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MH SET 2019: 23 June, Paper II, Physics

  • Date: 23 June 2019
  • Paper code: JUN-32219
  • Series: A
  • Language: Bilingual
  • 32 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 - 32219                                                                                          (To be filled by the Candidate)
Time Allowed : 2 Hours]                                                                                [Maximum Marks : 200
Number of Pages in this Booklet : 32                                                    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.
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2.         This paper consists of 100 objective type questions. Each question
           will carry two marks. All questions of Paper II will be compulsory.     2.
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2
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JUN - 32219/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.   If A       xeˆ x   yeˆ y   zeˆ j , then    2A         4.   At the origin, the function f(z) =
     will be :                                                   | xy| is not analytic because :
                                                                (A) The Cauchy-Riemann (C-R)
     (A) 1
                                                                    conditions are not satisfied at
     (B) 3                                                          origin.
     (C) 0                                                      (B) f (0) 0 and the C-R conditions
                                                                    are satisfied at origin.
     (D) – 3
                                                                (C) f (0) = 0 though the C-R
2.   If a vector field F            xiˆ 2 yjˆ 3 zkˆ,                conditions are satisfied at
     then         (     F) is :                                     origin.
     (A) Zero                                                   (D) f (0) = 0 and the C-R conditions
                                                                    are not satisfied at origin.
     (B) ĵ
                                                                           z2 dz
     (C) 2 ˆj                                              5.   I=                       , in the z-plane.
                                                                         2 1)( z2
                                                                     c (z           4)
     (D) 3kˆ
                                                                Here c is a contour as shown :
3.   A gas molecule moves equal
     distances           between successive
     collisions with equal probability in
     any direction. After a total of N such
     collisions, the mean square displace-
     ment of the molecule d 2 will be :
     (A) N                                                      then :
     (B) N 2                                                    (A) I =    /6
                                                                (B) I = – /3
     (C) N2 2
                                                                (C) I = 0
     (D) N2                                                     (D) I = /3
                                                       3                                          [P.T.O.
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6.   Consider a differential equation                  8.   A matrix is said to be of rank zero

                                                            if and only if :
              d2 x       dx
                     2        x   0
              dt 2       dt
                                                            (A) All the elements are non-zero,
     At time t = 0, it is given that x = 1
                                                                but the determinant is zero.
         dx
     and    = 0. At t = 1, the value of
         dt
                                                            (B) It is equal to its own inverse.
     x is :

     (A) 1/e                                                (C) All its diagonal elements are

     (B) 2/e                                                    zero.


     (C) 1                                                  (D) All its elements are zero.

     (D) 3/e
                                                       9.   The following Pauli spin matrices
7.   The solution of the differential
                                                                   0    1               0    –i
                 d2 y                                        x =            and   y =
     equation            – y = 0, subject to the                   1    0               i    0
                 dt 2

     boundary conditions y(0) = 1,
                                                            (A) Commute
     y( ) = 0 is :
                                                            (B) Anti-commute
     (A) cos t + sin t

     (B) cosh t + sinh t                                    (C) Do not possess commutation

                                                                relation
     (C) cos t – sin t

     (D) cosh t – sinh t                                    (D) Are inverses of each other.

                                                   4
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10. Fourier series for the function                  12. A projectile is fired with initial
                                                          velocity v0 making an angle      with
                    1     0
          f( )                       ,                    the horizontal axis. The range (R)
                  –1             2
                                                          of the projectile is proportional to,
    there are :                                           (Neglect the air resistance) :

    (A) Even cosine terms only                            (A) v0 and sin 2

    (B) Both odd sine and cosine terms                    (B) v0 and sin

    (C) Sine terms only                                   (C) v02 and sin

    (D) Odd sine terms only                               (D) v02 and sin 2

11. A circular hoop of mass ‘M’ and                  13. An artificial satellite revolves about

    radius ‘a’ rolls without slipping with                the earth at height H (H << R,

    constant angular speed               along            R = radius of earth). The orbital
                                                          period, for which a man in the
    horizontal x-axis in the x-y plane.
                                                          satellite will be in state of
    When the center of hoop is at a
                                                          weightlessness is given as :
    distance d =        2 – a from the origin,
    the magnitude of total angular                                  g
                                                          (A) 2
                                                                    R
    momentum of the hoop about the
    origin is :                                                     R
                                                          (B) 2
                                                                    g
    (A) Ma2
                                                                1   g
    (B)     2.Ma2                                         (C)
                                                                2   R
    (C) 2Ma2
                                                                1   R
                                                          (D)
    (D) 3Ma2                                                    2   g

