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MH SET 2018: 28 January, Paper II, Physics

  • Date: 28 January 2018
  • Paper code: JAN32218
  • Series: A
  • Language: Bilingual
  • 16 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.

JAN - 32218                                                                                          (To be filled by the Candidate)
Time Allowed : 1¼ Hours]                                                                            [Maximum Marks : 100
Number of Pages in this Booklet : 16                                                   Number of Questions in this Booklet : 50
                     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 50 objective type questions. Each question
          will carry two marks. All questions of Paper-II will be compulsory,    2.
          covering entire syllabus (including all electives, without options).
3.        At the commencement of examination, the question booklet
          will be given to the student. In the first 5 minutes, you are
          requested to open the booklet and compulsorily examine it as           3.
          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                     (ii)
                   cover page. Faulty booklets due to missing pages/
                   questions or questions repeated or not in serial
                   o rder or any other discre pancy 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
                   should be entered on this Test Booklet.                                (iii)
4.        Each question has four alternative responses marked (A), (B),
          (C) and (D). You have to darken the circle as indicated below on
          the correct response against each item.                                4.                        (A), (B), (C)   (D)
          Example : where (C) is the correct response.

                             A        B                 D
                                                                                                     (C)
5.        Your responses to the items are to be indicated in the OMR
          Sheet given inside the Booklet only. If you mark at any place                                    A         B            D
          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.
8.        If you write your Name, Seat Number, Phone Number or put               6.
          any mark on any part of the OMR Sheet, except for the space            7.
          allotted for the relevant entries, which may disclose your             8.
          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.       Use only Blue/Black Ball point pen.                                    10.
11.       Use of any calculator or log table, etc., is prohibited.               11.
12.       There is no negative marking for incorrect answers.                    12.
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                                     Physical Science
                                            Paper II
Time Allowed : 75 Minutes]                                              [Maximum Marks : 100

Note : This Paper contains Fifty (50) multiple choice questions. Each question
            carries Two (2) marks. Attempt All questions.


                              dz                        3.   Two unbiased dice are thrown. The
1.   Value of                     , c : | z | = 1
                         c ( z 2)                            probability that both dice show the
     is :                                                    same number is :

                                                                   1
     (A)      i                                              (A)
                                                                   3

     (B) zero                                                      11
                                                             (B)
                                                                   36
     (C) 2 i
                                                                   1
                                                             (C)
                                                                   6
     (D) –2 i
                                                                   1
2.   The inverse Fourier transform of                        (D)
                                                                   36
     e–|k| is :
                                                        4.   Eigen values of a nilpotent matrix

             1       1                                       A, i.e., a matrix satisfying AK = 0
     (A)
                  1 x2                                       for some integer K are :

     (B) e– x2                                               (A) Real and distinct

                                                             (B) Zero
     (C) e–|x|
                                                             (C) Purely imaginary
                 1
     (D)
             1 x                                             (D) Real and negative

                                                    3                                   [P.T.O.
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5.   Residue of cot (z) at z = 0 is :           8.   The average of function f(x) = sin x

            1                                        in the interval 0 to          is :
     (A)
            2
                                                     (A) 1/2
     (B) 0
                                                     (B) 2/
     (C) 2
                                                     (C) 1/
     (D) 1
                                                     (D) 4/

6.   Trace of a 3 × 3 matrix is 6. Two          9.   If r2 = x2 + y2 + z2, grad rn is :
     of its eigen values are 1 and 2. The
                                                     (A) 0
     third eigen value is :
                                                     (B) r n –1 r

     (A) 1                                           (C) nr n –2 r

     (B) 2                                           (D) n(n – 2)r n r

     (C) 3                                      10. A simple pendulum of mass m and
                                                     length l oscillates with a frequency
     (D) 6
                                                      0 . A piece breaks off from the
     d2 f
7.              2 sech2 x f – f   0.                 pendulum and the mass is reduced
     dx2
                                                     to m/2. The frequency of oscillation
     One of the solution is :
                                                       then becomes :
     (A) sech x
                                                     (A)      = 2 0
     (B) sech2 x
                                                     (B)      =    0/2
     (C) tanh x
                                                     (C)      =     0

