paper dec. 2014

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9.11x 1g-311<g
6.63 x 10-34, sec
1.6
1.38
k
c
IeV
aniu
G
&
Nr
grrrtf
x 10-1eC
x t}-zt1iX
3.0x1.08mlsec
ryfirf
x 10-1e;
L.67 x1:0-27kg
6.67 x1g'tt71^z7rn-z
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R *tr{itsfr{difi
B:.3I4JK-Lmole:L
,
usEEtrrl, EUNDAIIAnNTAL CONSTANTS
r1r
m.
Massofelechon
9.11x 10131I€
h
PlanclCs constant
e
Chargeofelecfton
Boltznann sonstant Velqcity of Light '
1.6 x t0-1el
L:67 xt0-27W
6.69,.1g_9alsec
. 1.6 x 10-1ec.
1,38 i LO-?3IIK
k
c
IeV
amu
xt0-rlN#kg-3
'
G
o.sz
&
Rydbcrgconsta$
Iro
8.85'* xlo-r4Fm-L
4n x L0-7 Hm-L
MolarGas constant
Na
to
R
Avogadro's number
3.0
x 109ml1es
-
x 107rn-1
6.022*lgzlmote-a
L.097
e.ZtqX- .\nio,Ie-r
4
[,ST OF TH E
Egd
Symbol
fdNim
Afniim
Atomic
Atod;
Number
we$r
.Ac
89
AI
13
95
sb
51
Ar
18
Asildlm
As
At
Eairo
Bn
8eft*rt
BK
33
85
56
97
Eeqim
Be
4
tlism$t
Bi
83
Borm
B
5
Broip
Br
35
cd
40'
AEer*;
Ceim
Ctim
.Ca
ffitim
' Cdur
cf
c
.6
Ceim
.Gs
55
Cldcip
0
l7
.Cr
24
Co
27
29
96
66
,Cu
'Cm
58.
Wq*wn
Eixliirn
Dy
Ertitrt
Er
Eqim
tu
'63
Fenrim
Fm
100
Ffiche
Frrr*m
Gaffi*m
Gf,rtl
Geimim
Es
'99
68'
I
.F
Fr
87
Gd
.64
Ga
31
GoU
Au
32
79
]t*im
Hf
72
t{dm
He
Ge
lhHm
Ho
l$ogen
hnm
lofu
lifn
hl
49
Fe
l(rtfloti
Lailranun
Larrencium
Kr
La
'Lr
Le6d
Pb
-. tllim
Li
Ltlbtm
Uagln*tm
Urrgilres€
f&ldeyfun
.
67
,|
lr
bm
2
.H
, .l
Symbol
53
77
26
36
57
1.03
a2
3
Lu
71
M,g
12
IVln
25
ild
i01
d,yg"n
10.81 ffi;m
79-CB phcfiorus
112.Q Hfrnr
lo.{n p1rbrnum
(2sl).
98
'Ce
Copet
Gtrigr
zog.g
20
Cclim
Clrcim
Cod
Ecrpnt
lilercury
{24
26.9 llolybdenum
t213) lleodyndum
121.75 Neor
39948 lkfttnium
74,92 leld
(210) tr5rti,m
137.34 lflrogen
Q4sl rthrxllm
9.012 Grl*un
'Am
Aminm
fffinury
lrgm
ATOMIC}1'EreHTS.OF THE ELEMENTS
.
'
i#.t,n
,
12o11 pdassium
140'12 Praeodymium
13291 prrqndhium
35./63 fficl6um
5200 Rdm
58-9:l Rdon
63'5rl Rsrium
(24? tuium
Hg
Mo
Nd
Ne
Atomic
Atomk;
Number
Weigm
80
200.5s
42
95.94
60
14.24
'10
20.t83
Np
93
(237)
t{
28
58.71
Nb
41
92.9t
7
102
14.007
190.2
o
76
8
Pd
46
106.4
P
t5
30374
Ft
78
195.09
Rr
e4.
12421
Po
84
(2ro)
K
t9
$:tq2
Pr
59
140.91
Rrt
6t
.(t44
Pa
91
(23t)
Ra
88
(226)
Rn
86
(772'
Re
75
186.23
r029t
N
No
Os
(2s3)
t5.99S4
Rh
45
Hllrrum
Rb
37
85.47
Rrilrenium.
SarElnim
Ru
44
.101.1
Sm
62
Scamrum
Sc
21
s€hniu;
Se
34i
sibm
si
14
stYer
sodum
A9
47,
107.870
Na
11
22.9898
Sr
38
87.62
S
16
s2.064
Ta
73
180.95
Tc
43. '
(s)
164.C1 Elriun
Te
t27.60
Terbium
ib
52:
65
TlaRm
TI
81
Thqium
Th
90
Thtum
Tm
69
?62:0/
168.$
Tn
Sn
50
118-69
Tlanium
Ti
Tugsten
.w
22
7492
183.85
16250
qfl)
.
t67.26
151.S
l'#
wJr
riz.zi
69.72 $mtium
7'g
196.97 st{fur'
178.49 halum
. 4.0.o . Tedneiium
t..'FO
ti4frt
l26.Ct
1C,.2
ss.os
. S3.B{i
136.9l
e54
201.19
. 6.qp
174.51
24-312
. 5C.94
(25i6)
$aium
.