                                                 5                                       [P.T.O.
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14. For repulsive inverse square force,
                                                      17. The radius of gyration of a rigid body
    the shape of the orbit is :

    (A) Circular                                           of mass M and moment of inertia I

    (B) Parabolic
                                                           is :
    (C) Hyperbolic

    (D) Elliptical                                         (A) (I/M)2

15. A unit charge q moving with initial
                                                           (B) (M/I)2
    velocity (v v iˆ ) is subjected to
                     x
    external electric field (E     E y j ). The
                                                           (C) (I/M)1/2
    number of degrees of freedom is :

    (A) 1
                                                           (D) (M/I)1/2
    (B) 2

    (C) Zero                                          18. The period of oscillation of the plane

    (D) 3
                                                           of Foucault’s pendulum is :
16. For a Lagrangian L( q, q, q, t), the
    equation motion is of the form :                       (" is the latitude)

          d2    L    L
    (A)            –          0                            (A) Directly proportional to the
          dt2   q!   q

          d2    L    d        L      L                            latitude (")
    (B)            –                     0
          dt2   q ! dt        q!     q
                                                           (B) Inversally proportional to sin "
          d2    L        d    L      L
    (C)                                  0
          dt2   q!       dt   q!     q
                                                           (C) Inversally proportional to cos "

          d2    L    d        L    L
    (D)            –             –        0
          dt2   q ! dt        q!   q                       (D) Directly proportional to sin "

                                                  6
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19. Two masses are connected by                  21. Current I is flowing through an
    springs (as shown in the figure). The            infinitely long wire placed along the
    potential energy matrix is :                     x-axis. The Cartesian coordinates of
                                                     the points A and B are A(2, 3, – 4)
                                                     and B = (– 8, 4, – 3). The ratio of
                                                     magnitudes of B at point A to that
                                                     at point B is :

                                                     (A) #0I


                                                           1
          2k     k                                   (B)
                                                           4
    (A)
           k     2k !
                                                           4
           2k    –k                                  (C)
    (B)                                                    1
          –k      2k !
                                                     (D) 1
           3k    –k
    (C)
          –k      3k !                           22. There is a space region where

          3k     k                                    E    E0 zˆ and B    B0 xˆ are both
    (D)                                              present. A charged particle with
           k     3k !
                                                                E0
20. A space ship is moving away from                 velocity        ˆy enters this region.
                                                                B0 !
    earth with velocity 0.4 c. It fires a
                                                     The trajectory of the particle in this
    rocket (away from earth) whose                   region is a :
    velocity is 0.5 c with respect to the
    space ship. The velocity of the rocket           (A) Straight line
    as observed from the earth is :
                                                     (B) Circle
    (A) 0.75 c
    (B) 0.80 c                                       (C) Cycloid
    (C) 0.60 c
                                                     (D) Circular helix
    (D) 0.90 c

                                             7                                     [P.T.O.
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23. The magnetic dipole moment of a                25. The magnitude of magnetic vector

    circular loop of radius R, carrying                potential at a distance r from an

                                                       ideal magnetic quadrupole is
    current I, is m. If radius is doubled
                                                       proportional to :
    and current is halved, then the
                                                       (A) r–1
    magnetic dipole moment becomes :

    (A) 4 m                                            (B) r–2

           m                                           (C) r–3
    (B)
           4
        m                                              (D) r–4
    (C)
        2
                                                   26. ABCD is a square and ‘O’ is the
    (D) 2m
                                                       point of intersection of the diagonals.
24. A rectangle of cross-sectional area
                                                       Charge Q is placed at corner A and
    ‘A’ is placed in a uniform constant
                                                       charge – Q is placed at corner C. If
    electric field E. The plane of the
                                                       electric potential at corner D is 1 V,
    rectangle makes an angle of 30° with

    the direction of the electric field. The           then the electric potential at point

    electric flux through the rectangle                ‘ ’ is :

    is :                                               (A) Zero V
    (A) AE
                                                       (B) 1 V
           AE
    (B)                                                       1
            2
                                                       (C)            V
                                                                  2
                 3
    (C) AE
                2                                                     1
                                                       (D)    1           V
    (D) Zero                                                           2!

                                               8
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27. A constant current I is flowing               29. If an electromagnetic wave is

     through a cylindrical conductor. The             propagating in a medium with

     direction of Poynting vector on the              permittivity $ and permeability #,

     curved surface is :                                         #
                                                      then         is :
                                                                 $
     (A) ẑ
                                                      (A) The refractive index of the
                                                            medium.
     (B) "ˆ
                                                      (B) The square root of the refractive
     (C) r̂                                                 index of the medium.