     (D) sech3 x                                     (D)     0 =        2 0
                                            4
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11. A propagating wave is reflected at          13. Time-order of two events can be
    a barrier. The phase of the wave
                                                    changed by making a Lorentz
    changes in the act of reflection by :
                                                    transformation only if they occur in :
    (A)   /2

    (B) zero                                        (A) Time-like region

    (C)                                             (B) Space-like region

    (D) – /2
                                                    (C) Light-like region
12. Two particles of mass m1 and m2 and

    charge q1 and q2 respectively are               (D) Speed of light can be exceeded

    constrained to move in a straight
                                                14. A satellite is moving around the
    line along x-axis. The Lagrangian
                                                    earth in a circular orbit at a height
    of the system (in esu) is :
          1    .     1    .                         of 2R, from the earth surface. R is
    (A)     m1 x12     m2 x22
          2          2
                         + q1q2/|x1 – x2|           the radius of the earth. The speed

          1    .     1    .
    (B)     m1 x12     m2 x22                       of satellite is :
          2          2
                         – q1q2/|x1 – x2|           (A) gR/3
            1    .    1   .
    (C) –     m1 x12 – m2 x22
            2         2                             (B) (gR/2)1/2
                         – q1q2/|x1 – x2|
         1   .    1   .                             (C) (gR/3)1/2
    (D) – m1 x12 – m2 x22
         2        2
                         + q1q2/|x1 – x2|           (D) gR/2

                                            5                                     [P.T.O.
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15. Virial theorem is expressed as              17. As shown in the figure a ball of mass

                                                    m suspended by an inextensible
                .            .
          p ·        = –     p ·                    massless string is released from

                                                    height h and collides elastically
    The theorem is valid, if :                      when it is at its lowest point with

                                                    a block of mass 2m at rest on a
    (A)         is bounded (remain finite
                                                    frictionless surface. After the
          over all values of time)
                                                    collision the ball will rise to a total
    (B) p       is bounded                          height equal to :

    (C) both        and p    are bounded


    (D)      is unbounded


16. Electron and positron annihilate and

    produce a single photon only when :


    (A) Electron and positron are at rest

                                                    (A) h/9
    (B) Electron is at rest

                                                    (B) h/8
    (C) Positron is at rest

                                                    (C) h/3
    (D) At least one particle is in a

          bound state                               (D) 2h/3

                                            6
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18. Uniformly charged solid sphere of
    radius R has a volume charge                  20. Points P and Q are at a distance of
    density . The strength of electric
    field, at a distance r, (r > R), from             10 cm and 20 cm respectively from
    its centre is :
                                                      the ideal magnetic dipole. The ratio
             r3
     (A)
           3 0 R2                                     of magnitude of vector potential at

             R3                                       point P to that at point Q is :
     (B)
           3 0 r2
                                                      (A) 4
            R3
     (C)
           3 0r
                                                      (B) 8
             r3
     (D)                                              (C) 1/4
         3 0R
19. Consider the figure shown. AB is an
    infinite, uniform line charge                     (D) 1/8
    distribution ‘ ’. P and Q are two
    points as shown in the figure. The            21. A circular loop of radius r is placed
    ratio of strength of electric fields at
    P and Q; i.e., EP/EQ is :                         in a magnetic field B(t) = B0 e– t z,

                                                      B0 is constant. If the loop is in xy

                                                      plane, then the induced emf in the

                                                      loop is :

                                                      (A) Zero

         (fig. not to the scale)                      (B)     r 2 B0e – t
     (A) 3 : 1
     (B) 1 : 3                                        (C) 2 rB0e – t
     (C) 4 : 1
     (D) 1 : 4                                        (D) 2 r B0e – t
                                              7                                      [P.T.O.
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22. Plane monochromatic electromagnetic           24. A point charge ‘q’ having mass ‘m’

    wave is propagating through a                     follows a circular trajectory of radius

    conducting material of refractive                 ‘R’ under the action of magnetic field

    index n + ik. The phase difference                 B . The magnitude of the angular

    between the fields E and B                        momentum of the particle is :

    associated with the wave is :                     (A) Zero

    (A) tan–1 (n)                                     (B) Bq 2R 2

    (B) tan–1 (k)                                     (C) Bmq 2R2

    (C) tan–1 (nk)                                    (D) Bq R 2

    (D) tan–1 (n/k)                               25. If ‘A1’ and ‘A2’ are the amplitudes

