                                                      (B) R2 = 2L/C
                       1
                 V1 V2 2                              (C) R =     L/C
    (A) RT ln
                V1     V2
                            !                         (D) R2 = 4L2C2

                V1                                52. Johnson Noise in resistor R is given
    (B) RT ln
                V2 !                                  by :

                                                      (A) vrms = (4KTR"f)1/2
                V1     V2
    (C) RT ln           1
                 V1 V2 2 !                            (B) vrms = (2qI"f)1/2 R

                                                      (C) vrms = A/f2
                V2
    (D) RT ln
                V1 !                                  (D) vrms = A/f

50. According to Weiss molecular theory           53. A 50 Hz noise signal of 1 mV peak

    near the critical point the isothermal            value is introduced at the input

    susceptibility of the magnetic system             of an op-amp based integrator
    behaves as :                                      (RC = 1 s). The output will be :

    (A) %T      |T – TC|                              (A) 3.2 nV

    (B) %T      |T – TC|–1                            (B) 3.2     V

    (C) %T      |T – TC|1/2                           (C) 3.2 mV

    (D) %T      |T – TC|–1/2                          (D) 3.2 V

                                             15                                    [P.T.O.
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54. In Millikan’s oil drop experiment the        56. In X-ray diffraction pattern the
                                                     positions of the peaks depend on :
    electronic charge e could be written
                                                     (A) size of the crystal
    as K&1.5, where K was a function
                                                     (B) shape of the crystal
    of other experimental parameters

    with negligible error, while the                 (C) texture of the crystal

    viscosity of air & assumed was 0.4%              (D) lattice constants of the planes
                                                         of the crystals
    too low. What was the error in e ?
                                                 57. For NMR spectra of proton nuclei,
    (A) 1.5%
                                                     the commonly used reference is :

    (B) 0.7%                                         (A) Ethyl alcohol

    (C) 0.6%                                         (B) Carbon tetrachloride

                                                     (C) Methyl alcohol
    (D) 0.4%
                                                     (D) Tetramethylsilame (TMS)
55. Which of the following experiments
                                                 58. To measure temperature of more
    provides verification of charge
                                                     than 3000°C, the most suitable
    quantization ?                                   thermometer is :

    (A) Millikan’s oil drop E                        (A) Platinum resistance thermo-
                                                         meter
    (B) Franck-Hertz
                                                     (B) Thermocouple
    (C) Davisson and Germer
                                                     (C) Radiation pyrometer

    (D) Zeeman Effect                                (D) Gas thermometer

                                            16
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                                                61. Symbols :
59. What is the temporal coherence

                                                   ID = Drain Current, VSD = Source
    length of a mercury vapour lamp
                                                   to Drain Voltage, VGS = Gate to
    emitting in the green portion of the
                                                   Source Voltage.
    spectrum at wavelength of 546.1 nm
                                                   In the operation of JFET, the pinch-
    with an emission bandwidth of                  off region has the following

    "' = 6 × 108 Hz :                              characteristics :

                                                   (A) The current ID increases with
    (A) 0.5 m
                                                       the increase in the VSD when
    (B) 2 m                                            VGS is negative, reverse biased

    (C) 0.25 m                                     (B) The current ID is constant when

                                                       the VGS is positive, forward
    (D) 1 m
                                                       biased and the VSD is near

60. Best vacuum that can be attained                   break down region

    with a rotary pump is :                        (C) The current ID is constant and

                                                       relatively independent of VSD
    (A) 10–3 Torr
                                                       but the gate is reverse biased,

    (B) 1 Torr                                         VGS negative

                                                   (D) The current ID is constant and
    (C) 10–6 Torr
                                                       relatively independent of VSD
    (D) 10–10 Torr                                     but the VGS is zero

                                           17                                    [P.T.O.
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62. In p-n junction photodiode, the              64. A full wave rectifier supplies DC
    reversing biasing :                              voltage to a load resistance of 2 k(.
                                                     The AC voltage applied to the diodes
    (A) Lowers the carrier transit period
                                                     is 300-0-300 Volts rms. If the diode
        through the depletion layer
                                                     voltage drop is neglected, the
        and reduces the depletion
                                                     average DC voltage across the load
        capacitance
                                                     is nearly :
    (B) Increases the carrier transit
        period through depletion region              (A) 300 Volts
        and also the depletion capaci-               (B) 270 Volts
        tance
                                                     (C) 150 Volts
    (C) Reduces the concentration of n-
        type impurity and increases the              (D) 100 Volts
        photoabsorption efficiency
                                                 65. A 5 mV, 1 kHz sinusoidal signal is
    (D) Increases the concentration of               applied to the input of an op-amp
        p-type impurity and photo-                   circuit shown below. Find the output
        absorption efficiency                        voltage :
63. The frequency of the following
    Hartley oscillator