     (D) – rˆ                                         (C) The intrinsic impedance of the
                                                            medium.
28. Vector potential A( r , t) is such that
                                                      (D) The energy density of the wave
              – #0 Q                                        in the medium.
     r .A             · The corresponding
               4   r2
                                                  30. A plane electromagnetic wave is
     electric potential V(r , t), under
                                                      propagating through a perfect
     Lorentz gauge condition is :                     dielectric medium with dielectric
                                                      constant equal to       . The phase
           Q
     (A)                                              difference between E and B
         4 $0 r
                                                      associated with the wave is :
               Q                                      (A) Zero
     (B)
            4 $0 r 2
                                                      (B)
          Qt                                                 4
     (C)
         4 $0 r
                                                      (C)
              Qt                                             2
     (D)
            4 $0 r 2                                  (D)

                                              9                                     [P.T.O.
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31. A boy of mass 60 kg is running with                                           – 2 d2
                                                  33. The Hamiltonian H =                 – &(x)
                                                                                  2m dx 2
    a velocity 12 km/hr. The de Broglie

    wavelength associated with him is                 is given for a particle. Using the trial

    approximately (h = 6.626 × 10–34 Js) :
                                                                                                 2
                                                      wave function %trial (x) = Ae– bx

    (A) 3 × 10–32 m
                                                      (with b as the variational para-
    (B) 3 × 10–34 m
                                                      meter), the bound on the ground
    (C) 3 × 10–30 m

                                                      state energy is :
    (D) 3 × 10–31 m

                                                                                   2
32. Which of the following functions can
                                                      (Given :        x2n e – x dx
                                                                  –

    be an acceptable solution for
                                                                              '(n 1 / 2) / n 1/ 2 )
    Schrödinger equation for all values

    of x ?
                                                      (A) – m 2 / 2 2

                           2
    (A) %( x)   Ae– x
                                                      (B) – 2m 2 /            2

                       2
    (B) %( x)   Ae x

                                                      (C) – m 2 /         2
    (C) %(x) = A tan x


    (D) %(x) = A sec x                                (D) m 2 /       2


                                             10
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                                                     35. A particle is constrained to move in
34. A particle is moving in a one-

                                                         a truncated harmonic potential well

    dimensional infinite potential well of
                                                         (as shown below). Which one of the


    width a. Using a normalized trial                    following statements is correct ?


                             15
    wave function %(x) =           (a2 – x2),
                           4a5/2


    variational calculation estimate for



    4a5/2 the ground state energy is :

                                                         (A) The parity of the first excited
          5 2
    (A)                                                       state is even.
          4ma2

                                                         (B) The parity of the ground state
          3 2
    (B)
          2ma2
                                                              is even.

          3 2                                                                             1
    (C)                                                  (C) The ground state energy is
                                                                                          2
          5ma2
                                                         (D) The energy of the first excited
          5 2                                                            7
    (D)
          2ma2                                                state is
                                                                         2
                                                11                                     [P.T.O.
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                                                          37. A system described by the Hamil-
36. The wave function for an electron                                        5   2       0
                                                               tonian H = 2      5       0 is perturbed
    in a hydrogen atom is given by                                           0   0       2!

                                                                             1       1        1
      (                 (
    %( r )   %200 ( r ) 2% 211 3% 210                          by H = $ 1            1       –1    where
                                                                             1    –1          1!
                                         2%21–1                ($ << 1). A pair of eigenvalues of the
                                                               perturbed system is :
                                                               (A) 3 + 2$, 2 + $
                        (
                                                               (B) 3, 2 + 2$
    where % n           ( r ) is the wave function
                  lml                                          (C) 3, 7 + 2$
                                                               (D) 3 + 2$, 7 + 2$
    for an electron in the eigenstate                                                              1 i
                                                          38. An electron is in a state ) =         6
    (n lml). The expectation value of                                                              2 / 3!

                                                                                                         1
    z-component of angular momentum,                           where the basis functions are
                                                                                                         0!

