Machine-translated by Google. Questions are authored in English.
Top

MH SET 2023: 26 March, Paper II, Physics

  • Date: 26 March 2023
  • Paper code: MAR-32223
  • Series: A
  • Language: Bilingual
  • 24 pages
MH SET 2023 question paper, 26 March 2023, Paper II, Physics, page 1 of 24
Page 1 of 24
Text of page 1
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.
MAR - 32223                                                                                                (To be filled by the Candidate)
Time Allowed : 2 Hours]                                                                                [Maximum Marks : 200
Number of Pages in this Booklet : 24                                                    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
           will be given to the student. In the first 5 minutes, you are           3.
           requested to open the booklet and compulsorily examine it as
           follows :
           (i)      To have access to the Question Booklet, tear off the
                    paper seal on the edge of this cover page. Do not accept                (i)
                    a booklet without sticker-seal or open booklet.
           (ii)     Tally the number of pages and number of questions in
                    the booklet with the information printed on the cover                   (ii)
                    page. Faulty booklets due to missing pages/questions
                    or questions repeated or not in serial order or any
                    other discrepancy should not be accepted and correct
                    booklet should be obtained from the invigilator within
                    the period of 5 minutes. Afterwards, neither the Question
                    Booklet will be replaced nor any extra time will be
                    given. The same may please be noted.
           (iii)    After this verification is over, the OMR Sheet Number
                                                                                            (iii)
                    should be entered on this Test Booklet.
4.         Each question has four alternative responses marked (A), (B),
           (C) and (D). You have to darken the circle as indicated below on        4.                       (A), (B), (C)   (D)
           the correct response against each item.
           Example : where (C) is the correct response.

                              A        B                 D                                           (C)
5.         Your responses to the items are to be indicated in the OMR                                       A        B              D
           Sheet given inside the Booklet only. If you mark at any place
           other than in the circle in the OMR Sheet, it will not be evaluated.    5.
6.         Read instructions given inside carefully.
7.         Rough Work is to be done at the end of this booklet.                    6.
8.         If you write your Name, Seat Number, Phone Number or put                7.
           any mark on any part of the OMR Sheet, except for the space
                                                                                   8.
           allotted for the relevant entries, which may disclose your
           identity, or use abusive language or employ any other unfair
           means, you will render yourself liable to disqualification.
9.         You have to return original OMR Sheet to the invigilator at the
           end of the examination compulsorily and must not carry it with          9.
           you outside the Examination Hall. You are, however, allowed
           to carry the Test Booklet and duplicate copy of OMR Sheet on
           conclusion of examination.
                                                                                   10.
10.        Use only Blue/Black Ball point pen.
                                                                                   11.
11.        Use of any calculator or log table, etc., is prohibited.
12.        There is no negative marking for incorrect answers.                     12.
MH SET 2023 question paper, 26 March 2023, Paper II, Physics, page 2 of 24
Page 2 of 24
Text of page 2
MAR - 32223/II—A




2
MH SET 2023 question paper, 26 March 2023, Paper II, Physics, page 3 of 24
Page 3 of 24
Text of page 3
MAR - 32223/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.
                                                 4.   A function f(x) satisfies the
1.   Which of the following is an analytic            differential         equation

     function ?                                       d2 f    2 f ( x) ( x a), where is
                                                      dx 2
                                                      positive. The Fourier transform
     (A) z     z       (B)   z2
                                                      F(k) =          f ( x)eikx dx and solution
     (C) zz            (D)   z/ z                     f(x) of the differential equations are
                                                      respectively :
2.   Which of the following statements
                                                               eika
                                                      (A)                                               and
     is true ?                                              k2        2

                                                             1
     (A) Trace (AB) = Trace (BA)                                 e i      x a     ei      x a
                                                            2

     (B) Trace (ABC) = Trace (BAC)
                                                               eika
                                                      (B)                                               and
                                                            k2        2
     (C) Trace (ABCD) = Trace (BACD)
                                                             1
                                                                  e i      x a       ei   x a
                                                            2i
     (D) Trace (AB) = Trace (A) Trace (B)

3.   Laplace transform F(s) of a function                      eika
                                                      (C)                                               and
                                                            k2        2

     f(x) = 1, for 0   x     is equal to :                   1            x a          x a
                                                                 e               e
                                                            2
     (A) 1/s           (B)   1/s2
                                                               eika                1            x a
                                                      (D)                  and       e
     (C) s             (D)   2s                             k2        2           2

                                             3                                                        [P.T.O.
MH SET 2023 question paper, 26 March 2023, Paper II, Physics, page 4 of 24
Page 4 of 24
Text of page 4
MAR - 32223/II—A

5.   The integral                                                        8.   Consider the following probability
                                                                              density function :
                                 z   1                                         P(x) = 0 x < –2 and x > 3
                           exp     t
             1                   2   t                                            P(x) = a –2 < x < 2
                                     n 1
                                                      dt ,
            2 i                  t                                                        1
                                                                                    P(x) =  2 < x < 3
     where n is an integer and the closed                                                12
                                                                              The value of a is :
     contour is a circle enclosing the
                                                                                    11                                         1
     origin, can be used to :                                                 (A)                                  (B)
                                                                                    12                                         12
     (A) generate Hermite polynomials
                                                                                   11                 1
     (B) generate Bessel’s functions of                                       (C)              (D)
                                                                                   48                48
           first kind                                                    9.   The Green’s function G(x, x 0 )
     (C) generate Legendre polynomials                                        satisfying the equation