U
'
150.35
'.
44.96
78.96
28.09
158.92
;
n437
47.90.
I
238.03
V
Xe
23,
s4.
131.30
Yterbium
Y&tum
TnE
Yb
7A
173.04
88.9r
Zn
39
30
Ziconium
Zr
40
91.n
Vandium
Xenon
50,94
65.37
'Easedonmassof Cr2atl2.O0O....Theratioof thesereil$lsof lhoseontheorderchemiial scale(inwhichoxygenof
isotopic composition was assigned a mass of t6-{X100...) is ,l.000050. (Values in parentheses represent the most
n*rd
st-b
lmown isolopes.)
.
.
.
5
A rectangle of length d and breadth dlT is
,.*lu"d-onc" complet"ly around is length
of
and once arbund its breadth' The ratio
volumes swePt in the two cases is
frr3{;qdRTfffi5f,r6aRffn
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Tfi 6I fnr * Et sre t r Gler +t
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l:2
l:4
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1.
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3.
2w2
2.
4.
l.
2001
2003
3.
of a product in different
yeus 1s shown in the histogrun -tt me
i"ttl*f bars irtdicate variability duingry
Average
3.
yield
,ft"n during which Year ws- F
Votr
'p"*Lrtt
of ilrat
variabitity over the averagg
year the least?
z',tT
4. aftre
ffie
A long ribbon is wound around aspoolup
ribbon'
io . tu'aiut R. Holding the tip of fie
iboY runs awaY fromthe s .ootwitha
*nJ*t speed haintaining the unwound
portion of th" ribbon horizontal' [n 4
'*i*t"t, the radius of the wound portion
becomesS.
ts
z. zfrae
.E fitrc
n
what furthertime, itwill
become ^R/2?
t50
!m
250
2m
150
t00
t0
2 min
20e0
3- 2'!Tmin
2. 2001
4. 2003
l. 2000
?. 2ffi2
dtz 6 $r sFeT 6t
as1g d ilrn
h fte si tro'qF
t'rr EF 3TTdI
fi Fre ff6 gtr{sFr
srdl
I at-fi EF 3ffi4 3nrfrdt 6r qqa
ffi
l. l:l
3. l:3
#
ffi
f
2.
4.
n
t
t
tt
.12
1:4
fr
n(nfi' trd Tqt-fi
4'
4 min
t, at
n}r+l:/1n+2)(n+3[n+4fntsXn+6i
.Rexrrdrq
t:
l. 3tAffiazta6'
2. t slttz t
3. ?t df+-fi I * afi
4. aaI 3t,azt
6
If n is a positive integer,
4.
then
(c) He takes VEG tunch for exactly 15 days
(d) He takes a totalof t4 NON-VEG meals
What is m?
l
,{r*l[;ti2xt?+3Xtd-4Xrr$(n+6)
,2.
. .'3.
'-
l.
3.
3and7
ThtnotS
Jr{rFT 50 fi., izo fi. tni ilo fr. t t'+
5- "ffi
'
drE{ f)t
or etlsd
r{-qra
l.
,' 3.
5.
Cdr
2.
4.
30005550
3.
7:
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aI rtgrffi{ fi trt qrd eflardrtl
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r
0)&*,,e Fd fr
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a-6
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(c) &-o rsfrnt-fr's-6 ilrflErtr.
rrfd llTiln
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; -(d) etrdtdrtr .:
T'".{ framt' rl.ffil f
tt
. n if iFrt 4r.{ P
;;:
l;lE:
3. 20.
...
frI
'
lrmch/dinner
(a) If he takes a NON-VEG lunch, 'he
have onlv VEG for dinner
& FE rrgPv f wff 'dsl EFqrP
l0
I 8, 15,
2,3,4,,7,6,
'- t'tt:-'
; !,
'12'
. . r.
3. l7
8.
'
O) He tates'nON-VnC dinner for exactly
l '.\'
u''
/'i.-'
-'
24.
sequence?
2,3,4,7,6,..1 1,8, 15,
:
'
13
19
What is the next number of the following
12
10..2.
..
:
,
t3
4... 19
3.r: l7
m
will
'I
4.
3. . 148
cfr qA 6I ttfr$-I q
$ra tm'Ktt 61 3ltt & G 6 l,r'o
.'
6o'drfi.49ffi.d[
,' ,. il
his
{,
2.
t.
-
VEG ot -a NON-VEG meal for
barnk Qffers a scheme wherein deposits
for 1600 days are-doubled in valie,
the interest-being compounded daily; Th9
interbst accrued on a deposit of Rs'100Q/over the first'100 days would be Rs'
r83
2s0
, 190
24
38
of a person for
190
4.
l-4s
;"d"
e.
,.i
'2.
4.
A
t.
Lmchdinner' .pattern.
