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---t
L V . (vx F) is
(1) 1
---t
(2) V2F
?) 0
--I
(4) V. F
2 . VIJ1 IS
(1)n- 3 ---t
nr r
)2)n- 2 -t
nr r
(3)n- 2
nr
(4)n --I
nr r
3 . IfV is the volume enclosed by a surface Sand 5.
-t
A is the vector field then
IS
viI) f f. ---t - - - t
A x dS
S
( 3) PGL/90l
If ijl and \I f are scalar point functions having
continuous derivatives at least of second
order, then I I I ($V2\jf - \jfV2!jl)dV is given
v
by
(1) I I (ijl2V\jf- 0/,2V'$-).dS
s
'(2) I I (ijlV'w-t - o/V'$) . dS ~s
(4) I I (ijlV'lp- \jfV'ljl).dSs
A matrix A is Hermitian if
(1)
(2) '"..= -a ..IJ Jl
v('3)~
a.. = a ..IJ JI
( 4 ) ' ".. = -fr..B u
I I -t ---t
( 2 ) A.dS
s
The matrix [;
1
~ j86. 0 o \. . . .
I f-t -t
\\
(3) S x dA 0o ~
s
» > a diagonal matrix
I I-t -t ( 2 ) a skew matrix
(4) S .dA(3) a Hermitian matrix
S
_j4) an orthogonal matrix
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PGLl901
7. The eigen values of the matrix
are
(1) 1,2, 3
y0,0, 2
(3) -1, 0,-2
8.
(4 )
(1) hermitian matrix
j!fi skew-hermitian matrix > - . \ ) .
(3) symmetric matrix
(4) unitary matrix
r
~. [:
he diagonal matrix of
J 2
(1) [:;] 3
(2) l J 2 ° 1./ : ~
~ l ·E i
5
3 •
If Aij is an antisymmetric tensor of second
order and ul is a tensor of rank one then
A..uiuj isu
(1) 1
J t f ' ! °, 1 ' > ' A..
IJ
(4)~i
11- The electromagnetic field tensor is of rank
\
- : 0 \_0 : 1 \ - - 0, \ -}; . -
(4) 0,-1,-2 f ) 1 , ) [ ' }').+_1.}..,.?1
' ) . . . . 0 ./1- - ).:>~--t~ . , . , > - " ' ; . 0+ :i' -
If the eigen values of a matrix are
imaginary, then the matrix is a
13.
(3)
[ : : ]
(4) [ 2 : ; ]
(1)
° S . ~ ~ , , , ,.- ~\~6""t-(2) 1
!7"") ~ ."\.
03) 2 ~L" 'CP , ~1)~(4) 3 (05 ~x
X ." " t - / ',\
\\
12. As per the definition of Christoffel's symbols
of first kind [).lv, a] + [crv,).l] is equal to
(1)agO! l
a x I)
1"
j P - )i3g!lv C {o - ~ Jaxo
_ 1 1
ag ~.(3) ~
ax v "(4)
ag! lv
ax!'
fix) = x sin x- is an even function Of x in the."~-
interval -11: < X < n, The Fourier expansion
series coefficient nO is given by
_ ) I f ) 0/
(2)
(3)
1
-1
(4)1
2
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I14.../
If f(t) =: Eo sin rot for 0 < tnt < n 17.
and f(t) = - Eo sin wt for -ll < cot < 0
then when n is odd, ret) as per Fourier series.
expansion is
( 5 ) PGLl901
(1)E---.Q.
2n
N
~
. -+ - - - +F.. 8r. = = 0 represents1 1
2E 4E
Lcos n oit
(2)__ 0
+__ 0
1[ 1t (n2-1)
n
~2E 4E
Lcos n wt__ 0
-(n2_1)1 : 1 1 :
n
2E( 4 )
__ 0
n
;I5. The coefficient aOin the Fourier series
expansion of the function eX in the interval
-1]; < x < 7t is given by
(1)sinh II
n
(2)cosh 1 1 :
l't
1 1 :
sinh 1 1 :
(4)1[
cosh 1[
j"'l
/) Principle of virtual work
(2) Hamilton's principle
(3) D'Alembert's principle
(4) Principle of least action
18. The Lagrange's equation of motion is given
by, where L represents the Lagrangian of a
system, qj the generalised coordinate and t
the time,
(3)
16. - - - > 19.If the force F acting on a particle is
conservative then
(4) o
J-+ -+
(1) F. dS "" 0
I. ---) ---)(2) "F.d S = 0
J-+ --4
(3) .. F.d S > 0
1 : --4 --4
(4) j F .dS > 0
If Tand V represent the kinetic energy and
potential energy respectively of a system,
then
t2
6 J (T - V) dt = 0 representst l
f/()'\.1. Hamilton's principle
(2) D'Alembert's principle.
(3) Principle of least action
(4) Principle of virtual work
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PGLlS01
~o. A bead of mass m is sliding on a uniformly 23.
rotating rod inclined at an angle 8 with
respect to the X-axis. The equation of motion
of the bead is givon by
(1) f ir -mrw2 + mg Sill wt = 0
(2) mr + mrw2
+ mg sin rot ." 0./
(3) mr -mrw2-mg sin (f)t - 0
( 4 ) mi'2
sin rot 0mrro - mg =
21. If qj is the generalized coordinate and T and
V represent respectively the kinetic and
potential energies then ~ aT (.) IS
c: aq . qj
J
given by
( 1 ) T. . . . r .
(2) 2T (\/'1
(3) V
( 4 ) 2V /
" V V22. If qi and Pi represent the generalized
coordinate and generalized momentum
respectively of the jth particle of a system,
then the canonical equation
given by
of Hamilton is
25.
'(:~ ~.
