CSIR Physical Sciences June 2012

8/17/2019 CSIR Physical Sciences June 2012

1/24

1.

(

'#fTir A

)

3 i ' ~ T f i r i i i f l lt'r

?J f if

Vii

if

rn i l l ~ r r

'l f

r;rrm

mrr..r,;r it 1

2.

rr :?fr it 1

3. "


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: 1.

' ~ n : l -

l l o : s wi-nch

;C\):U

lm i

br

n '

l : ~ : e n

hei.;;h

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r:11io

o

f t

he

m,1;se

;; of

Kl

:J

; :nm p

rism g

t v;n fD J

lO O:l l

) hose

n

o le

;; lV II

I

t

he

e

m 10

f•f 1

;;:

L

he•r.h

rs.

N

' rhc p

ile

h


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l

.

<

rl l'l

'

tlr-

lt

MW

fit

Wr

$

i

t .

2

.

12

P w

r li

."irt

t

;

t

ri

'

"' '

/i

3.

H

p

i i

r Re

'n

lJ S

;

;l {

{ fN

o

rtff

;

ftm;

rn

<

;Jm

U

lt

' r

I r

tr

l1fR

:

f


4/24

1

4.

p

2

p

2d

=

d

'

2

.

d >

2d

J

.

d

=2

d

4.

d

•:.

2

d

w

iJiT

R

o·:

ifh

ll f

i I

iif

ilfl'i:

1 d

lk

B

f m

mr

'

r

/

iii T

{ ' f{

'

, i

(

)( )"

<

; 3 R

i1 '

f f

f

l

l .

JIE .

f?:r

nif '

;

;t iJiT

R.

w

I

f A

:'if?

¢

: f t

B

if ll

' i;

r

lh

*

I

f f f l

1/'cl

on

3

f

ulcr

um

a

s

sho

wn

Ill

the

d and

d a

rc

rel

ate

d b

y

1

2d

d'

3. d

= 2

d'

4

d

and

IJ

O•E

, an

d

tW

l o

the

r p

oin

ts B

:rn

rl

B

on the same

longitudes, respectively, hut

at

L

ati

tude

6

0°

S. T

he

the

lati

tud

t"$)

tl

tt· po

int

l

a

nd

B,

B

' ar

e

by

I.

,{A

'

B

/1

2.

A

A'=

2

8B

'

3.

A

A

'=

(

B

B

' 4

.

A

A'=

B

B

1

4.

l i < J ~

l . · . r

S

n

(lw

ing

th r

ou g

h a

tub

e a

s

shO

I\1 1

.

T

he

c

ro:s

s-s

ecti

ona

i a

rea

s

a t

A and

C

ar

e

eq

ual

.

an

d

gre

ate

r rh

.ul

t1

1e

a.n

:a at

B.

If

the

t

1ow

i

s st

ead

y,

then

th

.: p

r.: '

*un

: o

n

tht

wa

lls

at

8

.

les

s m

an

ha

t ac

:\

and

th

at a

t

C

.

2

.

m

or e

tha

n th

at

A

a

nd

tha

t

II

C.

3<

?.a

me

&

,at

at

A

and

th

at

a

t C.

4.

m

or

e

t

han

tha

t

a

t

A

bu

t

k

ss

l

hal

l

tha

t

a

t C

IS . Matc h the tw o

lms

A

B

c

D

L

a

b

c

d

2

d

c

b

a

1

a

c

i

b

4.

d


5/24


6/24

www.examrace.com


7/24

25. '7

f"f

f i t ; ~ ~ iff

::

=x+ J'

"'T:f7li

MR

/ : ) W f f f ~

/ f. I

f(:J11lr

2·

J ~ f f

'i/l'T

t

y+xy

2.

xy

3.

)

'

:_xl

9

be t l ~ < : real part

of an

aru

tl)1tc

f

unction

f

z

of lhe complex vari

able

. The mugUla

tJ part of

f z)

is

y+xy

2

.

y

3.

4.

'

y·

26.

L


8/24

3.

2

9. ,..r,rm i 9

10

9

;, /

v

1

{ 1 w

. ~ t

G7 rrz

:::mi

f[ ili r : ; ;

: , r i f i I ~ J

~ ' f ;i

I f[il

i

P\

O.l

l c

i

7l t

r

rflr rt

vfl<

c

3 "

1 x

>fro

r

di f .to iifl'

f. 1 l im

rfrt

'' '

'

t.. t

~

?.T- 7

' f l ' i ? ' 11<

;Jr

q

1

6Q l?o

3.

20 l l:Q

2

r(x)

l

i 1

r(

x)

,

2

2

. 40

""

4 o

iro

2.

.>:

+V(x)

2x

4

,

V

(x)

2x

31 .

tfft

;;l

f 1'{:

ft.·r?


9/24

I.

mffN

N2v0 1

2.

\

Mitt

1ITtl1 JJR

2

3.

\M

itt

t:r f

J

ik l.O

I

4.

l1

mtff

1IT

tl1 NN t.

