Test Booklet Code & Serial No.

A
PHYSICAL SCIENCE
Signature and Name of Invigilator Seat No.
1. (Signature) ......................................... (In figures as in Admit Card)
(Name) ................................................ Seat No. ..............................................................
2. (Signature) ......................................... (In words)

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

JUN - 32219 (To be filled by the Candidate)
Time Allowed : 2 Hours] [Maximum Marks : 200
Number of Pages in this Booklet : 32 Number of Questions in this Booklet : 100
Instructions for the Candidates
1. Write your Seat No. and OMR Sheet No. in the space provided 1.
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.
 JUN - 32219/II—A

2
 JUN - 32219/II—A
Physical Science
Paper II
Time Allowed : 120 Minutes] [Maximum Marks : 200
Note : This Paper contains Hundred (100) multiple choice questions. Each question
carrying Two (2) marks. Attempt All questions.

1. If A xeˆ x yeˆ y zeˆ j , then 2A 4. At the origin, the function f(z) =

will be : | xy| is not analytic because :
(A) The Cauchy-Riemann (C-R)
(A) 1
conditions are not satisfied at
(B) 3 origin.
(C) 0 (B) f (0) 0 and the C-R conditions
are satisfied at origin.
(D) – 3
(C) f (0) = 0 though the C-R
2. If a vector field F xiˆ 2 yjˆ 3 zkˆ, conditions are satisfied at
then ( F) is : origin.
(A) Zero (D) f (0) = 0 and the C-R conditions
are not satisfied at origin.
(B) ĵ
z2 dz
(C) 2 ˆj 5. I= , in the z-plane.
( z2 1)( z2 4)
c
(D) 3kˆ
Here c is a contour as shown :
3. A gas molecule moves equal
distances between successive
collisions with equal probability in
any direction. After a total of N such
collisions, the mean square displace-
ment of the molecule d 2 will be :
(A) N then :
(B) N 2 (A) I = /6
(B) I = – /3
(C) N2 2
(C) I = 0
(D) N2 (D) I = /3
3 [P.T.O.
 JUN - 32219/II—A

6. Consider a differential equation 8. A matrix is said to be of rank zero

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

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

(B) 2/e zero.

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

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

boundary conditions y(0) = 1,

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

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

relation
(C) cos t – sin t

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

4
 JUN - 32219/II—A

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

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

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

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

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

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

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

constant angular speed along R = radius of earth). The orbital

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

5 [P.T.O.
 JUN - 32219/II—A

14. For repulsive inverse square force,

17. The radius of gyration of a rigid body
the shape of the orbit is :

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

(B) Parabolic
is :
(C) Hyperbolic

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

15. A unit charge q moving with initial

(B) (M/I)2
velocity (v v iˆ ) is subjected to
x
external electric field (E E y j ). The
(C) (I/M)1/2
number of degrees of freedom is :

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

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

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

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

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

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

6
 JUN - 32219/II—A
19. Two masses are connected by 21. Current I is flowing through an
springs (as shown in the figure). The infinitely long wire placed along the
potential energy matrix is : x-axis. The Cartesian coordinates of
the points A and B are A(2, 3, – 4)
and B = (– 8, 4, – 3). The ratio of
magnitudes of B at point A to that
at point B is :

(A) #0I

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

3k k E E0 zˆ and B B0 xˆ are both

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

7 [P.T.O.
 JUN - 32219/II—A

23. The magnetic dipole moment of a 25. The magnitude of magnetic vector

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

ideal magnetic quadrupole is

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

(A) 4 m (B) r–2

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

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

electric flux through the rectangle ‘ ’ is :

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

8
 JUN - 32219/II—A

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

through a cylindrical conductor. The propagating in a medium with

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

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

(D) – rˆ (C) The intrinsic impedance of the

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

9 [P.T.O.
 JUN - 32219/II—A

31. A boy of mass 60 kg is running with – 2 d2

33. The Hamiltonian H = – &(x)
2m dx 2
a velocity 12 km/hr. The de Broglie

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

approximately (h = 6.626 × 10–34 Js) :

2
wave function %trial (x) = Ae– bx

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

state energy is :
(D) 3 × 10–31 m

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

be an acceptable solution for

'(n 1 / 2) / n 1/ 2 )
Schrödinger equation for all values

of x ?
(A) – m 2 / 2 2

2
(A) %( x) Ae– x
(B) – 2m 2 / 2

2
(B) %( x) Ae x

(C) – m 2 / 2
(C) %(x) = A tan x

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

10
 JUN - 32219/II—A

35. A particle is constrained to move in

34. A particle is moving in a one-

a truncated harmonic potential well

dimensional infinite potential well of

(as shown below). Which one of the

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

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

variational calculation estimate for

4a5/2 the ground state energy is :

(A) The parity of the first excited

5 2
(A) state is even.
4ma2

(B) The parity of the ground state

3 2
(B)
2ma2
is even.