                                  (                                  0
    <Lz> in the state %( r ) is :                              and       · The respective probabili-
                                                                      1!
                                                               ties that a measurement of Sz yields
                                                               values      / 2 and – / 2 are :
    (A) 3 / 8
                                                                     1     1
                                                               (A)     and
                                                                     2     2
    (B)      /8                                                      2     1
                                                               (B)     and
                                                                     3     3
                                                                     1     3
    (C) 11 / 16                                                (C)     and
                                                                     4     4

                                                                     1     2
    (D) 15 / 16                                                (D)     and
                                                                     3     3

                                                     12
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39. The differential scattering cross-                41. Viscosity and surface tension are :
    section for a Gaussian potential
                         2   2                            (A) Both intensive variables
    V ( r) =      V0 e– r / a , using Born
    approximation is given by                             (B) Both extensive variables
                             2
                ( )   CeD sin ( / 2)                      (C) Intensive       and    extensive
    where C and D are constants and
                                                                 variables respectively
    (C and D > 0)            ( ) is maximum
    for     =                                             (D) Extensive       and    intensive
    (A)
                                                                 variables respectively
    (B) 2
                                                      42. A capacitor of capacitance C farads
    (C) 3

    (D) 2n , where n = 0, 1, 2, ....                      is charged from a battery of emf V

40. A particle is in the normalized state                 volts. Out of the work done by the
    |% >. |% > is a superposition of                                            1
                                                          battery an amount       CV2 is stored
    energy eigen states |E0 = 10 eV >                                           2
    and |E1 = 30 eV >. The average                        in the capacitor and the rest is
    value of energy of the particle in the
                                                          released as heat. The released heat
    state |% > is 20 eV. The state |%> is :
                                                          is :
        1                        3
    (A) |E0 10 eV *                |E1 30 eV>
        2                        4                        (A) Zero
          1                       2
    (B)         |E0 10 eV>          |E 30 eV>             (B) CV 2
            3                     3 1
                                                                 CV 2
        1             3                                   (C)
    (C) |E0 10 eV> –    |E1             30 eV>                    8
        2            4

          1              1                                       CV 2
    (D)      |E0 10 eV> – |E1 30 eV>                      (D)
           2              2                                       2

                                                 13                                       [P.T.O.
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43. van der Waals equation for one mole
                         a                               45. A system consists of two identical
    of gas is    p              (V – b) = RT. The
                 V2 !
    equation for n moles would be :
                                                             particles. Each particle can occupy
                an
    (A)    p            (V – nb) = nRT
                V2 !
                                                             on l y t w o en er gy l ev el s. E 1 = $ and
                 a
    (B)    p            (V – b) = nRT
                V2 !

                                                             E2 = 2$. If the particles satisfy
                an2
    (C)    p              (V – nb) = nRT
                 V2 !

                an                                           Boltzmann statistics, the partition
    (D)    p         (V – b) = nRT
                V2 !
44. The entropy of black-body radiation                                                        1
                                                             functions would be          +           :
                     4                                                                        kB T !
    is given by S =      V1/4U3/4 where
                     3
      is a constant V is the volume and
    U is internal energy of the system.                                e–3$+
                                                             (A) z
    The temperature of the radiation
    is :

                U1/ 4                                                  1 – +$
    (A) T                                                                (e       e –2+$ )2
                 V1/ 4                                       (B) z
                                                                       2

                U1/4
    (B) T
                                                             (C) z     e–2+$     e–3+$     e–4+$
                1     U
    (C) T        4    V!

                     V
                         1/ 4
                                                             (D) z    2( e– +$   e–2+$ )
    (D) T
                     U!
                                                    14
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46. Crystaline sodium has 2 conduction          47. The number of distinct ways in


    electrons per unit cell with lattice
                                                    which 4 particles can be distributed

    constant (cube edge) 4.28 Å. In the
                                                    in 7 energy levels if (i) they are
    free-electron model the Fermi

                                                    distinguishable and (ii) if they are
    temperature is (h = 6.62 × 10–27


    ergs, c = 3 × 10 10 cm/s, m e =                 indistinguishable bosons respectively



    9.1 × 10–27 gm) :                               is :



    (A) TF = 380 K                                            7 !            7 !
                                                    (A) (i)       and (ii)
                                                              4 !          4 ! 3 !



    (B) TF = 3800 K                                 (B) ( i) 47 and (ii) 210



    (C) TF = 38000 K                                                             7 !
                                                    (C) (i) 7 ! 4 ! and (ii)
                                                                               4 ! 3 !