O I

I

F

2.

-F

3.

F

o _

-

r

r•

4.

i'

30_

r

r

•

33 r[11f

~ f l 1 1 i'ft1

T

~ w:f -(:ICntia

J

1

2

wh

ere F s ll co

nstmt vec

tor, is

I

ft

2.

3.

.•

30

F

- r

4.

-t

.. 30_

F r

r'

JJ

A

n ele

erromag.nc

tic a ~ - e i

s

iru:idem

on

a

wall::

r-air

lntcr ce

. The p

hase of l

he perpe

ndicular

cc

mponi Tlt of

he ele

ctric field, o

f he

rd leeted

w:we into lhe

water is

found to remalt

l tbll sam

e for

a

il

angles o

f incidenc

e. The

of he rnagnec

ic

fr

cld

l

do cs ot

c hM

ge

2.

changes

by 3JT

/2

3.

ch

anges

by

;r

2

4.

changes

by

;:

3

4 fk t •

um 1

il1fr 1fR

fm f f pr r#

f i'f.?.}

34 T

ne magneti

c field at a

distar.ce

R

f

rom a long

ftrt'

Jft

Iff

mt qw

.JFj'11f1 if ~ t i f T

straight

wir

e c:uzying a

t c a d y

urrent 1 is

proportio

nal to

2.

i

/R

1

4.

I

I R

Js.

~

t

m

~

ilfVT

;t

J1iTil iVf

w

'iR 'i1i

'f111

Js.

#11

11 rn

r ii,

ff;m

, , n r , n J

it

TT lTV1

1m i

t

~ t

I

0

2.

1l

2

3

.

ll

±2(11

, +n

1

+

n,

4.

± :

2

2.

1/

R

2

4.

1

1

R

The

m p o n e m

along

an

ar bitrary

direction

;;

•

wi

th direction c

osmes

n,.ns,n,), of h

e spm ofa

. I.

. rc

dTh

·

spm

- 2 p:lttlC:

e IS mcasu

. e

I'< Sillt w

I

)

2.

±-·n

2

:

3.

h

..-n,

+n

,

4.

11

2

2

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10/24

www.examrace.com


11/24

40 .

N

;f

rrlfrr r r

iEiiff

t

L }V

+ l

2.

lv'( N

I

)

/2

3.

N(N +I)/2

4.

N

4 L lV ifiTJt

t 'l l i / f[il

i

ftrr fi:n M11 J.WIT'T J

l

Tl

ff lr rtfR

t ; p r r

F

lnfd

V(k

1

L

u 8

~ r d q ; i/

k

11

liiK«It;r

R'tlmq;

iJil

t'?fi e.:: lf . f

irr 1 >tvv iit1 J ~ ~ a f

OF iJlf

tt

2.

3.

4

.

2

3

Nk

,T

.) 2

42.

fir 'i

t:7ihl

ft1 uiili Jif i

llt

'iNil'fJi

~ f { r { ~

17 f.r#J

11 ri vr

V,

11);.;:

1

i Pttfl1

V

0

iJl1

1[('11

K

v - - - ~

3

.

0.33 v

IJIO V

43. ~ r q

J

'i$'('8

> 4)¢

i l l1m it I. 5

V ,'+1)/2

4

N

41 .

1'hc lh.-e

c n e r

of

a

gas of N

p

rtie

les m

a

volume

V

a

nd at a

lem

pe ilture T 1s

F = N k . T

n [ l i : . V

~ T l •

where

a,, lS

a

co

nstant and k , dc

nolc:s th

e:

l.k>l

lmumn

Wlll i t l nL

l l te

inter

nal energy o

f

he

g;.ll>

is

L

2.

5

2

3

N k . ~ n

u$V(k.r

)' )NJ-%

;vk"T

.vk

1

l ln

[

.,V

j

(k ,rf

42. In the op-amp

cm:mr show1

1 inlhe ~ ; u r c

below.

the mpui

v o h ~ g

V,

is

1

V.

The

valut

of1hc

ou tput

V:.

L

-0.33

V

3.

- 1.00

v

11(

2.

4.

Vo

i

::

11(

0.50V

0.25

v

43-.

31

U

V an d

5 rnA m

forwa:d

i:

'oiZt;:;.

an 80 externa

l efficiency

of he

LEP . ho

w

many

photo

ns arc emi

tted per sec

ond?

].

5. )

X

3.

0.8 )(

2

.

u

x

10

1

4.

2.5

www.examrace.com


12/24

44

.

4

3.

OOO

Q

t

l1R

tf t l

/?ml

.


13/24

1

5

(

~

c

J

f)

-

n

,

'

n

,

0

·

I

1

1

wr

ti

n

1

,

:

:r

n;

~ ~ I f

flC

-

t't ..

..

«

t l

l

..

.

~ J I P ~

48

.

rr

q;

'M

ill

r

t

#

I

. i Y

rrq

; ;/;

19

m

r;

v

J

J{J

; fflf

? m

"I

n

J

tq

;

fl

ff'a

t iJ

iill-

< r


14/24

4 1.