'days
is givenibelow..He has a ohoice of-a
'
.
7800
2.
4. 7800 :'
l. 3000.'
3. 5550'
38
t'+,
3250
Thc'area (in m2) of a tiangulbr park of
din€nsions 50 m, 120 m and 130 m is
3250
20
24
t*, q6'qlin-dr rq;ra orfr t ms*
tooo frd fi 'frqr {Gr zrqr Bilqr 3ITfr
qro
{a. 6r gtr-dl didr t, 165 q5*;ifri
+oo
looo/- t'friw 6
-!Bt r sqS
ffd d'srq qr &n sqt
183
2.
l. 250
1.
4:- reidrer 3 nor 7
2.
4.
l8
trq*i*lry.tWtiiaafr
3r{flrrr 60, $izt
-{d
iltqi ?offi.dr.
rte I 3oftrd
aqr il$q F-W
dlal,
sfi rit 6T qfr t r{fi
Erq ffi Erd f+tri t
t
dar{trqt-q56ifrfiqesaqt
srftd gfr
l.
3.
(ft qqr ts
'5oFfi.fr.
3516'.fr.
z. cs fit'.fr.
4. loffi.fi.
:::
9dap
i3
H
B
E
E
I
l.
3.
Two locomotives are running towards each
drer.with speeds of 60 and 40 km/h' An
object leePs on flying to and !o lom t{e
t*t tip oi'onu locomotive to the front tip
ottre other with a speed of ?0 km/h' After
i0 rintt t, the two locomotives collide
ind ftc olr;ect.is crushed. What distarce
di<t
2.
4.
35 km
B eqtrrql
ZrE
.frd
frt
fl
m,.72,74,.76, 78, 80,' 82, M, E6, 88, 90, 92, 94
.
ffifi a.aa too lq'.tr. aql
' 'lsfr'.ur. t qd tr lnffi eli t t dt
-A dt{
,,,
{,
aRd,
q6,6r Hq
:
.
10:'
l.
0fr'.rjr.
3.
1.6fr'.ur.
Weights
F.F.uf.
4.
r.sld'.q[.
Q,84,86,
12.
,- ll.
6afs
:
'
88,'9Q'
13.
nTIq?TI
lkg
l'8 kg
*
will
snafi
attain ttte
frl dd':
2.4
4.O
l.L
3.N
13.
Find ihe missing letter:
A?QE
CM
EK
GI
'r.Nl.L
2. ll48
4- 2574
lenin'followed by at most four identitnl
digts, Tlie code most have at least one
leftei and one digit- How many distinct
code can be generated using letters
and digits I to 9?
R*'
fi
A?QE
CMSC
EKUA:
GIWY
'11. A code consists of at most. two identical
'
znq
room
1. The bigger sPhere.' . 2. 'The smaller sPhere
3.. Both spheres will take the'same time
4. It will depend on the room temp€rature
ttt6 TC*u car$ ar 5-o.A F
- .1. 936
- '3. .Bn
ro
temPerature (constant) filst?
srtr+rrq d Trfu4 {3itIS)
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. s6F[, iTqr 3ffit'
qq t qa t'6'
3iq, 3i-dffi€ $ I mr&u fr
srr tti v6' 3iq, 6I FIdT tstf t I $trtT
s6,
ffi
I
2'
4.
rooqil.
Two solid iron spheres are hgatedto lOeC
and then allowed to coql. One has ttre size
of a football; the other has the size of a pa
.
:
2574'
I
Two new persons having weights 100'kg
aid 79 kg join the 'Soup' The average
weight ofthe grouP increases bY
t. Otg
-3.- 1.6 kg
dri
Which sPhere
2.
(in kg) of 13 persons are givbn
?8, 80,
+t
I
4.
f$ Eirs ftqr arar t r;r.jt I
(1t, $etna fi gr+rt fr ilr (fir' rc{ t
3*t"R f' t al +ta-sr rifdl ffi$ TCd
m',rtr<rq (ffir) ffi q(trrn
1. {5I rffrr
z. 6}dr rfdr
3. ffi rffr tnr'qFt
4. q5 ortrflrr tq fi*t &n
t:
rff ildfr.,t ccar
'l
' , -*lo't
?0, 12,74,76,
' .n9!
t ffi
l4t
2.
'
l0km
i, aga (f6.rr.) *
dI dte
&
object cover before being crushed?
45 km
50 kn
rh
l.
3.
'to.
12.
936
1872
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frdrr w rS $$ t: r Uer * uqt aqr
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B sFfiiTI t, dl S$f 6r ftaRg c trrre
17.
C'.
t
14.
43,47,53
3:
4.
St rd'dr
t
The least significant bit of an 8-bit binary
number is zeio. ,A binary number whose
yalue is 8 times the previous number has
l.
2.
3.
4.
l2 bits ending rvith three zeros
I bitCendingwirh four zeros
I bits ending with three zeros
l2 bits ending with four zeroes
.
I
I
G'
dq,ea Et {glif i' f* 6' 6}
sqtrogsl-* *ndT tr vffi asg f q6 rox
Sr FrA df4ar t mn {stl d' 15% ifir ars{
I Ts+'Fil drsTffi $r sfrffir Rr il
r.