    (D) TF = 38 K                                   (D) (i) 74 and (ii) 210

                                           15                                        [P.T.O.
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48. One block of certain metal is at           49. An ideal monoatomic gas at

    temperature T 1 and a second                   temperature 300 K is adiabatically

    identical block is at a temperature            decompressed so that the final

    T 2. These blocks are brought in               volume is 8 times the original. The

    contact and the system is thermally            final temperature is :

    isolated from the surroundings.                (A) 150 K

    Assume that the heat capacity at               (B) 37.5 K

                                                   (C) 2400 K
    constant volume C of each block is
                                                   (D) 75 K
    independent of temperature T. The
                                               50. For one mole the van der Waals
    increase in the entropy of the
                                                   equation is
    universe, when the system comes to
                                                               a
    an equilibrium is :                                   p           (V – b)   RT
                                                              V2 !

                 T1T2                              At the critical point the pressure
    (A) Cln
               |T2 – T1|
                                                   is :
                (T1 T2 )                                          a
    (B) C ln                                       (A) Pc
                 2T1T2                                        27 b2
                                                               a
             (T1 T2 )2                             (B) Pc
    (C) C ln                                                  27b
               4T1T2
                                                              a
                                                   (C) Pc
                                                              b
                2T1T2
    (D) C ln
                T1 + T2                                       a
                                                   (D) Pc
                                                              3b
                                          16
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51. To measure the temperature below             53. A l aser beam of i n t en si t y 50 W /cm 2

    the liquid Nitrogen temperature, we               falls on a perfectly reflecting plane

    need to use :                                     mirror for an hour. The area of the

                                                      mirror is 5 cm2. The average force
    (A) Thermocouple
                                                      acting on the mirror is few :
    (B) Semiconductor diode
                                                      (A) Newtons
    (C) Transistor
                                                      (B) Milli Newtons
    (D) Thermister
                                                      (C) Micro Newtons
52. In an experiment, the acceleration
                                                      (D) Nano Newtons
    due to gravity is determined by

    measuring the time period of a               54. When the movable mirror of

    simple pendulum. If there is an error             Michelson interferometer is shifted

    of 1% in the measurement of time                  through 0.0589 mm a shift of 200

    period, the error in the value of g               fringes is observed ? The wavelength

    is :                                              of light used in Å is :


    (A) 2%                                            (A) 5885


    (B) 1%                                            (B) 5890


    (C) 0.5%                                          (C) 5895


    (D) no error                                      (D) 6000

                                            17                                          [P.T.O.
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55. Photomultiplier can detect a feeble        57. A 10 stage photomultiplier tube has

                                                   a stage gain of 4 secondary
    optical signal because of :
                                                   electrons. The overall amplification
    (A) The shape of its photocathode
                                                   of the tube is :

    (B) Multiplication of the output               (A) 10 3

        pulse                                      (B) 10 4


    (C) Multiplication of secondary                (C) 10


        electrons                                  (D) 106

                                               58. In oil rotary pump for low vacuum,
    (D) Multiplication of photons
                                                   the oil primarily serves :
56. Which of the following gauges can
                                                   (A) As a lubricant
    measure the pressure in the range
                                                   (B) To     isolate   rotating   and
    of 10–10 to 10–3 Torr ?
                                                       stationary members of the

    (A) McLeod gauge                                   group

                                                   (C) To discharge the exhaust
    (B) Pirani gauge
                                                       against atmospheric pressure
    (C) Penning gauge
                                                   (D) To prevent air from leaking into
    (D) Ionization gauge
                                                       the pump side

                                          18
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59. For a typical laboratory sizes and          61. A silicon diode dissipates 5 W of

    specification which of the following            power when the dc current of 2 Amp

    has better resolving power ?                    flows through it. The bulk resistance


    (A) Prism spectrometer                          of the diode is :


    (B) Grating spectrometer                        (A) 0.6 ,


    (C) Fabry-Perrot etalon                         (B) 0.9 ,


    (D) Constant deviation spectro-                 (C) 1.2 ,


        meter                                       (D) 2.5 ,


60. In which of the following wave-             62. For fabrication of light emitting

    length region, the sources are                  diodes, the commonly used semi-

    comparatively weak and detectors                conductor materials are :

    insensitive    requiring   Fourier              (A) Pure crystals of silicon and

    Transform methods :                                 germanium

    (A) UV                                          (B) Thin waters of SiC and GaN

    (B) VISIBLE                                     (C) GaAs 1-y Py and GaP by

    (C) Infrared                                        deposition


    (D) X-rays                                      (D) ZnSe, CdS and ZnTe in powder

                                           19                                     [P.T.O.
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                                                  65. The output voltage (V o ) of the
63. The frequency of the following phase              following Op-amp circuit is :
    shift oscillator :




                                                                                      o




    is nearly equal to :