4'

1.

49,

50.

5{),

16

2N · l

l

,\ '

3

N. -1

+])

'-·

4.

3

2 2

•ont..nns lll::lllj'

ball;,, e a ~ h With a ntunber p.:tm

lt:tlun i 111c:re

an:

h :nc

t h < e : ~ l )

numbl:r

''

(n:lmc y one ball wl

th l t·.vo balls v


15/24

17

1,

the

particle will execute ttmple hannonic motion in the right well with

an

an ,,'Uiar frequtmcy

(j)=fi

2 tl1e particle will

exe}'


16/24

I

\•

r

.

8

4

fl

4

ii rsin

S/07

RD/12 5AH 28

www.examrace.com


17/24

1

9

56.

Whi

ch

o

f th e

fol

low

ing

is

a

sc:

I-ad

join

t ope

Tllt

or

in t

he

sph

er ic

al

po

w co

ord

ina

te s

yst

em

r,

J. fl')

1

l

ih

2.

ll

si

n

3

6

f)

}

8

3.

57.

F

-tr;r tj

'1fl;r

f.m

lv

E x

B j

2.

IE

l -IB

il

l.

5

7.

W

hich

ll f

he

fol

low

ing

q

uan t

ll1e

s

is

Lo

ren

tz m

vil

ri:m

t?

L

IEx

B

2

.

2.

i

3.

o

J

4.

4

.

.. .

.

0

0

- I

S i

l l

8

4,

5

8. \

ha r

gc s

Q

.

Q :U

l\1 -

Q

a

re pl:

1cc<

l 0

111

tbe

v

crt1

oes

o

f l n

eq

ui l

ate r

al U H

l.llgle

AB

C

of

s1d

cs o

f

a

a

s s h

ow n

in

the

ftgu

re

20

2

uQ

i

2

.

J

4.

www.examrace.com


18/24


19/24

2

1

L

l M

2

(0)

2.

I

M

2

(0)

T

-T,(

l

M.

z(O)

)

T

r

3.

I -M

1

4

.

1-

l> f

1

T

fc;

T

6

1 T

he

mag

:neti

T.ati

on

M

o

fa

ferr

om a

gnet,

as a

fun

ction

of

the

k:mp

ermu

re T

an

d the

ma

gnt:l

lc

fie

ld f l i

s

desc

ribed

by th

e equ

a tio n

M =

tan

h(

1

; . v

i

I

n th es

e un

it s t

he

zer

o·fic

:lu

m

agn

etic

SU

SiR


20/24

www.examrace.com


21/24

3

66

Jm117f I V

;f; fliP

1f tt

T qr:

fit<

1R

ft• - >

Trtl"'

7iftfrfi ' f

YfdJ: ' t

f

Vf11 r #

I Wt

f {tfff

: Jfl'-' '

~

F

trrr t m

I.

7

2.

3, 011

A

V

4

,

v

66

. Co n

sid er a

sinusoi

da l w av

efo rm

or amp l

itude

V and

f

rl iucnc

y

Stl>rting

lro

m an

> ~ l < l r y

m

ll alti

me, the

w a\'efo

nn

is

s

am pled

ut

intc

n• ah

of

J )

.

If

the corn

::spond

u1g Fuu

ri


22/24

2

(311

/ he

"'2 X I

o·

t

o>fm ?

,

J l

fi

3

4

1/

2

6

9. l11c

sp c;;t

r' .llhnc

l'Om::sp

unding

10

:m ~ t o m i c

tr

tli1Sitio

n from J

=

1

t

o J = 0

stmes

splits

ltl a

m< Jb T

chc fiel

d of

I

kG

ul

lO thn:e

comp<

>ncms

~ m t «

y l. 6;.;

l 0

.,

A

If the

1

,;;ro

tlcld

sp

ectral

me cm

rcspo11

ds

to l849

A w

ha.tts m

e

h

-

;, :zx

CIIL)

Pn

2

2.

}

2

2.

cx p(

-15)

co:n:s

pondm

g

10 t

he =

1 s

1otc' {Yo)

ll

m

ay

l/2

3. exp(1

5 )

exp(

30)

7

0. ll

1c ~ r ~

to cleat.

: a

lallJcc v:u:a:


23/24

25

J;f

f l({f f i tqq

t ) = t ~

s g . n -

J F l l l vrmr

f

g

eit>r t

iJi ilf

w

iFI11

i

l

2.

3.

4.

7

2. Co

nsider

n ele

ctron i

n

a

o

ox ofh

mg tlt L

With

pe nod 1

c bm.md

ary co

ndition

v; x

=VI

(x

+

L

73

.

If " l .

tl )

I

i

.

L

h2h2

h .

•"'

. .

ne e

ectron

1s m

1e

rp,

x

=

·

e ·

wnn energy

~ > ·

::--

w

at

IS

,,e

correcuon

£O

ns

JL

2m

ene

rgy, 0 se


24/24

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CSIR Physical Sciences June 2012

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