2.
3.
4.
15.
B
.:.
iFr
grs
v6'dlrft tsr
tra $fiqfirfq
4.
A
17.
ladder rests,against a ryall as shown. The
top and the bottom ends of the ladder are
marked A. and B. The base B slips. The
cenhal polnt C ofthe ladder falls along
< r%6rF
ot$
qfinrq.
w'afrfr
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l.
aft qr ilrfi ilff
A
person sells two objects at Rs.l035/each. On the first object he suffers a loss of
l0% while on the second he lains lS%.What is his net losslgain percentage?
l.
2.
3.
4.
16.
5Yo gain
< l% gaia
< l% los
ryq
2,
a,l
/t
drt rd:
5, lo, 17,2g,
16.
l.
no lossrno.gain
41, -,
l.
5g, ??, 100
2.
3.
4.
64,91,100
-,
-
apaiabola8
3.
4.
,
thearc'ofaciiclel
a straight
line
!t
:
a hyperbola
'6
18. frffi srs qrqwfi fi,BtrFhd
fr,
t-zox
Continue the sequence
2, _5, 10, 17,2E,41,-,-,_
tli * {iF'{Fr fi 3iT{ dt+,t qrd
tlsAqaHtErtwra*,$drfrS
Ti {'fi Fqtffiqt Jt t zox dffi qr*
t i {st il( * 16 Etrnff tirm4r t,
l.
2.
3. '25
rdilnt
43,47,53
55; t9, l13
at
59,77,100
64,
gl,
100
qrgrq
l. .12
i.
'
S ya ft-dil dtrr rftfid
3rlr
2; . 64
4.
100
.
'a
.
t:,.
'l':
.l:r
-Li
H
9.
1&
NP/o ofstudents of a particular course get
of
jobs within one year of passing.
jobs
of
end
the
get
by
students
remaining
ac
studenb
sec€md year of passing. If 16
still jobless, how many shrdents had
fu
2ff
pad
zt.
thcccone?'
l.
4.
19. frrffi fr'qfdTq{trq tfr
100
t
(l
+'f =6
+or*
af+.....+ar{.'W6iao, a1,....-,an n ${
61
Pgim
t
21.
n
4.
rf+n
I. Jon
,;i.
'1.
' 2.
3.
';4.
.-
tt'ffi
3iirr 6t3 (rfi' rtrf,r car
sq Ti rrt frtq irr ?iarffiT
t
Tt
Ts€'r trriqr
+,tq
*'
S tl
:racra
l.
3ilEqla
Tsts Fd& fdw,il
fi
f
rl
.20:
'
4.
3. 32km
tt
li
It
4.
,trym
,@n
The radius of Earth is approximately 6400
km. The height li at which the acceleration
due to Earth;s gravity differs.from g at the
Earth's surface by approximately l% is
2.'i 48 km
64km
* etr+{ tl
tsfi 3Trffia fi qq6 6 6,
5s+' gra
where
?:2. Tcfi f+, ff,flr t T'ltrr u*06.1Y.1 1d
St ra-f q{ Tcfr t Tsq fi'*rqur d
FrwT s t 5q$ arrcrrr l7o-3itr {GrcTI
Ffisr 5s ffi h tr{ qrqr artrrt
2.. 48fr',.fr.
l. 64fr'.fr.
4. 16fr',.*.
3. 32 fr'.fr.
20. rc'& f{Fqrsfr 6 1ffi, {f,d (rd& +lqt t,
?,
2.
3.JW
2.n
+n
-ln' ']
qrfffi
-f,*'+lnxl
constants. The frequency
of small oscillations about a point of stable
equilibrium is
+rf
fdr 6tf
lffi
4. ldffi
o,b ue positive
2.
Binontial thborem-in algebra gives'(l
= eo + at+ azi+.....+a^{, where 4,
or,....., an at|Y constants depending on z.
What is the sum oo * at * az*.... * an?
":'
v(x) =
. A particle of mass m is moving in the
:
t.'T
Etffi
z.
potential V(x) --
^2
5.n
sur
3. JW
a,g1 P
3. t.
i
(rfr'.
l. ,Iffi
.
r Azrme ast ar+oz+--.-
t. t.
19.
6l
-f,*'+!"ux* f rfttrf, t wr a iI{I b
tEf 3TiR 6; grS qrFIFr€r *' grR-cR
3rdrr EIffi 61 3nqfr t
2. .64
32
3. 25
+
rtFT m
23.
A sphere is made up of very thin concenric
sheils of increasing radii (leaving nq gaPs}
.The.mass of an'drbitrarilychosen shell is
3Trqffifidr A fdftTE fu,ta fr r,aw*
3flqrfr m il2rr Td ndIE'5re W 946
aPr
*l rrfr rrt:
equal to the mass of the preceding$ell
proportional to its l'olume
proportioflal to its radiUs
proportional to its surface area
3. v=c
r-ffi'
4. , = q(l*dJ
I
16km
10
23.