     (D) generate associated Legendre                                               d 2G x, x0
                                                                                                ( x x0 )
           polynomials                                                               dx 2
                                                                              with     boundary      conditions
                                           1                                  G(–L, x0) = G(L, x0) = 0 is :
6.   The value of                z exp       dz , where
                                           z
                                                                                         1
                                                                                                 L        x0       x       L        L       x       x0
     the closed contour is a unit circle                                             2L
                                                                              (A)        1
     traversed anticlockwise is :                                                                x0       L        L       x       x0       x       L
                                                                                     2L
     (A)        i                 (B)          2 i
                                                                                         1
     (C)                          (D)      0                                                     x0       L        x       L        L       x       x0
                                                                                     2L
7.   Consider vectors                      a     iˆ     5 ˆj   kˆ,            (B)        1
                                                                                                 x0       L        x       L       x0       x       L
                                                                                     2L
     b     iˆ       5 ˆj   kˆ and c        iˆ     kˆ . Which
     of the following statements is true ?                                           1
                                                                              (C)            x        L        x       L       L        x       L
                                                                                    2L
     (A) a, b, c are linearly independent
                                                                                         1
     (B) a, b, c are linearly dependent                                                          x0       L        x       L        L       x       x0
                                                                                     2L
     (C) a, b, c are orthogonal                                               (D)        1
                                                                                                 x0       L        x       L       x0       x       L
     (D) a, b, c are normalized                                                      2L

                                                                     4
MH SET 2023 question paper, 26 March 2023, Paper II, Physics, page 5 of 24
Page 5 of 24
Text of page 5
MAR - 32223/II—A

10. Two students solved the Poisson’s                         12. The order of magnitude of the error

                     2            0                               in estimating the value of integral
    equation                            (the symbols
                                  0                                10
                                                                   0
                                                                      (5 x   6)dx numerically using
    have usual meanings). They obtained
                                                                  trapezoidal method with a step size
                                                      2
    two different answers
                                               1   0x             of 0.1 is :
                                      1 ( x)
                                               2    0             (A) 0                    (B)       10–2
                                2                                 (C) 10–3                 (D)       10–1
                         1   0y
    and     2 ( y)                    . What is the           13. The deflection of a structure under
                         2    0
                                                                  loading is measured at five different
    reason ?
                                                                  values of the force applied X in kilo
    (A) Space is isotropic, hence x and                           Newtons (kN). The deflection Y is in
                                                                  centimetres. Data are given in the
          y are equivalent                                        following    table.   Employing
                                                                  Lagrange’s interpolation with
    (B) We       can         add        solution     of
                                                                  quadratic polynomial, compute the
          Laplace’s equation to both                              extrapolated value of the deflection
                                                                  Y for zero load (X = 0 kN). How many
    (C) The boundary conditions are                               points are used ?
          different in the two cases

    (D) One of them was wrong
                                                                  (A) 4.05, 2              (B)       2.50, 3
11. The equation tan (2x) = x2 – 4 has :                          (C) 2.00, 4              (D)       2.00, 5
                                                              14. Which of the following equations
    (A) One real root                                             represents a conservative force ?

    (B) Two real roots                                            (A) F      ( xy    z 2 ) iˆ    x2 jˆ     2 xzkˆ
                                                                  (B) F      (2 xy     z2 ) iˆ     x2 jˆ    2 xzkˆ
    (C) No real root
                                                                  (C) F      ( xy    z2 ) iˆ     x2 ˆj     2 xzkˆ
    (D) Infinitely many real roots
                                                                  (D) F      ( xy    z2 ) iˆ     x 2 ˆj    2 xzkˆ

                                                          5                                                   [P.T.O.
MH SET 2023 question paper, 26 March 2023, Paper II, Physics, page 6 of 24
Page 6 of 24
Text of page 6
MAR - 32223/II—A

15. For a particle moving under the
                                                  17. A circular platform is rotating with
    action of a central force, the correct
    relation between the energy (E) of
                                                      uniform angular speed             counter-
    the particle, eccentricity (e) of the
    conic section describing the orbit,
                                                      clockwise about an axis passing
    reduced mass ( ), angular
    momentum ( l ), and the force
                                                      through         its      center       and
    constant (k) is given by :
                k2 2                                  perpendicular to its plane (as shown
     (A) E         (e 1)
              2l 2
                k2                                    in figure). A person of mass m walks
    (B) E          (1 e2 )
               l2
                k2                                    radially inwards with a uniform
    (C) E          (1 e2 )
               l2
                k2 2                                  speed v on the platform. The
    (D) E          (e   1)
              2l 2
16. Consider two frames XYZ and xyz                   magnitude and direction of the
    having common origin. The frame
    XYZ is fixed and the frame xyz is                 Coriolis force (with respect to the
    rotating with angular velocity ( )
                                                      direction along which the person
    with respect to the frame XYZ. Here
        2txˆ 5t 2 zˆ , where t represents             walks) is :
    time. For a given position vector ( r )
    defined as r 4 t 2 xˆ 6tyˆ t 3 zˆ in
    the xyz coordinate frame, the
    velocities in frames XYZ and xyz for
    t = 1, will be respectively :
    (A) 8 xˆ 6 ˆy 3 zˆ               and
         38 xˆ 16 ˆy 15 zˆ                            (A) mv    towards his right
    (B) 38 xˆ 16 ˆy 15 zˆ            and
         8 xˆ 6 ˆy 3 ˆz                               (B) 2mv       towards his right
    (C) 8 xˆ 6 ˆy 3 ˆz               and
         38 xˆ 16 yˆ 15 zˆ                            (C) mv    towards his left
    (D) 38 xˆ 16 ˆy 15 zˆ            and
          8 xˆ   6 ˆy   3 ˆz                          (D) 2mv       towards his left