. .•• f \.~\
(1)
(2)
aR -qi = a p .
I
)0)a H
q. ---I O P
j
(4)o R
q. =I a p .
1
( 6 )
The principle of least action is expressed as
tz
r8
JP i c ii d t = 0
(2)
t l
tz
8 J p.q.dt = 0I I
tl
tz
8 J Piq,dt = 0
tl
tz
8 J p.ci.dt zz : aI I
tl
24. If F = L . qi Pi'. then F generates
(3)
(4)
(1) identity transformation with negative
sigy
(2) identity transformation
(3) point transformation
(4) mixed transformation
aIf [~, IjfJ be the Poisson bracket then at [ t I > , Ijf]
is given by
(1) [ I V . ~;l[~ • ~ 1
[0 $ . _ ] + [," O W ] (at ,. 1 . J 1 '1', o t
(3) [ a ~ ] [ · o w ]l . I 1 , a t · - at' Q l
(4)
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PGL/901
Poisson bracket of [Q, PJ is
26. If q '" J2 P sin e and p.=: J2P cos 9, the 29. If II' 12 and 13 represent the principal
r (1) 0 ,~(2) -1
r'\~
1
(4) ee
C o - Y27.
-:If II' 12 and 13 represent the principal
moments of inertia, tnen the kinetic energy T
of a freely rotating symmetric top is given by
I 'l~~e n 2j [ 1. /'
(03 (Ia-II)
(2)2j [ II
(Oa (13+11)
I \0T C 1
2(03 (I3 - 11)
1 C 11
2ma (13+11)
(4)
28. If II' 12 and Ia represent the principal
moments of inertia of a rigid body, then the
kinetic energy T of the rotating rigid body is
given by
(1)
(2)
1 .- I {O 2 +1 (J}2 +1 (02]2 1 1 2 2 3 3.
(4)
moments of inertia of a rigid body with
angular velocities (:()1' (:()2 and ( : ( ) a along the
three principal axes, then the z-cornponent of
the torque acting on the body is given by
30. The Lagrangian of a heavy symmetrical top
spinning under uniform gravitational field
with one point 0 on the symmetric axis fixed
in space is given by {where 11' 12 and 13
represent principal moments of inertia and
(:()I' (:()2 and ( : ( ) a the corresponding angular
velocities, and M represents the mass of the
top)
( 1 )
(2)
(3)
( 4 )
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' v . . . ~ i w
f- -+ --t 4n -- + 'x-
l3) E.d I = = - I
~
e , . . .
c
c 34.
. J
f- -+ - 'I 4n -1
(4) ExdI = = - Ic
c
PGLl901
- ' I - ' I31. If B is magnetic induction, E the electric 33.
- 'Ifield and I is the current passing through
the closed curve C enclosing the surface S
and c is the velocity of light, then the integral
form of Ampere's law is given by
(1) fB . d I = 4n 1J
c
c
f- ' I -" 41 t - ' I r
(2) BxdI= _.. I
c
c
32. Which one of the following is not the
"I Maxwell's equation? (Symbols have the usual
meaning)
( 1 )-- + v
s r , D = 4np
( 2 )
--t
-) 4n 1 a D 'jjH = _.-.J ---
c c a t
(4)
( 8 )
-"If I\ > and A represent the scalar and vector
potentials respectively, then according to- ' IMaxwell's equations the electric field E can
be expressed as (c is the velocity of light)
(1)
/
J¢b
_ r"P1 aAIl c a t )
(3)
(4)
- ' IIdA
- ' i l l ! > + --c a t
For a macroscopic system of sources and
electromagnetic fields in a medium of
dielectric constant s and permeability lA,the
energy density is given by
(1) _ ! _ (E E2 _ tlH2)8n '
( 2 )1-. (G E-!AH )8n
(3)1-(fE+~H)8n
J'4) _ ! _ (e ~ + !A H2)
8n
35.-"
The Poynting's vector S is given by, where c
is the velocity of light,
~~ (1) 4
cn( B x I i )
(Jc ( - ' I - " )
4n ~ x H '
(3) C ( - ' I - " )4n B. H
( 4)C ( - ' I - - t )4n E. H
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For plane electromagnetic waves propagating,
in a non-conducting medium, which one of 40
the following statements is true?
(1) The wave velocity is more than that in
free space
(2) The wave velocity is less than that in
free space
(3) The electric energy density is more than
the magnetic .energy density
(4) The magnetic energy density is zero
. For a plane electromagnetic wave
propagating in a conducting medium, the
average to total energy density is
0) proportional to square of the 4ectric
field ~ ~ (./-
!l},)Aproportional to the electric Jjel~ "
proportional to the magnetic field \
inversely proportional to the Square b f
the electric field
8. The skin depth of a conductor
(I) decreases if the conductivity decseases
)2) decreases if the conductivity increases
(3) decreases ifthe permeability decre}tses
(4) decreases if the frequency decreases
In which of one of the following materials, is
the skin depth high ?