According to &e special theory of relativity,
the ryccd a of a frce particle of mass rn and
.l
25.
The column vector
is a simultaneous
total encrryf is:
tl. e=sll-.lE
eigenvecta
2 ,=J#(l+g
'=ll I il-
t011\
3p1-snr
4.. !=alZ u b= -alz
f fffi frE fr
FqR €R* 6t Afu wdT t,
r= Fl. at
f.i=o
l;
2.
3.
4.
and
f.f=o.ad
V.i=
3
f.i=3
26. .ssrail Ary drisr rrsT EFr t
l. -2r
2. -tr
iln
3.x
?xi=f/r
26.
rct
f
l.
fxi=o
point in.thrcodimensional space, and
f i=0and f xi=7lr
i.i=0and Vzr=0
f .i = 3 ad vzi =ilrz
4.. V-i=3 and fxi=0
l.
2.
3.
\r1 I)
nft{r
l.
2.
3.
4.'
6r
F{
2.
i,
-tc
2n
rro Efd.tE dca t
qr€Fffi rI[ r = m-nrlt grfuoar
iia $ vfi qrst da t
?Terr
3.
$furqnmm
qfgF$d5'T{
t rqFn t
;
l= ,n+nT!f Y'€lloT ,.*t
4. qfgtrff il[ r= m-ni5I fiEIt EI;I
{mt6rre{t
t sfr
.:
b=0 Tlc= 0
b=a'QID=-2e
D=2a{[bj-a
b=alI4lh=
dr
iia
:.
t0 01\
2s. ciT sfr$
t=lo 1 ol
0, \rool
to1 1\
Ztt
27. A ffiir vt?trsfi w m?[trn, 61l.'pt-o
AFI 0,1,2,...,- il Sfi-& t, q1-5il ii6 fi
ry o.ta t, wq arsr qH p?r?rr v
t'qFfl al
l. qrsfu.q{ I=m*ng-rt #fiT
7 = |il.Then
o
X5
'-2n
3.7
Uimtb Se position vector of any
n=-lt
tinlo)
,-6
\
24.
.
4.
The principal value oftlre integral
[-
v2r=o
afr Yzi.=':lrz
and
and
1. b=0 orc= 0
2. b=a u b= -2o
3. b=2a or b= -o
3. "=rFffi
4. o = c(1+$
24. rfli fr, tBAr
01\
1 0l
00/
of ,=(|
-alT-
27.
Tvre independent random variables'm and
& which can take the integer values
.0, L,2,.
-
-,
o, follow the Poisson
di$ributi6n, with distinct mean values p
and v respectively. Ttren
the probability dishibution of the
rartdom variable I =
n is a
binomial disfribution.
l.
m*
11
2.
=
the probability distibution of the
random variable r = rn- n is also a
'foisson
dishibution.
the variance oftlre random variable
i.,.
l=m*nisequalto
4.
3. ni-W*#=o
4. n*+ff= o
.
qr srier qtrd
p(r) -po (1T) t A ildI t, tr6Y r
FS Bfttir t iltr pq, avd R tm gq<
fuqr n t'
1r*'v.
the me4n value of tlre random variable
r = m-
n
is equal to 0.
gr1-qrf
d
dtri
ifi nst
r.
{S lzl<-fifrq.Xp--*
fQ) = e'+ erlz
Fs$ frqr ardr
t
2. ft-{dqfao<Fl<1ta}€I
H=o(""*i")*
3. qlfroclzl<.fiRs
xLo('" -*)*
4: h{d ffi lzl< 1 d} fi Xf=--*
(rfi'
*s
ril-d
tt r=RfI gar * qft r=R/Z tR
Sry
z.=Ai
=l
'
Ftga
nat
f* *r qtfiur t.2sTdr t, dt a qr
2.
4.
1.2
3. lz
1
L/+
;;;;iltr "
A solid sphere of radius R has a charge
:
p(r) = ro
r
[t
\la L.)P.
ar\
'1.
-;,;,
:
where
The laurpnt series expansion ofthe
frrnction / (z)..= e" 1 r1:lz about z = 0 is
grven by
gd
thg valde of a is
< lzl < t
3' xflo(zr *,a')* forall o t Pl < o
'-n
4. Xil--h,ontyif lzl < 1
29;
R arepositive constants.
1.2
3. Llz
!
er'l!*' - Y(Dlfr
q,fr w'dr dr rfr {tr{,,.rur't: '
If the
field at
r = RlZ is 1.25 time that atr =
l. Xf=--fo foraltlzl <only if
isthe radial coordinate and po, a
magnitude of the elecnic
'n
2.' Xf=o("" *rt)r1
r
31..
2.L
4'
R, then
tl+
t' (16'dr t crtrd
@rdfro. {frtsr{ frI=rdrd tl
qK fif{ 3lriefi
srnr trsf{ TrJg Ir=
l. tni+Ymx+{=g '
'
i
mr+wi-#=o
' : 3. in|-Im**#=
" 4. mr +ff= a*
O
29.-' The equation of motion of a system
described by the timedependent
Iagrangian L
l.