                                              6
MH SET 2023 question paper, 26 March 2023, Paper II, Physics, page 7 of 24
Page 7 of 24
Text of page 7
MAR - 32223/II—A

18. Consider an inverted pendulum                19. A mass spring system consists of two
                                                     blocks of mass M and one block of
   comprised of a mass m attached to
                                                     mass m (<M). The blocks are
   a rigid massless rod of length l as
                                                     connected with two springs of same
   shown in figure. The point ‘O’                    spring constant (k), as shown in
   exhibits vertical motion (along                   figure. The system is constraint to
                                                     move along a straight line on a
   z direction) described by equation
                                                     frictionless horizontal surface. Let V
   z = a sin t, where         is constant.
                                                     represent the potential energy of the
   The Lagrangian of the system is                   system. Considering that the masses
   given as :                                        are exhibiting small oscillations, the
                                                     potential energy matrix (V) is given
                                                     as :




                                                              k     k            0
                                                         1
           1                                         (A) 2     k   2k             k
   (A) L     ml 2 2
           2                                                  0         k        k
                m( g   a 2 sin t)l cos
                                                              k    0              k
           1                                             1
   (B) L     m(l 2 2     a2 2 cos 2     t)           (B) 2    0    2k            k
           2
                                                               k    k            0
                               –mgl cos
           1                                               k        k        0
   (C) L     m(l 2 2     a2   2 sin 2   t)               1
           2                                         (C) 2 k       2k        k
                               –mgl cos                    0        k        k

           1
   (D) L     ml 2 2                                            k    0            k
           2                                             1
                                                     (D) 2    0    2k            k
                m( g   a 2 cos t)l cos                        k     k            k

                                             7                                        [P.T.O.
MH SET 2023 question paper, 26 March 2023, Paper II, Physics, page 8 of 24
Page 8 of 24
Text of page 8
MAR - 32223/II—A

20. Consider two persons A and B of             23. Hamilton’s principal function S and
    same age, 20 years. Person A                    Hamilton’s characteristic function W
    remains rest at origin, whereas                 for a conservative system, are related
    person B takes a roundtrip space                as :
    voyage to a star with velocity                  (A) S(qk, t) = W (qk) – E
    v = 0.99c relative to person A (where           (B) S(qk, t) = W (qk) + E
    c is the speed of light). The round             (C) S(qk, t) = W (qk) + Et
    trip distance travelled by the person
                                                    (D) S(qk, t) = W (qk) – Et
    B is 20 light years. When B meets
                                                24. For a particle moving in an inverse
    A after completion of the space
                                                                                    K
    voyage, their ages are :                        square force field, V(r )         , the
                                                                                    r
    (A) A : 40.2 yrs, B : 40.2 yrs
                                                    action angle variable analysis gives :
    (B) A : 40.2 yrs, B : 22.8 yrs
                                                    (A) only one frequency of oscillation
    (C) A : 22.8 yrs, B : 22.8 yrs
    (D) A : 40.8 yrs, B : 40.2 yrs                  (B) two similar frequencies of
21. The number of degrees of freedom                       oscillation
    describing motion of a swimmer in
                                                    (C) two dissimilar frequencies of
    a swimming pool is :
                                                        oscillation
    (A) 3             (B)   5                       (D) more than two dissimilar
    (C) 6             (D)   9                           frequencies of oscillation

22. For a conservative dynamical                25. If J is the current density and       is
    system, the area enclosed by the                the electric charge density, then
    phase space :                                   equation        j         0 represents :
                                                                          t
    (A) Increases with time
                                                    (A) wave equation
    (B) Remains constant with time
                                                    (B) continuity equation
    (C) Decreases with time                         (C) Poisson’s equation
    (D) Oscillates with time                        (D) Laplace’s equation

                                            8
MH SET 2023 question paper, 26 March 2023, Paper II, Physics, page 9 of 24
Page 9 of 24
Text of page 9
MAR - 32223/II—A

26. If the potential function is a step         29. When a monoatomic gas atom is
    function, the relevant equation is :
                                                    placed in a uniform electric field, the
    (A) Laplace’s equation
                                                    resulting induced dipole moment is :
    (B) Poisson’s equation

    (C) Maxwell’s equation                          (A) proportional to E

    (D) Ampere’s equation                           (B) proportional to E2
27. An electric field applied along the
                                                    (C) proportional to E3
    length of a long circular cylinder
    produces a polarization P. The                  (D) independent of E
    depolarization field produced in this
    configuration is :                          30. The reflection coefficient k r ,