S·~
~.3~~ IrY l~
( 1) Aluminium
(2) Gold
(3) Silver
(4) Graphite J
( 9) PGL/901
---)
A plane wave with wave vector k and
frequency (0 is incident from the medium of
permeability ).l and dielectric constant E and
is refracted into the medium of permeability
",' and dielectric constant 1 : . ' and propagates
---)
with wave vector k'. If iand r represent the
angles of incidence and refraction
respectively, then the ratio of electric field
E 'intensities _Q _ is given by
E1
(1) cos isin r
sinO + r)
(2)sln 1 cos r
sin(i+r)
/3) 2 cos isin r /sin(i + r)
(4)2 sin icos r
sin ti + r)
41. If E and ).l represent respectively the
dielectric constant and relative permeability
of a medium, then the phase velocity of the
electromagnetic wave propagating in the
medium is given by (c is the velocity of light)
(1)
(2)c
E ll
j3)
(4) CE) . l
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( 10 )PGLl901
A plane electromagnetic wave is incident
normally which is polarized such that its E
vector is parallel to the plane of incidence. flland [ . I . z and n
land n
zrepresent the relative
permeabilities and refractive indices of the
media respectively in which the incident
beam and refracted beam propagate. E ' andm
EOT represent the electric field intensities of
the incident and refracted waves. Then
[~:: ) is given by
A plane electromagnetic wave is incident
normally which is polarized such that its E
vector is normal to the plane of incidence. nl,
nzand [ . I . 1 ' [ . I . z represent the refractive indices
and relative permeabilities respectively.
Suffix 1 refers to incident medium and suffix
2 refers to transm ited illodium. IfE . and E t01 - 0
represent the elecLric field intensities of the
incident and transmitted waves then [~::)
is given by
[ n 2 + n , )
f2 [ n , )
(1)IA -z [ . 1 . 1 (1)
) , 1 1 ')
( n 2 n , ) ' 1 M (", + n 2 )~-;; III fl2
( n , : : )
n__1.
).11 (2) !il
,,2)
( n , n2 J ( ~ + ~ J
-+ fLl ).1z
f!1 !l2
( n 2 n ) 2 ( : : ) . . .
{ ~ 2 - ~ ~ / 6 y f )~
( n , " 2 )( " , n J
. ),il + 1 1 :; ; + ~
( " , n 2 )
~
; ; + ~ (4)fL 2
(4)
( ~ _ n 2 )( n , . n 2 )~ll + ~
fL l !iz
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( 11 )PGLl901
44. An electromagnetic wave traveUing in a 46. Which one of the fOnowing statements is true
medium of refractive index fir makes normal
incidence on .,he surface separating themedium of refractive index n
2, The coefficient
of reflection R is given by
(1)
[ : ; ] - 12
(2)
/ [ : J 1
(3)
[ : : ] _ 1 2
( : ; ] - 1
[ = : ) - 12
(4)
[:;) +1
6
45. A plane wave (electromagnetic) is incident on
the boundary separating the media of
refractive indices ill and D2 at Brewster
angle. Then '" \ "';'fN
(1) reflection coefficient is 1
(2)
(3)
transmission coefficient is 0 ..,..
transmission coefficient is 1 V " "
product of reflection coefficient
transmission coefficient is 1 t y J~
and
for Galilean Lransfonnation ?
,\:.
(1) The time interval between any two
events is not the same in all inertial
reference frames.
(2) It is consistent with constancy of speed
of light in all inertial reference frames.
J 3 ) It is inconsistent with the constancy of
speed of light in all inertial frames.
?
(4) The acceleration of a particle relative to
rest and moving inertial reference
fTames arc not equal.
47. In Michelson - Morleythe
distance between semi-silvered glass plate
and the mirror is 6 m and the wavelength of
monochromatic light used is 5000 A The
orbital velocity of the Earth is 3 x 104m s-l,
The fringe shift observed is
(1) 0·14,
?·24~
),1-0\00
(3) 0·34 t;,,00 "1..\0
(4) 0·44
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PG1I901 '
48. The position coordinates of a point in a 50.
stationary reference frame are (x, y, z, 't) and
as y:eferred to a frame moving relative to the
stationary reference frame with velocity v are(x', s', z', t/), Then, according to special
theory of relativity t' is given by
(2)
(3)
( t + x ; )
( v ' ) ' "--c2
(4) ( t - x ; j
( 1 - ::r
49.A rod of length 5 m i.s moving ill the
direction of its length relative to a
stationary inertial reference frame with a
velocity of 1·8 x lO R m s~l. The length of the
rod as observed by an observer instationary inertial reference frame is
(I) 4·50 m
(2) 0·45 m
7.00m
(4) 0·40 m
( 12 )
the
53.
The life time of n mesons is 2·5 x 10-8 sand
their speed is 2·7 x 108m 13-
1. The distance
travelled by 1[-mesons as seen by an observer
on the Earth during their life time is
(1) 15·5 m
) , 2 ) 6·75 m
(3) 155 m
(4) 675 m ~\~, S " . (I"L
t:.''\ '
51. A nuclear particle was observed to break into
two fragments which moved in opposite
directions. The velocity of each fragment was
found to be 2·5 x 108 m 8-1relative to the
laboratory., The velocity of one fragment
relative to the other is
(1) 2·85 X 108m s
-1 ",", ~ " -t
(2) 2.75 x 108 m s-1v . . , \ 0 \
~ . y -
(3) 2.50 x 108m s
-1
")/!
2.95 X 108 m s-l
52. The energy E and momentum P of a
relativistic particle are connected by therelation (rest mass is rna, velocity of the
light is c)
(1)
J!i)
(3)
(4)
2E :;:pc + mac
E2 :;: p2c2 + m
2c4
.. a
2E = pc - mac
E 2 = p2c2 _ m2c4
a
The velocity of a particle whose mass will be
5 times its rest mass is
~ 2.94 X 108m s-l
(2) 2.44 x 108m s
-1
(3) 2.74 x 108m s
-1~v
'\
(4) 2·14 x 108m 8
-1
\)
. .
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e covariant form of the Maxwell's field 56.