                                                            1
                                                     (A)      (cos 2000 t – 1) mV
                                                           20

                                                            1
                                                     (B)      (cos 2000 t – 1) mV
                                                           40
    is nearly equal to :
    (A) 139 kHz                                             1
                                                     (C)      (cos 2000 t – 1) mV
                                                           60
    (B) 159 kHz
    (C) 179 kHz                                             1
                                                     (D)      (cos 2000 t – 1) mV
    (D) 279 kHz                                            80
                                            18
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66. The AC Gain of the following        67. A flux quantum (fluxoid) is


   transistor amplifier                    approximately equal to 2 × 10–7


                                           gauss-cm2. A type II superconductor


                                           is placed in a small magnetic field,


                                           which is then slowly increased till


                                           the field starts penetrating the


                                           superconductor. The strength of the


                                           field at this point is (2/ ) × 105 gauss.
   is nearly equal to :

                                           The penetration depth of this

   (A) 200                                 superconductor is :


                                           (A) 10 Å
   (B) 300

                                           (B) 100 Å

   (C) 400
                                           (C) 1000 Å


   (D) 500                                 (D) 1200 Å

                                   19                                       [P.T.O.
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68. The most suitable gates to check            70. A pulse train with a frequency of
    whether the number of ones in a                 1 MHz is counted using a modulo
    digital word is even or odd is :                1024 ripple counter built with J-K
    (A) EX-OR                                       flip-flop. For proper operations of the

    (B) NAND                                        counter the maximum permissible

                                                    propagation delay per flip-flop stage
    (C) NOR
                                                    is :
    (D) AND and OR
                                                    (A) 10 nsec
69. In the following circuit, the diode
    current flows through the resistance            (B) 20 nsec
    10 ( :
                                                    (C) 50 nsec

                                                    (D) 100 nsec

                                                71. The Bohr radius of the hydrogen

                                                    atom and the Compton wavelength

                                                    of electron are given by :
    If the voltage drop across the diode
                                                                2                  h
    is 0.7 Volt, then the diode used                (A) a               and )c    m0 c
                                                              me2
    should have minimum power rating
                                                                                    2
    nearly :                                                  h2
                                                    (B) a         and )c
                                                              me2                 m0 c
    (A) 180 mW
                                                              h
    (B) 240 mW                                      (C) a        and )c
                                                              me                 m0 c2
    (C) 280 mW
                                                                2                  h
                                                    (D) a               and )c
    (D) 350 mW                                                mc    2             m0 c2
                                           20
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                                               74. The wavelength of hydrogen
72. For a singlet state of electronic
                                                   spectrum known as Balmer series is

    system the Landé splitting factor              given by :

                                                         1   1       1
    will be :                                      (A)                    RH n = 5, 6, 7 .....
                                                         )   42      n2 !

    (A) 1                                                1      1     1
                                                   (B)                      RH n = 4, 5, 6 .....
                                                         )   32      n2 !
    (B) 3/2
                                                         1   1       1
                                                   (C)                    RH n = 3, 4, 5 .....
                                                         )   22      n2 !
    (C) 1/2
                                                         1   1      1
                                                   (D)                   R H n = 2, 3, 4 .....
                                                         )   1      n2 !
    (D) 5/2

                                               75. The rotational spectrum of 12C16O
73. Te2+ ion has two d electrons in its
                                                   and 13C16O provide the values of
    outermost shell. With the aid of
                                                   rotational constants B and B

    Hund’s rule the ground term for the            respectively. If B is 1.92 cm–1, what

    d2 system will be :                            is the value of B ?