    (A) 2 kHz                                         (A) + 2

    (B) 5 kHz                                         (B) – 2
                                                      (C) + 4
    (C) 8 kHz
                                                      (D) – 4
    (D) 10 kHz                                    66. The voltage gain for the following
                                                      amplifier circuit
64. In a power supply circuit, the a.c.
    voltage of 100-0-100 Volts r.m.s. is
    applied to diodes of the full wave
    rectifier circuit. The output of the
    diodes is connected to a load of 5 k,.
    The D.C. current through the load
    resistance of 5 k, is nearly :

    (A) 15 mA                                         is nearly equal to :
                                                      (A) 0.5
    (B) 18 mA
                                                      (B) 1.0
    (C) 21 mA                                         (C) 1.5
    (D) 25 mA                                         (D) 2.0

                                             20
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67. Negative feedback for an operational        69. In the following zener diode circuit
    amplifier leads to :

    (A) Increase the input and output
         impedance

    (B) Increase the input impedance
         and the bandwidth
                                                    the current flowing through the
    (C) Decrease the output impedance
         and bandwidth                              zener diode is :

    (D) Does not affect impedance or                (A) 40 mA
         bandwidth
                                                    (B) 60 mA
68. The output of the following logic
    circuit is :                                    (C) 80 mA


                                                    (D) 100 mA


                                                70. Among the following A to D

                                                    converter, the slowest one is the :


                                                    (A) Parallel comparator type
    (A) AB + C(D + E)

                                                    (B) Successive approximation type
    (B) (A + B)C + DE

    (C) (A + B)C + D + E                            (C) Integrating type


    (D) (AB + C).DE                                 (D) Counting type

                                           21                                    [P.T.O.
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71. Value of radius for fifth orbital of        73. In many electron atoms which of
                                                    the following statements is not
    hydrogen is (first orbital radius is
                                                    correct ?
    0.53 Å) :
                                                    (A) In heavier atoms LS coupling
    (A) 0.529 Å                                          is dominant

                                                    (B) In lighter atoms jj coupling is
    (B) 0.26 Å
                                                         dominant
    (C) 8.4 Å
                                                    (C) LS coupling occurs irrespective

    (D) 13.25 Å                                          of atomic size

                                                    (D) Electrostatic forces couple the li
72. The S, L and J values that
                                                         vectors into single L vector and
    correspond to each of the following
                                                         Si into another vector S
    states 1S0, 3P2 are :                       74. A typical PR contour for vibration-
                                                    rotational spectrum for CO molecule
    (A) S = 0, L = 0, J = 0 and S = 1,
                                                    shows -. = 55 cm–1. The associated
         L = 1, J = 2
                                                    value of rotational constant B is

    (B) S = 1, L = 0, J = 0 and S = 2,              (Given; Boltzmann const. k = 1.38 ×
                                                    10–23 J/K, T = 300, h = 6.6 × 10–34
         L = 1, J = 2
                                                    J-s) :
    (C) S = 0, L = 1, J = 1 and S = 1,
                                                    (A) 1.8 cm–1
         L = 0, J = 2
                                                    (B) 1.6 cm–1

    (D) S = 1, L = 1, J = 2 and S = 2,              (C) 2.0 cm–1

         L = 0, J = 2                               (D) 1.4 cm–1

                                           22
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75. Which of the following is not correct        77. When excited with mercury line at
    (for number of fundamental modes
                                                     435.8 nm, Benzene shows first
    of vibration) ?
                                                     Raman shift at 606 cm–1. What will
    (A) Non-linear molecule has 3N-6
                                                     be the Raman shift if excited by
         modes
                                                     He-Ne Laser (632.8 nm).
    (B) Non-linear molecule has 3N-3

         modes                                       (Given : n = 6.6 × 10–34 Js) :


    (C) Linear molecule has 3N-5                     (A) 1200 cm–1

         modes
                                                     (B) 409 cm–1
    (D) Spherical top molecule has
                                                     (C) 803 cm–1
         3N-6 modes

                                                     (D) 606 cm–1
76. Direct confirmation about the

    quantization of internal energy              78. Nuclear Magnetic Resonance (NMR)
    states of an atom was first obtained
                                                     spectrometer normally operates at :
    from :
                                                     (A) Radio frequency region
    (A) Stern-Gerlach experiments

                                                     (B) Microwave frequency region
    (B) Compton scattering experiment

    (C) Millicon oil drop experiment                 (C) Audio frequency region


    (D) Frank-Hertz experiment                       (D) Ultraviolet frequency region