    (A) 4 P / 3       (B)   –4 P / 3                characteristic impedance Z0, and

    (C) 2 P           (D)   0                       load impedance ZL of a transmission

28. The    electric      field   of    an           line are connected together by the
    electromagnetic         wave       is
                                                    relation :
    E i 2 sin(kz     t)  V/m.    The
    average flow energy per unit area                            ZL   Z0
                                                    (A) kr       Z0   ZL
    per unit time, due to this wave is :
                                                                  Z LZ 0
    (A) 27 × 104 W/m2                               (B) kr       Z0 Z L

    (B) 27 × 10–4 W/m2                                           ZL – Z0
                                                    (C) kr       Z0   ZL
    (C) 27 × 10–2 W/m2
                                                                 ZL – Z0
    (D) 27 × 102 W/m2                               (D) kr        Z 0Z L


                                            9                                        [P.T.O.
MH SET 2023 question paper, 26 March 2023, Paper II, Physics, page 10 of 24
Page 10 of 24
Text of page 10
MAR - 32223/II—A

31. Using Biot-Savart law, the magnetic                   34. Charge Q is divided into two parts
    induction at a distance d, from an                        which are then kept at distance d
    infinitely long straight wire in which
                                                              apart. The force between them will
    current I is flowing along the
                                                              be maximum if the charges on two
    z-direction, is :
                                                              parts are :
    (A) (M 0 / 4 )kˆ
                                                              (A) Q/4 and 3Q/4
    (B) (M 0 / 4 )(2I / d) kˆ

    (C) (M 0 / 4 )(I / d) kˆ                                  (B) Q/3 and 2Q/3

    (D) (M0I / 4 )kˆ                                          (C) Q/2 and Q/2
32. Magnitude of electric field at large                      (D) any q 1 and q 2 such that
    distance r, from an ideal electric
                                                                  q1 + q2 = Q; q1 > 0, q2 > 0
    dipole is proportional to :
                                                          35. For uniformly charged solid sphere
    (A) r 2                 (B)    r–2
                                                              of radius R, which of the following
    (C) r –3                (D)    r–4
                                                              statements is correct about the
33. At the uncharged interface between
    two       linear    dielectrics         with              magnitude of electric field at a

    permitivities       1    and     2,   electric            distance r from the center of the
    fields E1 and E2 make angles 1                            sphere ?
    and 2 with the normal. The ratio
                                                              (A) E = 0 for r < R
     1 / 2 is equal to :
                                                              (B) E = non-zero constant for
    (A) tan 1/tan 2
                                                                  r < R
    (B) sin 1/sin 2

    (C) cos 1/cos 2                                           (C) E proportional to r, for r < R

    (D) cot 1/cot 2                                           (D) E proportional to 1/r, for r < R

                                                     10
MH SET 2023 question paper, 26 March 2023, Paper II, Physics, page 11 of 24
Page 11 of 24
Text of page 11
MAR - 32223/II—A

36. A particle of mass m is confined in           38. For a one-dimensional harmonic

    a three-dimensional cubical box of                oscillator, a+ and a are raising and
    size L. The number of eigenstates
                                                      lowering operators and |n > is the
    of the Hamiltonian with energy
    19 2 2                                            nth energy eigenstate.             Then
           is :
     mL2
                                                      a+ a|n + 1> is equal to :
    (A) 10                        (B)    4

    (C) 3                         (D)    9            (A) (n 1)| n


37. Consider an anisotropic two-                      (B) n|n + 1>

    dimensional oscillator given by the
                                                      (C)        n n 1 |n 1
    Hamiltonian

               2         2          2                 (D) (n + 1)|n + 1>
    H =
              2m         x2         y2
                                                  39. If     A    and    B    are   quantum
            1
              m 2x2               2m 2 y 2
            2                                         mechanical         operators,      then

    The eigen energy of the oscillator is                  A, B ! , B, A ! ! is equal to :
    given by :
                                                      (A) A B B A        BA AB
    (A) E n        (n    3 / 2)
                                                      (B) 0
    (B) E n        (n    1)

    (C) E n        (2n       1)                       (C) A A B         BBA

    (D) E n        (n    2 / 3)                       (D) [A, B]2

                                             11                                         [P.T.O.
MH SET 2023 question paper, 26 March 2023, Paper II, Physics, page 12 of 24
Page 12 of 24
Text of page 12
MAR - 32223/II—A

40. Sixteen non-interacting electrons                  42. A hydrogen atom is perturbed by a
    are confined in an infinite box of side                potential H1 = bx2. The first order
    a. The energies of the least energetic                 correction to ground state energy is
    and the most energetic electrons in                    (a0 is the Bohr radius) :

    the ground state of the system are :                   (A) ba02            (B)   2ba02