23. Under the Lorentz gauge condition,                of two electromagnetic waves (same

                                                      frequency) coming from two slits in
    the electric potential V, is related to
                                                      Young’s double slit experiment, then
    magnetic vector potential A as :
                                                      the    maximum          intensity   of
                              V
    (A)     ·A   (1 / 0 0 )         0
                               t                      interference fringe is :

                        V                             (A) A1 + A2
    (B)     ·A    0 0          0
                        t
                                                      (B) A12 + A22
                                   2V
    (C) –    ·A – (1 / 0 0 )            0
                                   t2                 (C) (A1+ A2)2

                        V                             (D)   A12     A 22
    (D)     ·A – 0 0          0
                        t
                                              8
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                                                    28. The electron in a hydrogen atom is
26. Given [xi, pj] = i   ij , i, j = 1, 2, 3,
                                                        in a superposition state described by

    [x1, p13] is :                                      the wave function

                                                                  1
                                                          (r)       [4 100 ( r ) – 2 211 ( r )
    (A) (i )3 p1                                                  6


                                                                    6 210 ( r ) – 10 21–1 ( r )],
    (B) i 2 p1

                                                        where        nem ( r ) is a normalized
    (C) 3i p12                                          eigenstate. The expectation value of
                                                        Lz is :
    (D) Zero                                            (A) – / 6

                                                        (B)     /6
27. Which of the following is not an
                                                        (C) 6

                                                        (D) –6
    eigenstate of linear momentum
                                                    29. Two coherent light sources of

    operator px ?                                       intensities I and 9I are used in an
                                                        interference        experiment.          The
                                                        resultant intensity at points where
    (A) Aeikx                                           the waves from the two sources
                                                        superpose with a phase difference
    (B) Ae–ikx                                          zero is :

                                                        (A) 16I

    (C) Ae–x                                            (B) 9I

                                                        (C) I
    (D) A sin kx                                        (D) Zero

                                                9                                          [P.T.O.
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30. The number of distinct (n, l, ml) states               32. Addition of angular momentum
     of hydrogen atom with n = 3 is :
                                                               states j1 = 1/2 and j2 = 1/2 will

     (A) 5                                                     result in 4 states, of which number

     (B) 9                                                     of linearly dependent states with

                                                               magnetic quantum number m = 0
     (C) 3
                                                               is :
     (D) 2
                                                               (A) Zero
31. The condition for two distinct
                                                               (B) 1
     quantum          mechanical            states,

     represented by wave functions                             (C) 2

      1(x) and       2(x) respectively, to be
                                                               (D) 4
     orthogonal is :

                                                           33. In the Born approximation, the
     (A)
             –     1 * ( x) 2 ( x) dx   1
                                                               effective cross-section of scattering

                                                               depends :
     (B)
             –     1 * ( x) 2 ( x) dx   0

                                                               (A) L inear ly on scat t er ing angle
     (C)
             –     1 * ( x) 2 ( x) dx
                                                               (B) on p sin2

     (D)         [ 1 * ( x) 2 ( x)
             –                                                 (C) on p sin /2


                            2 * ( x) 1 ( x)] dx   1            (D) only on the momentum p

                                                      10
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34. A system consists of two indistin-                36. Let f(T, l) be the tension in a rubber
                                                          band of length l , T being the
    guishable fermions. Each particle                     absolute temperature. Let F denote
    can occupy only two energy levels                     Helmholtz free energy and S the
                                                          entropy. Then :
    E1 =       and E2 = 2 . The canonical
                                                                 F            F
    partition function is :                                (A)          S,           f
                                                                  l T         T l

    (A) Z = e–         + e–2
                                                                 F            F
                                                           (B)          f,           –S
                                                                  l T         T l
    (B) Z = e–3
                                                                 F             F
    (C) Z = 3e–                                            (C)          Sl,              fl
                                                                  l T          T l