2.
.
mi+Wi:+ff=o
.dv
mx +Ymx
'r
b.
= ertli^tt' - r{r)]
-E = U
is
q$ (tI r w @rdtro Fara +T rrrrr
tr t:
5q{rff slinoT ry
gry
lr
3:
r'2
2. r-l
4. r-3
.l
12
31.
The electrostatic.lines offorce due to a
systerp of for point charges is sketched
belo.w..
the component in thc plane normal to the
magnetic field.
I
r
t
-l
Theratio
otfu
At alarge di$ancer, the leadtng asymptotic
2.
,f
3.. r-2
q-6' 3TtR
tr$fq
qt{
ITq
f{ t
6tgamfE1mtr
I
I
-l' F
*
l. 714n,
3. 3714n
A parallel
d4=rfir61fe
m td qr rq-fr
2.
l2n
4.
Un'
ofwavelength ,1 is
incident normally on a thin polymer film
wittr air on both sides. If the film has a
refractive index n ) 1, then second-order
brigbt fringes can be observed in reflection
whcn the drickness ofthe film is
1.14n
1./2n
beam of light
2.
4.
Un
fA. r+Wu;fi$ dtrrril{
0=
azt.'*
ar
ortr'*
{r-r v{ ffi, g6i f,-,
qiluf{T
dtrr d6rdt 12 rttt L; t Ery
wrarUfg
2.
4x
4.
lE
ilrn.
32.
charged-prarticle moves in a helical path
' A
unde.r the influence of a constant magnetic
field. The initial
sffi'd
3. u,l+yt
dffidt-3iilrd r
l. nlz
3. 2tr
t
f
6sqfuwfIffi6tt
AEil qrnpf
l.
t
q?r
2. 4r
4. t
3lrrdaTuIi6' n>1
t
*sffi
to the radius R
r13
# sild *'siq{ ('fi'
\q' IEtrfi
helical path is
l. rl2
3. Ztr
r
r-!
IR TfrrNd Tt
untilt
sirfun rrfr t{r t h dT€I{
qrf,r szff', g"€fq qt{ ii{ grctut * sirfi'
3TrAftTd 6qT
of the prtgh
aizrid r gEil nq sqiil r+rqr Ss,
alal rw 6{r t trtt qr rtrfr dfrfr{
trar q{ ii{ Jfiqfrd il qfa fua ar
behaviour of$e electo$atic potential is
proportional to
l.r
l/R
* l'-
velocity is stch tliat the
component along the magnetic field is twice
nffi1-5
t
;6IRI:
3tmdrnFrfi sffir
flat l(l + 1)h'z irelr rnh *-
qrql sfiffiFm aFrn uqd-Ti?Fr{3F: tr
EFr G $fiirqnfrfi
Ot, at
I1 "*
l.
Q1 =-Q3=j1 az=
E
11
2.
Qt= os=it . az= 72
11
az= 3.
41 = a3-lt
G
4-
t
Or=A2=Cr=E
13
Qonsider the
Q
=
36.
urralized wavefunction
q{n* az{n*
a3tlt1-1
where fi,n b a simultaneous normalized
eigenfirndim of tre angulaq momentum
with. eigenvalues
operators Lz ud
l(t + 1)h2 aod mh respectively. If is an
eigenfuncrln of the operator Lx with
eigenvaluc fr, tton
L,
1.
a1
in
1. -ih,r(x*-)
{
2. -ma(xft+i)
=-&3=-rt .oz= fr
o1= g=f,,
4.
r',1=or=g,
3. -ihuxft
1
az= G
't
ilio
4'
-Tx&
A
az=-fi
orl.=or=f,,
1
--2
' '/3
37.
at f.aFffiTo, lx,pe-Pl+,l qrfi t
7. i{I l. i(1 -P)e-n
tl
P21e-o
tpe:P
3. i(\- e+)
/P
Let 'x ard p denote, respectively, the
coordinate dtd momentum operators
35.
.
satisffing dte canonical commutation
relation [r,pl = i in natural units (h = 1).
Then the cmrmutato r lx,pe-tl is
l. . .i(l:p)e-t
3. i(l - e-r)
2. i(I - Pz)s-o
4. iPe-n
.
ari fo, {, irtn {z
z'
(Ez-El)
2(82-E1|-
and rP2 denote. the normalized
eigenstates of a particle :with eneiry
eigenvalues E1 and E2 respectively, with
Ez) &. At time t = 0 the Particle- is
.v(t
.r'
sFi-dl, s
^hn
tJ'
.
.lhbil
4' -Tt
at
::
a(Ez-E1|.
W {,
w'rirqfr tr*,rq €r
tffi t Il =r,xp,ufr artnfi'3{tt{ f,
dtlr r qf, p 35rff: Fna (ii d'drr tt
miz{ qifufi 4 trftria Acqur fi :d'rra
r. -iho(!L-!)
2. -ina(x**t)
3. 'it*#
@-n
.hn
L
fat
3.
Mnryqifr6r f
Ir
htt
A
l.
37.
