.Polytechnic Lectuers Exams 2011 Physics Question Paper

8/3/2019 .Polytechnic Lectuers Exams 2011 Physics Question Paper

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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



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



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



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)



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 )



' 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



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



( 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



( 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



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

\)

. .



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



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



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



--- --=--._--

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



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



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)



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.\.



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



-~

\..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)



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)

/



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


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



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



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


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



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



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.

.Polytechnic Lectuers Exams 2011 Physics Question Paper

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.Polytechnic Lectuers Exams 2011 Physics Question Paper