3 2 1
(C) (C) The ground state energy is
2
5ma2
(D) The energy of the first excited
5 2 7
(D)
2ma2 state is
2
11 [P.T.O.
 JUN - 32219/II—A
37. A system described by the Hamil-
36. The wave function for an electron 5 2 0
tonian H = 2 5 0 is perturbed
in a hydrogen atom is given by 0 0 2!

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

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

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

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

12
 JUN - 32219/II—A

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

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

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

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

13 [P.T.O.
 JUN - 32219/II—A

43. van der Waals equation for one mole

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

E2 = 2$. If the particles satisfy

an2
(C) p (V – nb) = nRT
V2 !

an Boltzmann statistics, the partition

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

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

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

V
1/ 4
(D) z 2( e– +$ e–2+$ )
(D) T
U!
14
 JUN - 32219/II—A

46. Crystaline sodium has 2 conduction 47. The number of distinct ways in

electrons per unit cell with lattice

which 4 particles can be distributed

constant (cube edge) 4.28 Å. In the

in 7 energy levels if (i) they are
free-electron model the Fermi

distinguishable and (ii) if they are

temperature is (h = 6.62 × 10–27

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

9.1 × 10–27 gm) : is :

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

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

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

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

15 [P.T.O.
 JUN - 32219/II—A

48. One block of certain metal is at 49. An ideal monoatomic gas at

temperature T 1 and a second temperature 300 K is adiabatically

identical block is at a temperature decompressed so that the final

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

contact and the system is thermally final temperature is :

isolated from the surroundings. (A) 150 K

Assume that the heat capacity at (B) 37.5 K

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

T1T2 At the critical point the pressure

(A) Cln
|T2 – T1|
is :
(T1 T2 ) a
(B) C ln (A) Pc
2T1T2 27 b2
a
(T1 T2 )2 (B) Pc
(C) C ln 27b
4T1T2
a
(C) Pc
b
2T1T2
(D) C ln
T1 + T2 a
(D) Pc
3b
16
 JUN - 32219/II—A

51. To measure the temperature below 53. A l aser beam of i n t en si t y 50 W /cm 2

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

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

mirror is 5 cm2. The average force

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

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

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

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

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

is : of light used in Å is :

(A) 2% (A) 5885

(B) 1% (B) 5890

(C) 0.5% (C) 5895

(D) no error (D) 6000

17 [P.T.O.
 JUN - 32219/II—A

55. Photomultiplier can detect a feeble 57. A 10 stage photomultiplier tube has

a stage gain of 4 secondary

optical signal because of :
electrons. The overall amplification
(A) The shape of its photocathode
of the tube is :

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

pulse (B) 10 4

(C) Multiplication of secondary (C) 10

electrons (D) 106

58. In oil rotary pump for low vacuum,

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

(A) McLeod gauge group

(C) To discharge the exhaust

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

18
 JUN - 32219/II—A

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

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

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

(A) Prism spectrometer of the diode is :

(B) Grating spectrometer (A) 0.6 ,

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

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

meter (D) 2.5 ,

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

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

comparatively weak and detectors conductor materials are :

insensitive requiring Fourier (A) Pure crystals of silicon and

Transform methods : germanium

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

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

(C) Infrared deposition

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

19 [P.T.O.
 JUN - 32219/II—A
65. The output voltage (V o ) of the
63. The frequency of the following phase following Op-amp circuit is :
shift oscillator :

is nearly equal to :

(A) 2 kHz (A) + 2

(B) 5 kHz (B) – 2

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

(A) 15 mA is nearly equal to :

(A) 0.5
(B) 18 mA
(B) 1.0
(C) 21 mA (C) 1.5
(D) 25 mA (D) 2.0

20
 JUN - 32219/II—A

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

(A) Increase the input and output

impedance

(B) Increase the input impedance

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

(D) Does not affect impedance or (A) 40 mA

bandwidth
(B) 60 mA
68. The output of the following logic
circuit is : (C) 80 mA

(D) 100 mA

70. Among the following A to D

converter, the slowest one is the :

(A) Parallel comparator type

(A) AB + C(D + E)

(B) Successive approximation type

(B) (A + B)C + DE

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

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

21 [P.T.O.
 JUN - 32219/II—A

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

(B) In lighter atoms jj coupling is

(B) 0.26 Å
dominant
(C) 8.4 Å
(C) LS coupling occurs irrespective

(D) 13.25 Å of atomic size

(D) Electrostatic forces couple the li

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

(B) S = 1, L = 0, J = 0 and S = 2, (Given; Boltzmann const. k = 1.38 ×

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

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

L = 0, J = 2 (D) 1.4 cm–1

22
 JUN - 32219/II—A

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

modes (Given : n = 6.6 × 10–34 Js) :