             2 2
                                                           (C) ba02/2          (D)   ba02/4
              32 2 2
    (A)     ,                                          43. Consider a particle of mass m in a
        2ma2 ma2
                                                           one-dimensional box with walls at
              32     2 2
    (B) 0,                                                 x = 0 and x = L with ground state
               ma2
                                                           energy E1. If the separation between
             2 2          2 2                              the walls is adiabatically (slowly)
    (C)            2
                     ,
            2ma          2ma2                              increased to 2L, the change in the
                                                           ground state energy is given by :
             2 2
               128 2 2
    (D)      ,
        2ma2     ma2                                                                 2
                                                           (A) 0               (B)     E
                                                                                     3 1
41. Using the triangular trial wave
    function :                                                    3                  3
                                                           (C)      E          (D)     E
                                                                  8 1                2 1
             Ax                 for 0   x   a/2
                                                       44. In scattering theory of spherically
                                a
   " ( x)    A (a        x) for    x a                     symmetric potential, the incident
                                2
             0              otherwise                      particles on z-axis are represented
                                                           by :
    an upper bound on the ground state
    energy of the one-dimensional                          (A) A exp (ikz)
    infinite square well is :
                                                                   exp(ikz)
                                                           (B) A
            8 2                         7 2                           r
    (A)                         (B)
            ma 2                        ma2                (C) A r exp (ikz)

            6 2                         5 2                        exp(ikz)
    (C)                         (D)                        (D) A
            ma 2                        ma2                          r2

                                                  12
MH SET 2023 question paper, 26 March 2023, Paper II, Physics, page 13 of 24
Page 13 of 24
Text of page 13
MAR - 32223/II—A
                                                  47. For Klein-Gordon equation, the
45. Using WKB approximation, the
                                                      probability current density is given
    allowed energies En, (n = 1, 2, 3...)             by :
    for a one-dimensional harmonic                           i c
                                                      (A)        " "* "* "
    oscillator are :                                         2m
                                                              i
                1                                     (B)       " "* "* "
    (A)   n                                                  2m
                2
                                                              i
                                                      (C)       " "*       "* "
                1                                            2m
    (B)   n
                2                                           i
                                                      (D)        " "* "* "
    (C) (2n – 1)                                           2mc
                                                  48. A particle of mass m is confined in
    (D) (2n + 1)                                      an infinite square well with a shelf
46. Two Stern-Gerlac apparatus S1 and                 of height V0 extending half way
                                                      across so that :
    S2 are kept along the z-axis with the
                                                                V0    for 0 # x # a / 2
    directions of their magnetic fields
                                                                           a
                                                        V( x)   0      for # x # a
    along the positive x and y directions                                  2
                                                                      otherwise
    respectively. Each apparatus allows
                                                      Using WKB approximation, the
    only those particles to pass which                allowed energies En (n = 1, 2, 3,....)
    have their spins aligned in the                   for this particle are,          (given

    direction of its magnetic field. If an             E0n   n2 2 2 / 2ma2 are the energies

    unpolarised beam of spin ½ particles              of particle in an infinite well with
                                                      no shelf) :
    is made incident on S1, the ratio of
                                                      (A) E0n    V0
    the intensities Ii : If of the initial
                                                      (B) E0n    V0 / 2
    and final beams is :                                         V0         V0
                                                           0
                                                      (C) E n    2
                                                                      1
                                                                           4E0n
    (A) 8 : 1          (B)   4 : 1
                                                           0
                                                                 V0         V0
    (C) 1 : 0          (D)   2 : 1                    (D) En     2
                                                                      1
                                                                           8E0n

                                             13                                       [P.T.O.
MH SET 2023 question paper, 26 March 2023, Paper II, Physics, page 14 of 24
Page 14 of 24
Text of page 14
MAR - 32223/II—A

49. In a one-dimensional random walk,             52. The temperature T of a blackbody
                                                      enclosure is doubled, then the total
    the probability of step of unit length
                                                      number of photons inside the
    in positive direction is 2/3 and in               enclosure increases by a factor of :
    negative direction is 1/3. The mean               (A) 2             (B)   4
    displacement of the walker after n                (C) 8             (D)   16
    steps is :                                    53. For an adiabatic process involving
                                                      gas     having   volume       V   and
    (A) n/8             (B)   2n/3
                                                      temperature T, which of the
    (C) n/3             (D)   0                       following        is          constant
50. In a two-state system, one with                   (here $ = Cp/Cv) :

    energy 0 and other with energy                    (A) TV            (B)   TV $
                                                      (C) TV $ –1       (D)   T$V
        0 . The system will have both
                                                  54. Helmholtz free energy function is
    the levels equally occupied when :                defined by :
    (A) T = 0                                         (A) F = U + TS
                                                      (B) F = U – TS
    (B) T is infinite
                                                      (C) F = U + PV
    (C) T is very low                                 (D) F = U + PV – TS
    (D) T is very high
                                                  55. The Maxwell-Boltzmann distribution
51. A system of three indistinguishable               holds for :
    particles has a total energy of 4 .               (A) distinguishable particles
                                                      (B) all indistinguishable particles
    There are four single particle energy
                                                      (C) particles with half integral spin
    states with energies 0, , 2 and 3 .               (D) particles with integral spin
    The number of microstates accessible          56. For all the quantum states with
                                                      energy greater than Fermi energy
    to the system will be :                           to be empty in a Fermi-Dirac system,
                                                      the temperature should be :
    (A) 4               (B)   1
                                                      (A) 273 K         (B) 373 K
    (C) 2               (D)   3                       (C) 0 K           (D)   100 K