-t a B -t
E + ~ = 0 and \1. B = 0 isa tquations \1 x
epresented as, where F A i J . ' F i J . " and F vi\. are
ctromagnetic field tensors,
aF~a x - Ilojll = 0
v
J•
/The covariant form of the Maxwell's field
equations-t 1 aE -t
\1xB = --- + !.l Jc2 a t 0 '
-t P\1.E =En terms of electromagnetic field
o
tensor is given by
( 1)
4
L :,,=1
a F pIl v--=
-. Eo
(2) 02A = -)1 j~Il 0
)44 aF
/3) L ~ = [ . L a jj.l, . . . - t . . . / '
a xv=1 11
(4)
( 13 )
and
PGLJ901
The volume of phase space for a three
dimensional particle ofmass rn and of energy
E moving ina volume V is given by
(1)4n V (2mE)1I2
3
4n V (2mE}3/2
3
(3) 8n: mEV3
(4)4n
mEV3
57. If qi and Pi represent the generali.zed
coordinate and generalized momentuID of a
particle in phase space, then the rate of
change of density of distribution function D is
expressed as
(l)
( ~ ~ \ . ' P 'I~ [ a D . a D ' 1~-q +p. oq lOp. I
I I I
, -
(a D ) _ L : [ ' an q , + a D p . 1 . . /at q p ,oq. I ap. I
i' ii' I I
(4)
58. Ifup' urn and urrepresent the most probable
velocity, mean velocity and root mean square
velocity respectively of a particle of a gas at
temperature T, then {
(l)
(2)
(3)
JA{
Up>Um>Ur
up < um > uT
Jlp
> urn -c ur
up -c um< ur
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PGL/901( 14 )
The rotational partition function of a diatomic
molecule at temperature T, whose moment of
inertia about the axis of rotation is I, is given
b y
59. A monoatomic gas containing particles of 62.
mass 65 x 10-2 7 kg is at temperature of
500 K The mean velocity of the particles of
the gas is . Ji < 3 \ :(1) 450 m s-1 ~ ~
(2) 318 m s-1
,7 520 m s-1
(4) 260 rn 8-1
8n2IkT
2h
(2)
60.
~\
According to equipattition theorem, the total
mean energy of a diatomic gas at
temperature T K is given by
(3)
(1) ~ RT2
(4)
5RT
2\¢
61. A system can take only three different energy
states of energy El = = 1·38 X 10-21
J,
E2 := 2·76 X 10-21
J and E3 := 4·14 x 1O~21 J.EI, 13
2and 13
3occur in 2, 3 and 4 different 63. The vibrational partition function of a
ways respectively. The probability that the molecule at temperature T is proportional to
system at temperature 100 Kmay be in one
(3) RT
(4) ' ! . . . RT2
of the microstates of energy 1 3 2 is given by
(Boltzmann constant k := 1·38 X 10-23
JK-1)
3e-2
(1)
(2e-2 + 3e--3 + 4e-2)
y3e-2
(2e-1+ 3e-1+ 4e-1)
3e-2 I(3)
(2e-1 + 3e-2 + 4e-3)
3 -2(4)
e .
(2e-3 + 3e-2 + 4e-1)
(2) ( 1 )T2
(3) T
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64. A system can exist in two states, one ground 66.
state of degeneracy go and excited state of
degeneracy gl of energy t1· The electronic
heat capacity of such a system is given by
( 1 )
(2)
( 3 )
(4)
The particles that obey Bose - Einstein
statistics are
(1) electrons
(2) protons
(3) neutrons
c % photons\
( 15 )
•
PGL/901
The Fermi - Dirac distribution is given by
(2)g.
o. = I
1
[ ('i - ' ) I k T ]-1
g.
(3) T I · =I
I [ e ( ~ l -EJ/kT + 1 ]
g.
( 4 ) n· =1
1
[e(!-l-EJ/kT - 1 ]
67. Identify the statement which is true for a
sYSTem obeying Bose - Einstein distribution.
(1) Particles are indistinguishable half half
integral spin
There is no restriction on the number of
particles in a given quantum state
(3) There is a restriction on the number of
particles occupying a given quantum
state
(4) At high temperature the distribution
approaches Fermi - Dirac distribution
68 If nr and Dn represent the super fluid
. . . .-;r particles and normal particles, theo according
to two fluid model of helium II at Lambda
transition temperature
(1) ns = ~
(2) Os > on.'
(3) nil < Do
(4) Os = 0
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--- --=--._--
69. Identify the statement true of liquid helium. 71. Identify the statement true of the wave
function W of a system whose Hamiltonian is
(1) Iv; per two fluid model, below transition H.
temperature T). all the molecules of
liquid helium arc in the ground state
PGLlB01( 16 )
(2) As per two fluid model above Lambda
transition temperature a fraction of the
molecules of helium are in the ground
state
(3) The heat capacity docreas€<l smoothly
as the temperature of helium goes
from 4 K to 0 It
(4) As per two fluid model at 0 K liquid
helium consists of only super fluid
particles
70. Identify the statement true of the velocity of
second sound in helium~II.
(1) Velocity of second sound is proportional
to the temperature in the range 0 K to
Lambda temperature
(2) Velocity of second sound is proportional
to the square root of temperature in the
range 0 K to Lambda temperature-
(3) Velocity of second sound tends to zero
at Lambda transition temperature
(4) Velocity of second sound is inversely
proportional to the entropy of helium-II
where A . is ~eigen value of the1\
operator A.
(2) J i W [ 2 d't = 1 ../
(3) A
(4). . . .a ' l l1,1- =
a x
1\
72. The Hamiltonian operator II of a particle of
mass M and potential energy V is given by
(1) _ [ [ & ) V ' + V 1
I (2) _ ( _ h ) , \72
+ V8n2M
(3)(h2)
'\ 72
+ V--8n2M
(4) _ [ S : , M ) V ' + V
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Which one of the following statements is true 76.
of a state function of a system?
(1) The state function of a system gives
definite information of the system at
any instant of time t.