                                            23                                    [P.T.O.
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79. Which of the following identity is not        81. The primitive translational vectors


     correct as regards the hybridization             of the body centered lattice are given

     of atomic orbitals to form MO :                  by

                                                      (      a ˆ             (
     (A) sp2-Trigonal – BCl3                           a =     (i   ˆj – kˆ ), b = a (– iˆ   ˆj   kˆ )
                                                             2                     2

                                                      (       a ˆ ˆ
     (B) sp-linear – CO2                                        (i – j   kˆ ),
                                                       c =
                                                              2

     (C) sp3-square planar – PtCl42–                  where a is the side of the


     (D) sp3-Tetrahedral – CH4                        conventional unit cube and iˆ, ˆj, kˆ


80. Which of the both sequences                       are orthogonal unit vectors parallel


     represent an increasing order of                 to the cube edges. The volume of the


     orbital energy ?                                 reciprocal lattice of bcc cell is :

                                                             1 3
     (A) 2p, 3s, 3p, 3d & 3s, 3p, 3d, 4s              (A)      a
                                                             2

     (B) 3s, 3p, 3d, 4s & 4s, 5s, 6s, 7s              (B) 2(2 /a)3


     (C) 3s, 3p, 4s, 3d & 5s, 3d, 4f, 4p              (C) ( /a)3


     (D) 3p, 4s, 3d, 4p & 2p, 3s, 3p, 4s              (D) (2 /3a)3

                                             24
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82. In a simple cubic crystal of lattice
                                                84. In an MX molecule, suppose M atom
    spacing a = 3 Å, a positive edge

    dislocation 1 mm long climbs down               has an ionization potential energy

    by 1 #m. The number of vacancies
                                                    5 eV and X atom has an electron
    created or lost in the crystal is :


    (A) 1.10 × 1010                                 affinity. The amount of energy

    (B) 5.00 × 1012
                                                    required to transfer an electron from
    (C) 5.00 × 1014

                                                    M to X when they are at a distance
    (D) 8.00 × 1015


83. The Debye temperature of diamond
                                                    of 5 Å is :
    is 2230 K. The molar heat capacity

    of diamond at 10 K is :                         (A) 0.50 eV

    (R = 8.314 Jmol–1K–1)
                                                    (B) – 2.88 eV
    (A) 0.025 Jkmol–1K–1


    (B) 0.175 Jkmol–1K–1                            (C) – 1.88 eV

    (C) 0.235 Jkmol–1K–1
                                                    (D) – 4.20 eV
    (D) 0.350 Jkmol–1K–1

                                           25                                    [P.T.O.
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85. A linear diatomic lattice of lattice
                                                    86. If the interatomic potential energy
    constant a with masses M and m
    (M > m) are coupled by a force                      function can be expressed as
    constant C. The dispersion relation
                                                                         A    B
    is given by                                               U(R)   –              ,
                                                                         R6   R12
      2 =       1     1
            C                                           where A and B are constants, the
                M     m!
                                                        atomic spacing R0 for which the
                       2                1/ 2
                1   1    4C2                            potential energy is a minimum is
     / C2              –     sin 2 ka
                M   m!   Mm
                                                        given by :
    Which       one   of   the   following
                                                        (A) A/4B
    statements is incorrect ?
                                                        (B) (2B/A)1/6
    (A) The atoms vibrating in trans-
         verse mode correspond to the                   (C) A2/4B
         optical branch
                                                        (D) 4B2/A
    (B) The maximum frequency of the
                                                    87. For an ideal Fermi gas in three-
         acoustic branch depends on the
         mass of the lighter atom m                     dimensions, the electron velocity vF

                                                        at the Fermi surface is related to
    (C) The dispersion of frequency in
         the optical branch is smaller                  electron concentration n as :

         than that in the acoustic branch               (A) vF 0 n2/3
    (D) No normal modes exist in the
                                                        (B) vF 0 n
         acoustic      branch    for    any
         frequency greater than the                     (C) vF 0 n1/2

         maximum frequency at k = /a                    (D) vF 0 n1/3

                                               26
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88. A phosphorous doped silicon semi-
                                                 90. A flux quantum (fluxoid) is
    conductor     (doping     density   :
    1017/cm3) is heated from 100°C to               approximately equal to 2 × 10–7
    200°C. Which one of the following
    statements is correct ?                         gauss-cm2. A type II superconductor

    (A) Position of Fermi level moves
                                                    is placed in a small magnetic field,
         towards conduction band