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

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

(D) 606 cm–1

76. Direct confirmation about the

quantization of internal energy 78. Nuclear Magnetic Resonance (NMR)

states of an atom was first obtained
spectrometer normally operates at :
from :
(A) Radio frequency region
(A) Stern-Gerlach experiments

(B) Microwave frequency region

(B) Compton scattering experiment

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

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

23 [P.T.O.
 JUN - 32219/II—A

79. Which of the following identity is not 81. The primitive translational vectors

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

of atomic orbitals to form MO : by

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

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

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

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

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

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

orbital energy ? reciprocal lattice of bcc cell is :

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

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

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

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

24
 JUN - 32219/II—A

82. In a simple cubic crystal of lattice

84. In an MX molecule, suppose M atom
spacing a = 3 Å, a positive edge

dislocation 1 mm long climbs down has an ionization potential energy

by 1 #m. The number of vacancies

5 eV and X atom has an electron
created or lost in the crystal is :

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

(B) 5.00 × 1012

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

M to X when they are at a distance

(D) 8.00 × 1015

83. The Debye temperature of diamond

of 5 Å is :
is 2230 K. The molar heat capacity

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

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

(B) 0.175 Jkmol–1K–1 (C) – 1.88 eV

(C) 0.235 Jkmol–1K–1

(D) – 4.20 eV
(D) 0.350 Jkmol–1K–1

25 [P.T.O.
 JUN - 32219/II—A
85. A linear diatomic lattice of lattice
86. If the interatomic potential energy
constant a with masses M and m
(M > m) are coupled by a force function can be expressed as
constant C. The dispersion relation
A B
is given by U(R) – ,
R6 R12
2 = 1 1
C where A and B are constants, the
M m!
atomic spacing R0 for which the
2 1/ 2
1 1 4C2 potential energy is a minimum is
/ C2 – sin 2 ka
M m! Mm
given by :
Which one of the following
(A) A/4B
statements is incorrect ?
(B) (2B/A)1/6
(A) The atoms vibrating in trans-
verse mode correspond to the (C) A2/4B
optical branch
(D) 4B2/A
(B) The maximum frequency of the
87. For an ideal Fermi gas in three-
acoustic branch depends on the
mass of the lighter atom m dimensions, the electron velocity vF

at the Fermi surface is related to

(C) The dispersion of frequency in
the optical branch is smaller electron concentration n as :

than that in the acoustic branch (A) vF 0 n2/3

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

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

26
 JUN - 32219/II—A

88. A phosphorous doped silicon semi-

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

(A) Position of Fermi level moves

is placed in a small magnetic field,
towards conduction band

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

towards conduction band

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

(B) 3 (C) 1000 Å

(C) 4
(D) 1200 Å
(D) 5
27 [P.T.O.
 JUN - 32219/II—A

91. The wavelength of 10 MeV proton 93. Nuclear forces are :

(A) Spin dependent and have no

is nearly equal to : (1F = 10–15
non-central part
meter)
(B) Spin dependent and have a non-

(A) 7 F central part

(C) Spin independent and have no

(B) 9 F
non-central part
(C) 11 F
(D) Spin independent and have a

(D) 13 F non-central part

94. Given : Masses of 80 80

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

[Mass of 197Au = 3.2707 × 10–25 kg, MeV Nucleus 80 80

35 Br decays to 34 Se

by emitting a positron. The end

r0 = 1.2 × 10–15 m]
point energy of the emitted positron

(A) 3.96 × 1017 kg/m3 is nearly :

(A) 0.511 MeV

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

(D) 8.38 × 1017 kg/m3 (D) 1.022 MeV

28
 JUN - 32219/II—A

95. 1H3 nuclei undergoes beta decay at 96. A gamma-ray of 3.43 MeV energy

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

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

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

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

is : energy of the positron is nearly :

(A) 10.2 KeV (A) 0.511 MeV

(B) 8.5 KeV (B) 1.022 MeV

(C) 6.4 KeV (C) 1.20 MeV

(D) 4.3 KeV (D) 1.40 MeV

29 [P.T.O.
 JUN - 32219/II—A

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

If the R value of this reaction is

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

the counter. are broadly classified as :

(A) Leptons
(C) Only a fraction of the gas atoms
(B) Quarks
of the G.M. counter are ionised
(C) Baryons
and therefore the energy
(D) Mesons
information is lost.
100. Considering U, d, S Quarks, the
(D) All the atoms of the gas are quark content of proton and neutron
are respectively :
ionised irrespective of the
(A) UUS and ddS
energy of incident radiation.
(B) UdS and dSS
The information about the (C) UUS and USS
energy of the radiation is lost. (D) UUd and Udd
30
 JUN - 32219/II—A

ROUGH WORK

31 [P.T.O.
 JUN - 32219/II—A

ROUGH WORK

32