(2) The state function is large where the
particle is less likely to be found.
The scalar product of a state function
with itself gives the probability density ..
(4) The state function of a system can be
observed directly.
The time independent Schrodingcr wave
equation of a particle of total energy E,
potential energy V and characterized by the
wave function \If is given by
(1) 2 2 m [ 1 l a ]'\l 1jf + - -:-- 'I' - VII'. :;;;;0
1 ' 1 2 I a t
\.f2J
(3)2 2m
'i1 \ I T + -2 [V - E J 1 j . I = 01 '1
(4)
According to Ehrenfest's theorem, if < x » is
the expectation value of the position of the
wave packet, then, the velocity of the wave
packet is given by
(4) None of the above
{ 17 )
l o - " , . t - " ~ \ . .~ ~ \l ~
-q, .... ~ « . J '~ -""), \., 1""1)
\ .The potential seen by 'illparticle has the form
Vex) = = 0 for x < -a; vex): : : : -Vo for -a < x < a;
Vex) =: 0 for x > 8. Identify the statement true
of the particle.
(1) When E < 0, the probability of fmding
the particle in the region -a < x < a is
small
PGL/9Q1
(2) For E > 0, the energy eigen values of
the system arc discrete
For very low energies (E ~ 0), the
reflection of the particle is almost total
when incident at the boundary of the
potential weU
A i > the energy E increases slowly, the
reflection coefficient steadily decreases
(4)
77. A particle of mass m is executing simple
harmonic motion with a frequency wOo If
a "" [mwo), Lhen the wave function ur (x) of
n n
the simple harmonic oscillator is given by
(1)
(2)
2C D : :
e :2 H (xJri)n
(3)[ ]
112 .
1/4 1 _ax2
a . .1/2.. e H (xJCi)2nn!rr . . n
(4)
78.. The total degeneracy of the energy level En
characterized by principal quantum number n
of hydrogen atom is
(1) n
(2) 2n
(3) 2n
(4) (2n + 1)2
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PGLl901
79. The fine structure constanL a. is given by
he: /"(1)
c
tic
~
e2
tJ2c
e2 Iic
( 2 )
(3)
(4)
( 18 )
(1)to change the energy of the state of E
system
82. According La time dependent perturbatio
theory, the effect of first order perturbation i.
to induce a transition of the state of ~
system
(3) negligible
(4) to split the energy level of the system
According to Fermi's Golden Rule, the
transition probability between a discrete
state n to a continuum of states around the
energy Ek is
(1) proportional to the square of the matrix
element of the amplitude of the
harmonic perturbing term between
states D and k
(2) proportional to the matrix element of
the amplitude of the harmonic
perturbing term between states n and k
80. The secondorder perturbation correction to
the eDergy of a non-degenerate. system Hi 83.
given by
1\ 2
(1) L '\<m\H'\n>\
/(E~-E:n)II
1\ 2
( 2 ) L'\<m\H'\n>\
( E ~ - E ~ )II
1\
(3) L '\<mIH'ln>1
III( E O _ E O )
n m
1\
( 4 ) L 'l<mIH'\n>\
( E ~ - E ~ )II
(3) proportional to the square of the density
I' of final states
(4) inversely proportional to the density of
final states
The wave function corrected to first order
perturbation of a non degenerate system is 84.
given by
81.
( 1 ) ' 1 1 : : : ; ; ' 1 1 0 +~<mIH'ln> I . °'1 1 >
11 n ( E ~ + E ~ J n
ry ' l i n = =\ 1 1 0 + L ' <mlli'ln> I
0. 'If >n ( E ~ _ E ~ ) n
~<mIH'ln> I °
\1 1 = = W o + 'I f >II n III (E~_E~) n
The de Alembertian operator is given by
( 1 )
( 2 )
(4)
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85~ According to Born approximation, the 8)1scattering amplitude f eB ) for waves scattered
at an angle e is given by
reS) = = 2[1. ' " ' J sin (qr') VCr') 1" 2 dr'
tt2 qr'o
where q = 2k sin (0/2) and J . l is the reduced
mass of the system. The scattering
cross-section cr(8) for scattering by the
V e-ar
or' where v,ukawa potential VCr) =
and 0: are constants, is given by
(1)
(2)
4[1.2V2n
(3)
The plate voltage (Eb), plate current (lb) and
grid voltage (Ee) on the .linear portions of
static characteristics of a vacuum triode arc
as follows:
Eb 150 V 150 V 100V
I b 10 rnA 5mA 7mA
E -1·5 V - 3'OV -1·5 Vc
The amplification faeLor of the triode is
(l) 50·5
J2 ) 55·5
(3) 45·5
(4) 40·5
{ 19 ) PGLl901
The amplificai.ion factor of a pentode lies in
the range
y10 to 100
(2) around 500
(3) 1000 to 5000
(4) 5000 to 10,000
88. When the load resistance is equal to the plate
resistance of a full wave rectifier using
vacuum diodes, the efficiency of rectification
is
y·812
(2) 0·505
(3) 0·406 j
(4) 0·202
89. Identify the correct statement pertaining to
the working of a diode rectifier,
(1) The tipple factor of a bulk wave
rectifier is larger than the ripple factor
for a half wave rectifier ,
(2)
\
The ripple factor is smaller for 1t section
filter than for L section filter
(3) The efficiency of a rectifier is maximum
jf the forward resistance of the diode is
large I f(4) The maximum efficiency of a central tap
full wave rectifier is half that of the
bridge type fuU wave rectifier
90. For an R-C coupled amplifier, which one of
the following statements is correct?
(1) The gain is large at low frequencies~
(2) The gain is large at high frequencies.
/3) The gain is large and varies wit1:y
frequency in the mid frequency region.