                                             14
MH SET 2023 question paper, 26 March 2023, Paper II, Physics, page 15 of 24
Page 15 of 24
Text of page 15
MAR - 32223/II—A

57. Fluctuation of magnetization M,               60. For the following transistor circuit
                      # M2          #M   2            assume VBE = 0.7V, 'dc = 100; then
    given as % M
                          #M                          the current flowing through RE is :
    for N magnetic moments with two
    allowed orientation & M in an
    external field H at temperature T
    is :
                      1
    (A) % M
                            H
                 N cosh
                           KT
                      1
    (B) % M
                            H
                 N tanh                               (A) 4.0 mA
                           KT
    (C) % M 1 / N                                     (B) 8.0 mA
                                                      (C) 4.3 mA
                      1
    (D) % M                                           (D) 3.6 mA
                         H
                 N sinh                           61. For the following differential
                        KT
                                                      amplifier circuit, the output voltage
58. Consider ideal Fermi gas in three
                                                      Vout is :
    dimensions. The density of energy
    states   is proportional to :
    (A)   1/ 2       (B)        –1 / 2

    (C)   0          (D)        2


59. Consider a system of two Ising spins

    S1 and S2 taking values & 1 with
    interaction energy E = –JS1S2. For
    large temperature T, the average                  (A) +10.0 V
    energy of the system varies as
                                                      (B) –10.0 V
    C/(kBT) with C given by :
                                                      (C) –1.0 V
    (A) –J2          (B)     –2J2
                                                      (D) +1.0 V
    (C) J 2          (D)     4J2

                                             15                                     [P.T.O.
MH SET 2023 question paper, 26 March 2023, Paper II, Physics, page 16 of 24
Page 16 of 24
Text of page 16
MAR - 32223/II—A

62. In the following circuit, the              64. The following digital circuit acts
    transistor functions as :                      as a :




                                                   (A) Half-Subtractor
    (A) OR gate       (B)   AND gate               (B) Half-Adder
                                                   (C) Half-Adder/Subtractor
    (C) NOR gate      (D)   NAND gate              (D) 2’s   complement      Adder/
                                                       Subtractor
63. Identify the function ‘F’ generated
                                               65. For the following diode circuit, the
    by the logic network shown                     voltage drop across each diode is
                                                   0.7 V. The current flowing through
    below :                                        the resistor R is .............




    (A) F = (A + B) C

    (B) F     C   B   BA
    (C) F = BC (B + A)
    (D) F = ABC                                    (A) +10.1 mA     (B)   –10.1 mA
                                                   (C) +8 mA        (D)   –8 mA
                                          16
MH SET 2023 question paper, 26 March 2023, Paper II, Physics, page 17 of 24
Page 17 of 24
Text of page 17
MAR - 32223/II—A

66. When the modulating signal controls         69. The difference between the indicated
                                                    value and true value of a quantity
    the amplitude of a carrier wave, it
                                                    is known as :
    is known as :
                                                    (A) Gross error
    (A) frequency modulation
                                                    (B) Absolute error
    (B) amplitude modulation
                                                    (C) Dynamic error
    (C) phase modulation                            (D) Relative error
    (D) pulse amplitude modulation              70. The ratio of frequencies of the first

67. A digital multimeter normally uses :            line of the Lyman series and the first
                                                    line of the Balmer series is :
    (A) Flash ADC
                                                    (A) 4/27           (B)    8/27
    (B) counter ADC
                                                    (C) 27/5           (D)    27/8
    (C) Successive approximation ADC
                                                71. The     number     of    fundamental
    (D) Duel slope ADC
                                                    vibrational modes of CO2 molecule
68. Which of the following gauge is used            is :

    to calibrate gauges employed to                 (A) Four : 2 are Raman active and

    measure low pressure of the order                      2 are infrared active

    of 1.0 × 10–6 torr ?                            (B) Four : 1 is Raman active and
                                                           3 are infrared active
    (A) Pirani gauge
                                                    (C) Three : 1 is Raman active and
    (B) Penning gauge
                                                           2 are infrared active
    (C) Thermocouple gauge
                                                    (D) Three : 2 are Raman active and
    (D) McLeod gauge                                       1 is infrared active

                                           17                                        [P.T.O.
MH SET 2023 question paper, 26 March 2023, Paper II, Physics, page 18 of 24
Page 18 of 24
Text of page 18
MAR - 32223/II—A

72. A Co2+ ion has the spectroscopic             75. Frank-Condon principle predicts
    term factor :
                                                     large intensity spectral line for
    (A) 6S 5/2         (B)   4F
                                  3/2                electronic transitions :
    (C) 5D0            (D)   4F
                                  5/2
                                                     (A) in monoatomic gases
73. The coherence length of laser light
    is :                                             (B) between the vibrational energy

    (A) directly proportional to the                     levels of any electronic state

           length of the active lasing               (C) between the vibrational energy
           medium
                                                         levels of two electronic states of
    (B) inversely proportional to the
                                                         a    constant      internuclear
           width of the spectral line
                                                         separation
    (C) directly proportional to the
           width of the spectral line                (D) between the v = 0 vibrational