    (D) Z = e–         + 2e–2                                    F            F
                                                           (D)          0,           f
                                                                  l T         T l
35. Consider 5 independent magnetic
                                                      37. An insulated chamber is divided into
    moments. Each moment has only two                     two halves of volume. The left half
    directions +m and – m. Hamiltonian                    contains an ideal gas at temperature
                                                          T0 and the right half is evacuated.
    of such system is given by                            A small hole is opened between the
         5
                                                          two halves, allowing the gas to flow
    x=         mi . If the total magnetization            through and the system comes to
         i 1                                              equilibrium. No heat is exchanged
    of the system is equal to m, the                      with walls. What is the final
                                                          temperature of the system :
    entropy is equal to :
                                                           (A) 2T 0
    (A) k ln(10)                                                 3
                                                           (B)     T
                                                                 2 0
    (B) Zero
                                                           (C) T 0
    (C) k ln(20)
                                                                 1
                                                           (D)     T
    (D) k ln(5)                                                  2 0

                                                 11                                           [P.T.O.
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38. Consider a mixture of equal number
                                                 40. What play the role of thermo-
    of non-interacting single atomic gas

    and diatomic gas. The internal                   dynamic     potential     in   micro-
    energy per particle is given by :
                                                     canonical ensemble ?
    (A) 2 kT

    (B) 4kT                                          (A) Entropy

          3
    (C)     kT
          2                                          (B) Enthalpy

          5
    (D)     kT
          2                                          (C) Gibbs potential

39. Consider an ensemble of systems
                                                     (D) Internal energy
    having only two energy levels

    having energies 0 and   respectively.
                                                 41. For a metal CV =      T + T3 at low
    The average energy of the system

    at temperature T is :                            temperatures. The entropy is :

    (A)
          e– / kT 1                                  (A)   + 3 T2

    (B)
          e / kT 1                                   (B)   T + 3 T2


    (C)                                                             T3
          e– / kT – 1                                (C)   T +
                                                                    3

    (D)                                                        T3
          e / kT – 1                                 (D)
                                                               3
                                            12
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42. In which of the following detectors
                                               44. Air Ballast valve in a rotary pump
    P-N junction diode is used ?
                                                   is used for :
    (A) G.M. Counter

    (B) Scintillation detector                     (A) Reducing the noise

    (C) Surface Barrier detector
                                                   (B) Removing the condensable
    (D) Proportional counter
                                                          vapors
43. The X-rays emitted by a target
    consist of continuous range of                 (C) Reducing the back streaming
    wavelengths superimposed by
                                                   (D) Increasing the ultimate vacuum
    characteristic X-rays named K , K
    etc. It is found that :                               to 10–5 Torr

    (A) K has high intensity and lower
                                               45. A signal of one V is burried under
        wavelength compared to that of
        K .                                        1V RMS noise. Which of the

    (B) K has low intensity and lower              following devices is suitable to detect
        wavelength as compared to that
                                                   it ?
        of K .

    (C) K     has high intensity and               (A) High gain linear amplifier
        higher wavelength compared to
        that of K .                                (B) Band pass filter

    (D) K     has lower intensity and              (C) Notch filter
        higher wavelength compared to
        that of K .                                (D) Phase sensitive amplifier

                                          13                                     [P.T.O.
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46. Steady state response of an electric           48. Frequency Bandwidth of CRO is
                                                       decided by :
    circuit is generally tested by giving
                                                       (A) Horizontal amplifier
    following waveform at the input :
                                                       (B) Vertical amplifier
    (A) Sinusoidal
                                                       (C) Delay line

    (B) Square                                         (D) Triggering circuit

    (C) Triangular                                 49. Resolving power of a 2 cm2 site
                                                       grating having a rulings of 600 l/
    (D) Swatooth                                       mm in order one is approximately :

47. An inductance ‘L’, resistance ‘R’ and              (A) 10

    capacitance ‘C’ are connected in                   (B) 102

    series to resonate to frequency ‘‘fs’’.            (C) 103

                                                       (D) 104
    When they are connected in parallel,
                                                   50. A dual slope digital voltmeter has
    the resonance frequency is ‘‘fp’’.
                                                       a gate time of 400 ms reflecting the
    (A) fp < fs                                        measurement cycle. The frequency
                                                       bandwidth of this instrument is :
    (B) fp > fs
                                                       (A) 2·5 Hz
    (C) fp = fs
                                                       (B) 1·25 Hz

    (D) There is no relation between the               (C) 0·8 Hz

         two                                           (D) 0·6 Hz

                                              14
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    15                [P.T.O.
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Source: Savitribai Phule Pune University. Question paper published by Savitribai Phule Pune University.