(4} The impedance matching is poor.\.
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PGLl901
91.A three stage amplifier has a first stage 95.
voltage gain of 100, second stage gain of 200
and third stage gain of 400. The total voltage
(20 )
The frequency of oscillations of Colpitts
oscillator is given by
gain in dB is
/l138
(2) 56·9
(3) 86
(4) 40
1(1)
92.. A three stage amplifier has a power gain
of 30 at each stage. If a negative feedback of
10 dB 13 employed, the resultan.t gain in dB is
(1) 134·3
< y 34·3
(3) 48·6
(4) 107·3\ ~\
1(2)
2nL(C1+Cz )
C1Cz 11
(
(3)
93. Identify the correct statement associated with (4)
the working of a negative feedback amplifier.
(1) Negative feedback decreases the
stability of the amplifier ' k . . . .
1
2nLC
1Cz j
(C1+CZ )
Negative feedback reduces non-hnear
distortion in large signal amplifier V
Negative feedback reduces the
bandwidth of an amplifier
(4) Negative feedback decreases the input
i.rnpedance of an amplifier
(3)
94. The frequency of oscillations of Hartley
oscillator is given by
1(1)
1(2)
1(3)
(4)1
96.In an astable multlvihrator if Rl '" R2 =
e o kt2 and C1= C
2= 0-02 )IF, the frequency
of the square wave produced is given by
(1) 1-8 kHz
(2) 7·0 kHz. ..
. " t i ) 2·5 kHz
( 4 ) 4:0 kHzy,
97.Identify the correct statement.
(1) An external signal applied to a
monostable multivibrator has no effect
on the state of the multivibrator
(2) An astable multivibrator requires no
external pulse for its operation \.. I'
(3) A bistable multivibrator automatically
switches from one state to the other
alternatively 1 -(4,) A multivibrator generates only square
waves
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-~
\..d\, In a sawtooth wave generator, the capacitor " "I t
across which the output is taken gets charged 104, The Miller indices of a plane that makes .A
between intercepts of 2 A, 3 A and 4 A on the
Tho deflection sensitivity of eRO is
0·05 mm V-I. The unknown voltage applied
to the horizontal plates of eRO when the
deflection is 4·5 mm is
( 1 ) 225 V
/2) 50 V
y) 90 V~
( 4 ) 100 V~J?r? \
A pattern consisting of 5 10qpS on the
horizontal line is obtained when two signals
of different frequencies are applied to the
vertical and horizontal plates of eRO. If the
frequency of the signal applied to the
horizontal plates is 500 _Hz, then thefrequency of the signal applied to the vertical
plates 1 S ':\)\:J L,. ~')
, 0 . ) 2500 Hz ~;1~ ~(2) 100 Hz /' ~
'e:.~
(3) 1000 Hz ~ ~ r
(4) 250 Hz - . J ~
(1)1 4- th and - th of the supply voltage5 5
2 1- rd and - rd of the supply voltage3 3
(3)1 1and - of the supply voltage
2 2
(4)1 3- th and - th of the supply voltage4 4
. The rotational symmetry associated with
boron trifluoride is
( 1 ) two fold rotation t> ?~2) three fold rotation
, . . .(3) four fold rotation
(4) SlX fold rotation
( 21 ) PGL/901
1 0 2 . The number of space groups associated with
cubic system are
/ 1 ) 36 -v
(2) 68 \17(\'
(3) 25 \\, . . . . . . . . . .
(4) 59 V{
L. 1 '\ \
(1)
(2)
~3)
(4)
\
coordinate axes a,o, ewhere a : b : c = 4 : 3 : 2 I
are given by "
( 1 ) ( 1 2 4 )
(2) (4 3 2)
(3) ( 2 3 4 )
/'( 4 2 1 )
... '1 \(\,i:I I 'Y
t...105. The Bragg angle corresponding to a
reflection from an isotropic cubic crystal for
which (h2 + k2 + [2) = 9 is found to be 30°. If\ ' ' ' : »
the wavelength of X-rays used is 1·54 A, the Ilattice parameter of the crystal is ,~ .1\,\
, 9 - ) 4·62 A
1,54 A~~
(2) \.Iv\ , , "
3'08 A I . .yP'3) ..,/
o - s r A Y vt(4)
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PGL/901,r
1106.
\__./
_0
( 22 l
The potential energy of a'-system of two atoms
is given by U = - ~ + ~ o where A and Br r
are constants and r is the interatomicdistance. A stable molecule is formed with'
the release of 8 eV energy when the.
interatomic distance is 2·8 A . . The constant A
is given,by
(1) 1·656x 10-37
"J m2
; - 6 ) 2·256 x 10-37 Jm2
(3) 1·256 x 10-37Jm
2
(4) 2·656 x 10-37 Jm2
107. The bond between the atoms of a crystal
which is very strong and directional is called
(1) metallic bond
_ p 2 ) covalent bond
(3) ionic bond
(4) van der Waals bond
108. The Madelung constant for infinite line of
ions of alternate sign is
lI) 2 loglO2
2 l l J _ . 2 I
-(3) loglO2
(4) in 2
109. The Bloch function representing Ihe electron
in a three dimensional crystal with the wave
vector k is given by
110. The energy E of an electron in a crystal
given by E = C (k - ko )2 where C is
constant. The effective mass of the electron:
given by
(1)
\t~
) 2 )tl2
\ _ ' ( .- l2C ,
(3)2C
1 i2
( 4 )2C
h2
111. The first Brillouin zone of an f.c.c. lattice has
the shape of a
(1) square
(2) rhombic dodecahedron
(3) truncated octahedron
(4Y cube
112. The (h2 + k2 +' [2) values of the reflections of
an isotropic crystal are 3, 4, 8, 11, 12, 16 and
19. The unit cell of the crystal is
(1) \Vk(x) = e
ikx
like)!) (1) simple cubic
(2) () -ik l' ()\11k x = e Uk x
(2) body centred cubic
- - - 1 ' - - - 1 '- - - 1 ' e-i k.r
- - - 1 '
(3) \Vk( r ) = uk( r ) (3) diamond cubic
~-t -14) face centred cubic'--4
eik.r(4) Wk( r ) ~ uk(r)
/
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113.