    (D) inversely proportional to the                    levels of the two electronic states
           length of the active lasing           76. If the average separation between
           medium
                                                     the adjacent lines in the rotational
74. The gN value for F19 nucleus is
                                                     IR spectrum of CO molecule is 3.844
    5.256. If it is placed in a magnetic
                                                     cm–1, then the value of rotational
    field of strength 1.0 T, the relative
    population in two spin states at 300             constant is :

    K will be,                                       (A) 7.688 cm–1
    (Given N = 5.05 × 10–27 JT–1 and
                                                     (B) 1.922 cm–1
    k = 1.38 × 10–23 JK–1) :
                                                     (C) 3.844 cm–1
    (A) 1.0            (B)   2.0

    (C) 0.5            (D)   2.5                     (D) 5.766 cm–1

                                            18
MH SET 2023 question paper, 26 March 2023, Paper II, Physics, page 19 of 24
Page 19 of 24
Text of page 19
MAR - 32223/II—A

                                               79. The D 1 and D 2 lines of sodium
77. An electron in atomic hydrogen has
                                                    (2P1/2 ( 2S1/2 and 2P3/2 ( 2S1/2)
    g = 2.0032. In an ESR spectrometer              will split on application of a weak

    at 9.250 GHz, two lines from the H              magnetic field into :

                                                    (A) 3 lines each
    atom appeared at 353.3 mT and
                                                    (B) 6 lines each

    306.6 mT. The hyperfine coupling                (C) 4 lines each

                                                    (D) 4 and 6 lines, respectively
    constant will be :
                                               80. The first reflection from FCC crystal
    (A) 1.6 × 109 Hz
                                                    is observed at Bragg angle       = 21.5º,

                                                    the    corresponding to the second
    (B) 1.6 × 1010 Hz
                                                    reflection is :
    (C) 3.2 × 109 Hz
                                                    (A) 13.5º          (B)   18.5º

    (D) 3.2 × 1010 Hz                               (C) 25.0º          (D)   36.8º

                                               81. A pair of Li+ and Cl– ions, with their
78. Relative intensities of successive
                                                    radii 0.60 Å and 1.81 Å respectively,

    lines in the observed Raman spectra             touch each other. The attractive

                                                    force between them is :
    of nitrogen molecule is :
                                                    (A) 1.96 × 10–9 N

    (A) 3 : 4        (B)   1 : 2                    (B) 2.96 × 10–9 N

                                                    (C) 3.96 × 10–9 N
    (C) 2 : 3        (D)   1 : 3
                                                    (D) 4.96 × 10–9 N

                                          19                                         [P.T.O.
MH SET 2023 question paper, 26 March 2023, Paper II, Physics, page 20 of 24
Page 20 of 24
Text of page 20
MAR - 32223/II—A

82. Heat capacity Cv of a metal is                       85. A solid superconductor of type I is
    measured      as       a    function       of            placed in an external magnetic field
    temperature        T       in       the   low            and is then cooled below its critical
    temperature region. Assume that                          temperature. The superconductor :
    the measured Cv is due to both                           (A) retains its magnetic flux
    electronic and lattice contributions,                         because the surface current
    then the plot of (Cv/T) versus T is :                         supports it

    (A) linear in T                                          (B) expels out its magnetic flux
                                                                  because it behaves like a
    (B) quadratic in T
                                                                  paramagnetic material
    (C) cubic in T
                                                             (C) expels out its magnetic flux
    (D) inversely proportional to T
                                                                  because it behaves like an
83. The number of independent elastic                             antiferromagnetic material
    constants in an isotropic cubic solid                    (D) expels out its magnetic flux
    is :                                                          because the surface current
    (A) 1              (B)          2                             induces a field in the direction
    (C) 3              (D)          4                             opposite to the applied field

84. For an intrinsic semiconductor, me*                  86. The dispersion relation for a simple
    and m h * are respectively the                           cubic crystal is given by :
    effective masses of electrons and
                                                              E(k)     E0    2'
    holes near the corresponding band
                                                                     (cos kx a    cos ky a   cos kz a) ,
    edges. At a finite temperature, the
    position of the Fermi level :                            where ' is constant having
    (A) depends on me* but not on mh*                        dimension of energy and ) is lattice
                                                             constant. The width of the energy
    (B) depends on mh* but not on me*
                                                             band is :
    (C) depends on both me* and mh*
    (D) depends neither on me* nor on                        (A) 2'                  (B)     4'

           mh *                                              (C) 8'                  (D)     12'

                                                    20
MH SET 2023 question paper, 26 March 2023, Paper II, Physics, page 21 of 24
Page 21 of 24
Text of page 21
MAR - 32223/II—A

87. Consider the energy E in the                 89. If the static dielectric constant of
                                                     NaCl crystal is 5.6 and its optical
    Brillouin zone as a function of the
                                                     refractive index is 1.5, the ratio of
    magnitude of the wave vector k for
                                                     its ionic polarizability to its total
    a crystal of lattice constant ‘a’.               polarizability is :
    Then :
                                                     (A) 0.5             (B)   0.7
    (A) the slope of E versus k is                   (C) 0.8             (D)   0.9
        proportional to the group
                                                 90. A lattice is characterized by the
        velocity                                     following     primitive         vectors
                                                     a 2(iˆ ˆj ),          b         2( ˆj kˆ ),
    (B) the slope of E versus k has its
                                                     c 2(kˆ iˆ ) .
        maximum value at k             /a
                                                     The reciprocal lattice corresponding
    (C) the plot of E versus k will be               to the above is :
        parabolic in the interval                    (A) fcc with cube edge 2
             /a#k#    /a                             (B) bcc with cube edge