                                                                    (h = 6.6 × 10–34 Js)
    (A) ML = 2, MS   = 1/2, Term = 2D
                                                   (A) B = 2.12 cm–1
    (B) ML = 3, MS = 1, Term = 3F
                                                   (B) B = 1.83 cm–1
    (C) ML = 2, MS = 2, Term = 5D
                                                   (C) B = 1.06 cm–1

    (D) ML = 2, MS = –1/2, Term = 2D               (D) B = 4.24 cm–1

                                          21                                           [P.T.O.
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76. For proton (1H), placed in a magnetic        78. Which of the following molecules
    field of 2.3 Tesla, the resonant                  give no infrared or microwave
    frequency observed in an NMR                      spectra but Rotational Raman
    spectrometer is (Given : gN = 5.58,
                                                      spectra ?
    # N = 5.05 × 10 –27 JT –1 and
                                                      (A) HCl, HCN
    h = 6.6 × 10–34 Js)

    (A) 100 kHz                                       (B) CO2, CH4

    (B) 1 MHz                                         (C) O2, H2

    (C) 1000 MHz                                      (D) CO, H2O

    (D) 100 MHz                                  79. Auger electron emission cannot be

77. In CO2 Laser it is possible to obtain             obtained from :

    laser radiations at wavelengths of                (A) Nickel
    9.6    m and 10.6    m. The energy
                                                      (B) Carbon
    levels corresponding to the two
    transitions are :                                 (C) Oxygen

    (A) (10°0) * (02°0) and (02°0) *                  (D) Hydrogen
          (01 0)
                                                 80. The correct order of increasing “first
    (B) (00°1) * (10°0) and (00°1) *                  ionization potential” is :
          (02°0)
                                                      (A) Li, Na, K, Rb
    (C) (02°0) * (01 0) and (01 0) *
                                                      (B) Li, Be, B, C
          (00°0)
                                                      (C) Be, Mg, Ca, Sr
    (D) (00°1) * (02°0) and (00°1) *
          (10°0)                                      (D) B, Al, Ga, In

                                            22
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81. In a powder diffraction pattern               84. If there are p atoms in the primitive
    recorded from a face centered cubic               cell, the phonon dispersion relation
    sample using X-rays, the first peak               will have :
    appears at 30°. The second peak will
                                                      (A) 3 optical phonon branches
    appear at :
     (A) 32.8°                                        (B) 3p-3 optical phonon branches

     (B) 33.7°                                        (C) 3p-1 optical phonon branches

     (C) 34.8°                                        (D) 3p optical phonon branches

     (D) 35.3°                                    85. The kinetic energy of a free electron
                                                      at a corner of the first Brillouin zone
82. A single crystal of copper contains
    a low angle tilt boundary on (001)                of a two-dimensional square lattice
    plane with a tilt axis parallel to                is larger than that of an electron at
    [010]. The tilt angle, if the spacing             the midpoint of a side of the zone
    of the dislocation in the boundary                by a factor b. The value of b is :
    is 3 × 10–6 m and their Burgers                   (A) b =     2
    vector is 0.4 × 10–9 m, is :
                                                      (B) b = 2
     (A) 2.00 × 10–4 rad
                                                      (C) b = 4
     (B) 2.60 × 10–4 rad
                                                      (D) b = 8
     (C) 0.50 × 10–4 rad
                                                  86. In a p-type semiconductor, the
     (D) 1.33 × 10–4 rad
                                                      Fermi level lies 0.4 eV above the
83. Atomic weight and density of gold
                                                      valence band. If the concentration
    are 197 and 1.9 × 10 4 kg/m 3
                                                      of the acceptor atoms is trippled and
    respectively. If the velocity of sound
                                                      kT = 0.03 eV, the new position of
    in it is 2100 m/s, the Debye
                                                      the Fermi level will be :
    temperature for gold will be :
     (A) 200 K                                        (A) 0.250 eV

     (B) 240 K                                        (B) 0.100 eV

     (C) 300 K                                        (C) 0.525 eV

     (D) 370 K                                        (D) 0.367 eV

                                             23                                      [P.T.O.
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87. In a dielectric, the power loss is              90. Considering the BCS theory of
    proportional to :                                   superconductivity, which one of
                                                        the following statements is not
    (A)
                                                        correct ?
    (B)   2
                                                         (A) Presence of energy gap at
    (C) 1/                                                   temperature below the critical
    (D) 1/ 2                                                 temperature

    where is the angular frequency of                    (B) Different critical temperatures
    applied electric field.                                  are possible for isotopes