( 23 )
The dependence of energy E of an electron of
mass m in a cubic crystal is quadratic on the
wave vector k. If the electron were to behave
( d 2E )s a free electron then dk2. must be
h2(1)
2m
~
(2)m
r, 2
(3)li2
--/ 2m
/j2
.. _
(4)» :
m' 1 ' 1 \
114. If E and k represent the energy and wave
vector of an electron respectively, then the,effective number of electrons .in a band is
proportional to
(1) E
(2)
( : )( 3 2
(4) (d E ) 2dk
115. An insulator is characterized by
(1) all bands are either full or partially
filled
(2) /tand being fun upto a particular level
/ and rest of the bands beyond this level
are empty
(3) a small forbidden energy gap
(4) high at moderateonduction
temperature
PGL/901
116 The disintegration constant of Pb214 is
4·31 x 10-4 s-1. The amount of Pb214 which
has an activity of1Cj is
(lY 2·8 x 10-11 kg
(2) 3-1 x 10-11 kg
(3) 1·5x 10-11 kg
(4)-11 .
3·5 x 10 kg
117. The activity of a radioactive substance after
10 minutes is . ! . of its original activity. The¥ { / 5
mean life of the radioactive substance is
(1) 261 s b b v
'"r
(2) 151 s
(3) 361 s
(4) 61 s
118. Identify the correct statement pertaining to
secular equilibrium.
(1) The parent decays faster than the other
members of the chain.
(2) The parent lives longer than the
daughter, but, the half life of the parent
is not very long. /
(3) The parent decays slower than the
other members of the chain.
119. A piece of wood from an ancient boat Was
found to show C14 activity of 5 counts per
minute. An equal amount of wood of recent
date gave a count rate of 20 counts per
minute. The halflife of C14 is 5568 years. The
age of the boat is
22272 years .'
1392 years
34146 years
(4) 11139 years
r - : , \ 0 \ % 1~"1- s- 3 ' ) ; ) .- ~~h
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PGL/901
20.
(24 )
IfAis the disintegration constant of Ci-emitter 124.
and Eet is the energy of the a-particle emitted
and also if C and D are slowly varying
functions of the charge number of thea-emitter, then laglo A is given by
(1) C+D
El/2
et
(,2) C+D
Eet
(3) C-D
El/2
et
(4) C-D-E0:
121. In electron capture reaction
(1) a neutrino is created ./
(2) an antineutrino is created
(3) ~+ is emitted
(4) 1 3 - is emitted
122. The Kurie plot is \::(1) a straight line with positive gradient
d(2) a straight line with negative gradient
(3) a parabola with negative gradient
(4) a parabola with positive gradient
123. The minimum energy required for photon to
give rise to pair production when it interacts
with matter is
(1) 0·501 MeV
0/1'02 MeV
(3) 2·04 MeV
(4) 3·06 MeV
An :;<-ray photon of energy 0·25 MeV incidc
on a target un dergnes Com pton scatterin
The energy of the scattered photon at L
angle of 60° is given by
(1) 0"25 MeV
(2) 0·50 MeV
(3) 0·20 MeV ./
(4) 0·15 MeV
125.. A nuclide is exceptionally stable if its
J(1) neutron number is a magic number
(2)proton number is a magic number
(3) proton number and neutron number ar
magic numbers
(4) mass number is an even number
126. The asymmetry energy associated with th
binding energy of a nuclide of mass number J
and charge number Z is proportional to
(l) A
(2) (A - 2Z)
(3) (A - 2Z)2
(4) A2
The five constants associated with ths
binding energy formula for a nuclide based
on liquid drop model are a = 14·0 MeVv
a = 0·64 MeV a = 13·1 MeV a = 19'4 MeVe ~ S , a
and 0 = 270 MeV respec.tively corresponding
to volume energy, coulomb energy, surface
energy, asymmetry energy ami pairing
energy. The binding energy of the last
neutron in 82Pb207 is
(1) 5·96 MeV
(2) 5'30 MeV
(3) 6·62 MeV
(4) 4·66 MeV
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When a particle enters the medium of a
detector n ion pairs are produced. The GM
detector operates in the region where
(1) the charge collected is less than ne
/2)(3)
(4)
the charge collected is equal to ne
the charge collected is more than ne
the charge collected is independent of
ne/
129. A beta particle of energy 1·0 MeVenters a
thin window detector tube filled with
methane and argon and initiates an
avalanche of 5.x 1010 ion pairs. The average
energy loss per ion pair creation is 50 eV. Themultiplication factor is \-4-\~
, t ~ ' - \l " J o J -:"14\~
( 25 )PGL!901
132. Identify the COITectstatement associated with
working of spark chamber.
(1) The detection is made by collecting the
ions produced in the chamber
(2) The length of the trajectory of the
particle depends on the medium of thechamber _
Light metal plates are used in the
chamber
(4) High energy particles are detected
133. Identify the correct statement associated with
the working of semiconductor particledetector.