    (D) the slope of E versus k is non-              (C) bcc with cube edge 2
        zero for all k in the interval               (D) fcc with cube edge
             /a#k#    /a
                                                 91. What is the binding energy per
                                                                         55
88. Eu 3+ ion has outer electronic                   nucleon for isotope    Mn ?
                                                                         25
    configuration 4f65s25p6. Its ground
                                                     (Given : M N = 1.008665 amu,
    state is characterized by one of the                                       55
                                                     M p = 1.007825 amu,
    following spectroscopic terms :                                            25
                                                     Mn = 54.938050 amu)

    (A) 7F 0         (B)   8S
                                7/2                  (A) 8.7 MeV         (B)   9.2 MeV

    (C) 7F 6         (D)   6H
                                15/2
                                                     (C) 9.5 MeV         (D)   9.9 MeV

                                            21                                        [P.T.O.
MH SET 2023 question paper, 26 March 2023, Paper II, Physics, page 22 of 24
Page 22 of 24
Text of page 22
MAR - 32223/II—A

92. What should be the energy required,            95. The quark content of baryon * 0
                                                       with strangeness S = –2 is given by :
    if an electron is used as a probe for
                                                        (A) u s s          (B)   d s s
    studying the nuclear structure,
                                                        (C) d s s          (D)   u s s
    shape and distribution. (Consider
                                                   96. Experimentally it is observed that
    nuclear radius is 10–13 cm) :                      neutron (n)-proton(p) system
                                                       (deuteron) is bound, but the proton-
    (A) 0.1 GeV        (B)    0.2 GeV                  proton and neutron-neutron systems
                                                       are not bound. This is due to :
    (C) 0.3 GeV        (D)    0.4 GeV
                                                        (A) unequal nuclear force between
93. To penetrate the Coulomb barrier of                     n-p, n-n and p-p systems
    a light nucleus ( 11 H ), a proton must             (B) unequal total charges of n-p,
                                                            n-n and p-p systems
    have a minumum energy of the
                                                        (C) Pauli’s principle
    order of (Consider radius of nucleus
                                                        (D) non-conservation of angular
    ~ 1Fm) :
                                                            momentum
    (A) 1.44 TeV       (B)    1.44 GeV             97. In the nuclear shell model, orbitals
                                                       are filled in the following order
    (C) 1.44 MeV       (D)    1.44 KeV                 1s       1         1      1      2
                                                          1/2 , p 3/2 , p 1/2 , d 5/2 , s 1/2 ,
                                                       1d
94. What is the energy released in the                    3/2 , .......... etc. The splitting
                                                       between the p3/2 and p1/2 orbitals
    following nuclear reaction :
                                                       is caused by :
         6 Li + 2H ( 2 4 He   Q
         3      1      2                                (A) angular momentum of the
    (Given      :     6 Li = 6.01693 amu,                   nucleus
                      3
    2                                                   (B) only the spins of the nucleus
    1 H = 2.01471 amu,
    4 He = 4.00388 amu )                                (C) spin-orbit coupling of the
    2
                                                            nucleus
    (A) 11.4 MeV       (B)    22.4 MeV
                                                        (D) angular momentum and spin of
    (C) 33.4 MeV       (D)    44.4 MeV
                                                             the nucleus
                                              22
MH SET 2023 question paper, 26 March 2023, Paper II, Physics, page 23 of 24
Page 23 of 24
Text of page 23
MAR - 32223/II—A

98. Based on the additive quantum
                                                 100. Parity    non-conservation     was
    numbers such as strangeness (S),

    baryon number (B), charge (Q), and               established in '-decay when it was

    isospin (I), indicate for which among
                                                     observed that from polarised Co66
    the four options given below, the

    following nuclear reaction cannot be             nuclei :
    induced
                                                     (A) electrons were emitted equally
           +    n ( +º   K

    (A) Q, B, S are conserved, but I3 is                 in all directions
        not conserved
                                                     (B) more electrons were emitted in
    (B) Q and B are conserved, but S

        and I3 are not conserved
                                                         direction opposite to that of
    (C) Q and I3 are conserved, but B
                                                         magnetic field
        and S are not conserved

    (D) B, S and I3 are conserved, but
                                                     (C) electrons were not emitted in
        Q is not conserved
                                                         any direction
99. Parity is not conserved in :

    (A) strong nuclear interactions                  (D) more electrons were emitted
    (B) gravitational interactions
                                                         perpendicular to the direction of
    (C) weak interactions
                                                         magnetic field
    (D) electromagnetic interactions

                                            23                                    [P.T.O.
MH SET 2023 question paper, 26 March 2023, Paper II, Physics, page 24 of 24
Page 24 of 24
Text of page 24
MAR - 32223/II—A

ROUGH WORK




    24
Page 1 of 24

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