Fq
f
prepared in a
36.
trrnT: 5at
$frdnFm rFt E1atlr Ei (Ez > &) gffi
(rif isuf h rflrfiq-fr 3lfffrHFrfi.
wrrq t = o tK isut
trrRiqt
qarqr qrdr tl
Y(r=o) =fi{rtr+gr)
qfifi Srrq T,ilE Y(t = ?), W(t:0) t
difffi tFn, rO t
tr
r- asr o mt: H&Iifi aelr
tidzl dmr+ Frqr ldFa rqFfrrq
ddtr sqfu 3fu tn = 1) f [x,p] = i tl
ard,
the
in
representation, is
11
2.
3.
Suppo# the Hamiltonian of a conservative
grutun in classical mechanics is fI = @4 ,
wtrcre ar is a constant and x and p 4Te the
position and momentum respectively. The
quantum
conesponding llamiltonian
coordinate
mohanics,
state
;
= o) = #(u,
+Qi).
W(t = T) will
is'
Y(t
0)
to
=
htc
2."
(Ez
The shortest tirrre T at which
be orthogonal
tZfu
'
@-n
4.
z(Ez-E)
f
hE
qfiFrel
ssS
frt ari t:
, :l(v 'l.0for
d'd3
-Er)
htt
4(82-ElD
fi t-Y:tf;fcrerur
0.7) /soo
for V >- 0.7
v <0.7
-.
14
rd vdrffi f atn t
qret
l=
2.
3.
4.
mrq{ d'qrq
l
I
1K
S a factor of
increasedby a factor of
decreased
38.
+{ur {tr
f
fd?Tdtlm
rnA'
6.2 mA
i
t
arr
mr
2.
4.
10.0
93
- l.
{(V
-
0-7)
mA\
6J mA
qtrd f;.Td qrqr rrqr Ffi
rdJtd fi t tr6l Y 6{ +.ur irl
*'qr
z{rFd ca
l. 2.08
3.6
0
fortl<O.7
I is
measured in amperes.
1Kt
t0v
is
Z. 9.3 mA'
The current I in the circuit
1.
3.
39.
mA
6.2 mA
10.0
i
4. 6.7 mA
fr'w qq alt 6r*-sild
W, Frd wu>W), t ('ifi' dfd
6r4-s6fr wM
3rrtfg;95, qlat
tr
drdr
6r
(rs, rirrq
qf4 3idrr1€
f
tIrT
wmlr
6}
fdEgil
f{
dra 1mr cgrar t af $furffi d' slqe
:Hrftil
l.
2.
3.
4.
39.
tF'r
t
ftifd t, Td c IRII b 3lir tt qfr eiq
6l qi{ffifi grjltrd Yo t,
a}
si{fffi
?Trf,
ffi dgr qra 6'l; T6ra fr
Rq frnrq d dqfrd ffi sr* tr{ frqr
pn
t
Zpo
rrqr mr4
t
.'l; or!%
t.
semiconductor of.work fundfun Ws \Irith
the elecftic field at
2. 0.09
4.3
;
(o*bpo)poVs
,. (T*T)ot,
A junction is made between a rnetal of
work function Wu, and a doPed
W. If
$qqr sfrerd 3Tfiftrtrdr
. in the measured force is
' l. 2.08
2. 0.09
4.3
3.6
41. ffi nq in qFI P Tsh Tircqr qtrd p t,
$irFlf Sfifluf P = op* bpz ii-dRr
2.
e Tnr q6rar arfSt
3 TflT ifirT ifiGIr qrftt
3 laf cqrar qrFt
16 Tilr ox,rfi'rrlr atftt
Wu >
f
40. In'a measurement of the viscous drag force
experienced by spherical particles in ?
liquid, the force is found'to be proportional
i to V1./3 where I is the measured volume of
each particle. If 7 is measured to be
30 mm3, with an uncei'tainf bf 2.7 mm1,
, the resulting relative percentage uncertaintSt
/500 fgr tl >0.7
where Y is measured in volts and
tq;rdt
ErFd 3{rrrfi H qfa Y 3lRftYcrdr
2.7mmt figtq, 3omm3 arqr grdr t, aI
The l-v characteristics of thediode in
the circuit below is given bY
't
3
3
decreasedbyafactorof V3
Eil v1l3 t
l.
3.
9
F f 'dffiq 6urt t qt{Ra
10v
qfrqq
$ra factor of
increased
the
interface has to be increased by a factor of
3, then the dopant concentation in the
semiconductor would have to be
(alnz+
hpu)piYo
.
of a fluid is related to its
numbpr densrty p by the equation of state
D
f
;-f*ff1.
Ir the initiat
where a and
volume of th fluid is Vs, the work ddne on
the sptem u,&en it is compressed so as tb
15
tb
increase
value of:po
l.
2.