~l)
(2)
(3)
( 4 )
2'5 x 106
2 x 104-
500 alpha particles of energy 5 MeV enter
ionization chamber per second. The energy
required for ion pair creation is 25 eV. The
ionization current produced is
Yl'6 x 10-11A
(2) 9 x 10-17 A
(8) 3·2 x 10-11 A
(4) 18x 10-17 A
(1) The energy expended by the particle in
a semiconductor particle detector to
produce an ion pair is larger than that
necessary to produce an ion pair in a
gas chamber
Semiconductor particle detector is used
to detect low energy particles
Semiconductor particle detector has
thin depletion layer
(4) The semiconductor particle detector is
usually operated at laboratory
(2)
(3)
temperatures
134. The force acting between the nucleons inside
the nucleus of a nuclide is
31. Identify the correct statement pertaining to
the working of a bubbJe chamber.
(1) The liquid in the chamber is kept
always at a temperature less than its
boiling point
(2) The liquid used shouldbe 135. The set consisting of only magic numhers isnon-conducting
The liquid used in the chamber should
have high surfaea tension
The liquid used should have low vapour
pressure
(4)
(1) short range repulsive "..
(2) long range repulsive 1
(3~short range attractive. .
(4) long range attractive
(1)
( 2 )
(3)
2, 8, 16,~, 50, 80
2, 8, % ' 4 ; , 56, 120
2, 20, 50, 8 , Q , 126
(4) 2, 8, 20, 50, 82
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137. The fine structure of spectral lines of
hydrogen atom is due to
j ) 6 relativistic variation of mass of the
electron in the orbit 142. If ML and MS represent the magnetic
(2) quantization of azimuthal momentum of , quantum numbers, the selection rules giving
the electron rise to Paschen - Back effect are
(3) quantization of radial momentum of the
electron
(4) elliptical nature of electron orbit around
t,he nucleus
PGL/9Q1
136. The wavelength of the third spectral line of
the Brackett series of hydrogen atom, given
the Rydberg constant as 1·097 x 107 m-I, is
(1) 972 A(2) 4340 A
~3) 12740 A
(4) 21651 A
13S. A beam of electrons enters a uniform
magnetic field of flux density 1-5 T. The
energy difference between the electrons,
whose spins are parallel and antiparallel to
the field, is
/(1) 1·74 x 10-4 eV
(2) 0-87 x 10-4 eV
(3) 3-48 x 10-4 eV
(4) 2-50 x 10-4 eV
139. The principal series of alkali spectra arise
due to the transitions from
(1) S-levels to the lowest of P-levels
. j f t !J . D-Ievels to the lowest of P-levels
( 9 , J P-levels to the lowest of S-levels
(4) F-Ievels to the lowest of P-levels
140. The intensity
doublet is
(1) 1:3~(2) 2:3
(3) 2:1
(4) 1:5
141. Calcium line of wavelength ')... =: 4226 Aexhibits normal Zeeman effect when placed in
a uniform magnetic field of 10 Wb m-2. The
Zeeman shift in the wavelength of the
calcium line is
Pf' 0-55
(2) 0·60
(3) 0-65
(4) 0-33
(1) t: . (ML - MS) = OJ ± 1
(~6 (ML - 2 MS) = 0, ± 1
(3 ) t: . (ML+ Ms) = 0, ± 1
(4) 6 (ML+ 2 MSJ = 0, ± 1
143. Identify the correct statement associated with
Stark effect.
(1) Stark effect occurs when the electric
field applied is small!
(2.) Stark effect is non-linear when the
electric field applied is low,
(3) St~l)f effect is observed when
m?g:~etic field applied is very higb
the
The Stark shift for the level n = 1is
zero
144. For a field strength greater than 107 Vm",
the Stark effect observed in hydrogen IS
called as
(1) First order Stark effect
(2) Second order Stark effect ,.
(3) Quadratic Stark effect
~ Zeroth order Stark effect
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145. If nand nland n
2represent the total 148.
quantum number and new parabolic quantum
numbers respectively, then the shift
observed, when a field F V em-1
is applied, is
(1) proportional to F2
(2) proportional to n2
(3) inversely proportional to the charge
number of the atom
rroportional to (nz - n~)2
( 27 ) PGLlS01
In a transition for J = 0 to J = I, the
absorption lines occur at 1·153 x lOll Hz in
e12oI6 and at 1·102 x lOll Hz in enO IS. The
mass number of carbon isotope is
(1)
(2)
11
13
/>(4) 15
14
149. A substance shows a Raman line at 4560 A .146. Identify the correct statement regarding the
band spectrum of a molecule.
(1) Band spectrum consists of a series of
bands arranged in an irregular order
(2) The intensity of spectral lines in any
given band increases from the band
head to the band tail
(Zj Any change in the structure of the
given molecule results in a change in
the band spectrum of the original
molecule
when the exciting line of wavelength 4358 A .is used. The wavelength of the Stokes line for
the same substance when the exciting line
has a wavelength of 4047 A . is
(1) 3739 A .
?3887 A
(3) 4220 A/'
(4) 4410 A
(4) The spectral lines in a band are equally 150. According to Franck - Condon principle,
spaced which one of the following statements is
correct ?
147. A band occurring in the near infrared region
is due to
(1) transitions between two vibrational
levels of the same electronic level
(2) transitions between two vibrational
levels belonging to two different
electronic levels of the system
transitions between the rotational levels
associated with the same vibrational
level of a given electronic level
(4) transitions between the rotational levels
of different vibrational levels of a given
electronic level
(1) Electronic transition occurs with change
in the internuclear distance of the
vibrating molecule.
The intensity of a vibrionic transition is
proportional to the square of the
overlap integral between the vibrational
wave functions of the two states
involved in the transition.
(3) Transition can occur from one
vibrational level to another vibrational
level belonging to same electronic level.
(4) Transitions take place when !::.v= 0, ± 1
where v represents the vibrational
quantum number.