    (B) Position of dopant level moves              which is then slowly increased till

         towards conduction band
                                                    the field starts penetrating the
    (C) Position of Fermi level moves
         towards middle of the energy               superconductor. The strength of the
         gap
                                                    field at this point is (2/ ) × 105 gauss.
    (D) Position of dopant level moves
         towards the middle of the                  The penetration depth of this
         energy gap
                                                    superconductor is :
89. For a rare earth ion the ground state
    energy level is characterized by the
                                                    (A) 10 Å
    term value 4I9/2. The number of 4f
    unpaired electrons in this ion is :
                                                    (B) 100 Å
    (A) 2

    (B) 3                                           (C) 1000 Å

    (C) 4
                                                    (D) 1200 Å
    (D) 5
                                            27                                       [P.T.O.
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91. The wavelength of 10 MeV proton              93. Nuclear forces are :

                                                     (A) Spin dependent and have no
      is nearly equal to : (1F = 10–15
                                                         non-central part
      meter)
                                                     (B) Spin dependent and have a non-

      (A) 7 F                                            central part

                                                     (C) Spin independent and have no
      (B) 9 F
                                                         non-central part
      (C) 11 F
                                                     (D) Spin independent and have a

      (D) 13 F                                           non-central part

                                                 94. Given : Masses of 80        80
                                                                       35 Br and 34 Se
92.   The nuclear density of a 197Au
                                                     are respectively 79.918528 amu and
      nucleus is nearly :
                                                     79.916520 amu. Use 1 amu = 931.5

      [Mass of 197Au = 3.2707 × 10–25 kg,            MeV Nucleus 80              80
                                                                 35 Br decays to 34 Se

                                                     by emitting a positron. The end
                  r0   = 1.2 × 10–15 m]
                                                     point energy of the emitted positron

      (A) 3.96 × 1017 kg/m3                          is nearly :

                                                     (A) 0.511 MeV
      (B) 5.80 × 1017 kg/m3
                                                     (B) 0.84 MeV
      (C) 6.54 × 1017 kg/m3
                                                     (C) 1.84 MeV

      (D) 8.38 × 1017 kg/m3                          (D) 1.022 MeV
                                            28
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95. 1H3 nuclei undergoes beta decay at          96. A gamma-ray of 3.43 MeV energy



    a rate of 1.27 × 1017 particles/hour            undergoes pair production. The



    and produce 21 calories of heat per             electron and positron formed move



    hour in a medium. The average                   with equal kinetic energy in opposite



    energy of the beta particle emitted             direction to each other. The kinetic



    is :                                            energy of the positron is nearly :




    (A) 10.2 KeV                                    (A) 0.511 MeV




    (B) 8.5 KeV                                     (B) 1.022 MeV




    (C) 6.4 KeV                                     (C) 1.20 MeV




    (D) 4.3 KeV                                     (D) 1.40 MeV


                                           29                                    [P.T.O.
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97. A gas filled G.M. counter cannot be         98. The following nuclear reaction is
                                                    induced by bombarding neutrons on
    used to measure energy of radiation             the 13C target.
    because :                                            13C + n ( 10Be + 4He

                                                    If the R value of this reaction is
    (A) The electrons and ions produced
                                                    – 3.835 MeV, the minimum neutron
        in the counter recombine and                energy required to induce the
        therefore energy information is             reaction is nearly :
                                                    (A) 2.13 MeV
        lost.
                                                    (B) 4.13 MeV
    (B) The window of the G.M. counter
                                                    (C) 4.835 MeV
        is thick and therefore a large
                                                    (D) 5.835 MeV
        fraction of the energy of               99. The following particles
        radiation is lost while entering                K+, K–,   +,   0,   –, K0

        the counter.                                are broadly classified as :
                                                    (A) Leptons
    (C) Only a fraction of the gas atoms
                                                    (B) Quarks
        of the G.M. counter are ionised
                                                    (C) Baryons
        and therefore the energy
                                                    (D) Mesons
        information is lost.
                                                100. Considering U, d, S Quarks, the
    (D) All the atoms of the gas are                 quark content of proton and neutron
                                                     are respectively :
        ionised irrespective of the
                                                    (A) UUS and ddS
        energy of incident radiation.
                                                    (B) UdS and dSS
        The information about the                   (C) UUS and USS
        energy of the radiation is lost.            (D) UUd and Udd
                                           30
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ROUGH WORK




    31                 [P.T.O.
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ROUGH WORK




    32
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Source: Savitribai Phule Pune University. Question paper published by Savitribai Phule Pune University.