88. If the static dielectric constant                    (C) Presence of Meissner effect can
    of NaCl is 5.6 and its optical                           be observed
    refractive index is 1.5, the ratio of                (D) Quantization of magnetic flux
    its electric polarizability to its total                 in superconducting ring in the
    polarizability is :                                      units of (h/e)
    (A) 0.5                                         91. As per the nuclear stability rule, the
    (B) 0.6                                             following nuclear decay :
                                                                5          4
    (C) 0.8                                                     3 Li   *   2 He + P

                                                         can be possible because :
    (D) 0.9
                                                         (A) The mass of 5Li is smaller than
89. The ground state of an alkali metal
                                                             the sum of the masses of 4He
    is a 2S1/2 state. The difference in
                                                             and P
    energy levels arising in the presence
    of a weak magnetic field B, given                    (B) The spin of 5Li is less than the
    in terms of Bohr magneton                                sum of the spins of 4He and P
                                          B
    is :                                                 (C) The mass of 5Li is greater than
    (A)                                                      the sum of the masses of 4He
          BB
                                                             and P
    (B) 2 BB
                                                         (D) The spin of 5Li is greater than
    (C) 4 BB
                                                             the sum of the spins of 4He
    (D) 6 BB                                                 and P
                                               24
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92. The binding energy per nucleon for          95. The beta particles emitted by a
    107Ag
         47 nuclei is nearly :
                                                    radioactive source have continuous
    [Given :
                                                    energy spectrum, with end point
    Mass of proton = 1.007825 amu
                                                    energy Emax. This is due to sharing
    Mass of neutron = 1.008665 amu
                                                    of disintegration energy by :
    Mass of silver = 106.905091 amu

    1 amu = 931.5 MeV]                              (A) Emitting nucleus and the beta

    (A) 8.10 MeV/nucleon                                particle in the form of recoil

    (B) 8.54 MeV/nucleon                                energy

    (C) 8.95 MeV/nucleon                            (B) Neutrino and gamma-ray
    (D) 9.25 MeV/nucleon
                                                    (C) Beta particle and neutron in the
93. The violation of CP invariance
                                                        nucleus
    theorem was observed in the :

    (A) Decay of beta particles                     (D) Beta particle and neutrino

    (B) Decay of alpha particles                96. A gamma-ray of 1 MeV energy is
    (C) Decay of heavy ions                         scattered by the process Compton
    (D) Decay of K° meson                           scattering. If the angle of scattering
94. A nucleus decays from its spin state            is 180°, the energy of the scattered
    5–/2 to spin state 3–/2 by emission
                                                    gamma-ray will approach to :
    of gamma-ray. The gamma-ray
    decay mode can be classified as :               (A) 0.511 MeV
    (A) E1, M2, E3, M4
                                                    (B) 0.551 MeV
    (B) M1, E2, M3, E4
                                                    (C) 0.352 MeV
    (C) E2, M3, E4, M5

    (D) E3, M4, E5, M6                              (D) 0.255 MeV

                                           25                                     [P.T.O.
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97. A comparison between HPGe and
                                                 99. The following nuclear reaction
    NaI(Tl) detectors for recording
    spectrum of gamma-rays, it is
                                                           P + P * K+ + ++
    observed that in general :
    (A) the energy resolution and                    is   not    allowed   due   to   non-
        efficiency of HPGe detector are
        higher as compared to those of               conservation of :
        NaI(Tl) detector
                                                     (A) Baryon number and isospin
    (B) the energy resolution and
        efficiency of HPGe detector are
                                                     (B) Strangeness       and    baryon
        almost the same as those of
        NaI(Tl) detector
                                                          number
    (C) for HPGe detector, the energy
        resolution is high and efficiency            (C) Charge and strangeness
        is low as compared to those of
        NaI(Tl) detector                             (D) Isospin and charge
    (D) for HPGe detector the energy
        resolution is low and efficiency         100. To obtain splitting in the nuclear
        is high as compared to those of
                                                     energy levels, the concept of spin-
        NaI(Tl) detector
98. After absorbing a thermal neutron                orbit interaction was used in the
    by 235 U nucleus, the following
                                                     nuclear :
    fission reaction is induced :
        235           90
         92 U + n   * 36 Kr + X + 2n                 (A) Liquid drop model
    The fission fragment X is :
    (A) 145La                                        (B) Collective model

    (B) 144Ce
                                                     (C) Optical model
    (C) 145Cs
    (D) 144Ba                                        (D) Shell model

                                            26
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Source: Savitribai Phule Pune University. Question paper published by Savitribai Phule Pune University.