An ideal Bose gas is confined inside a
container that is connected to a .particle
reservoir. Each particle can occupy . a
number densrg from an initial
toZpois
apoVs
discrete set of single-particle quantum
$at€s. If the probability that a particular
(o+bpo)poVs
quantum state is unoccupied is 0;1, then the
avenge number of bosons in that state is
3. (f,[email protected]"
4. (aln2+ bpo)poVs
('fi
tr?T
tl;T'3ttr{
6
f
rrfreffr
l.t
3.
w ffifu6
q;UT
3rFT irFT
fr
fr rfl6l
Til rfrt D s Eo t,'flI srEgn sflR *
cr{ ari qraTr gr{ffid [g K gs r6K
trfr t:
T6 f{qr rrqr-t
l. io"
gas' at low
temperahre, .only the banslational and
rcatiofial rirodes of the molecules are
excited. The specific heat pOr molecul'e of
h low density o)rygen
Eo
Jd
Ep .R 3rrfrd;r6t
The Hamiftonian of
t
a classical
the gas is
r'
particle
'movingin one dimension is
''n2 fl -*-+aqr
Zm
io"
2.
t;ot
4' f,'"
3:
where,c is a positive constant and p fid q
are its momentum and position respectively.
Given that its total enerry E < Es the
available volume of phase space depends on
kB
El 3fq-(rd Ar ct?rrAzTiri1 (rT' {iEtlfi
sftqrr, qI fud fr'nfqr rrqr *'qlt d'
t
lclilKt
Eo as
4.
ks
r'3i!
3'
4.
3.
2.
3' io"
-O
2,
l.
2.
wI t
FffIq
,
rr.
f s-* qa;E fi' 3Hrfff its
f, qut * h{fl erniafr* tii q.ota
drs dtrd eti tt Fs its fi q'fr 3q
t wi p allI q rqir: Tst liirr
pna.Fr
.2. 9
4. ll
lo
E3l+
Eo
rE,
is idependentof
Es
('fi 3{tq* a)lr tts, (rfi. 6sr-sisR t g}
(rfi ril'T * 3i{t sad $1 5q mur, \r6Gr-
ffiia
t $6' rf{ff
sflzrqfr6s661 ilqfrffiftia
3r+Frr t frtrd 16A *I sfr+"r 0.1 t, dI
Ts 3r*qr f dffirdT 6t qrt. :dwr t:
E6ur
l.
3.
8
io
3ffiFrufi
2. 9'
4. ll
-.
qfr nmq
koe
r.
z.
a)
ac Tiaffi
sh 6r sfretqr
5g
frH s?ril d'+ta-sr s€t p
t
fr'e,4r gFnrFs'd[ S€Rq
ffi qld cfrEFn r E-a sfrm tt
qRgq S e,4r 3ilqerr6-dr SflRq t
qntqq
t
fr
Tfd cf6qpn R * rEa
6q tl
16
3.
g;t{ itFtr st strtFa
t'a, mI 5cnm m
ffi
ffdr qfrqtr
interface show that the ratio of the electric
field amplitude at tte mo(ima and the
minima is 5. The ratio of the reflected
intensity to the incident intensity is
t. 4/e
213
sfii tt
4. qfa aFs dafi €I im{r 6t frJir
, +t q+.pv'rrat t, * qnqq tr Ar
or tbn $rEqrrfi'tt
45.
Consider the amplifierciroritcornprising
of'the two op-antps A1 and A2 as shown in
2.
4. tls
3. 2/s
47.
tril ift,t)
g.'e'=q-# d?rl
i,-V' =i+VE, r6i'f,i ?rer r tnl (,i5.
st€'r, dild t?i :r{rffiiq trTd .t irfi
Brfftil H iliil tr qft gsh Fq{ 6q
dlt"fismr ffiiq
$frqr qd qfrer frrrc a(i,t)
(tzF TrqFI s.qtirtpf
the figure.
1U
.
V.tr+ !g=o
6I sfi ar{ 6t
at
wra 66,4 fi
R(t ('fi dmEq ilur t: gc5i a,,f fgqg{
3t{t S, a' = cl1l * urrq
If the input ac pignal sdurcc has an impedarice of 50 kft,.which oftrc following
statements is tiue?
As is required in the circuit because the
source impedance is mrrch greater than r
2.' Ar is required in the circuit beause the
source impedance is mrrch less than R
3. . Ar can be eliminated ftorn frecircuit
v,rithout affecting the overall gain
,f A1 is required in the circuit if the
output has to follow thc plrase ofthe
l.
,
.
l.
2.
3.
4,
*dr
coshEi
sinh art
cor[.i
coshart cosE
cosh
i
art coshE i
t
47. The scalar and vector potartials [email protected], t),'and
AG,q are determinod up to a gauge
transformation g ) g' = rp -#
and
i -V' = 7 + V6. wtrcr f is an arbitrary
input signal
grfi
cosarc
"i!
/ PART 'C'
i
continuous and differentiable function of
and t.If we further impose the Lorenzgauge
condition
ldto
-1
v'A+;ar
46. F{:ifr req *. str6 s{ iiqrd JrqRil wffinT
frTdgn-firq atzr 3ffrrffi sffid 6tfi
il limrrya *. inri fi trd f rfi grrfr
aier qr fst rFf lrrrd t qdr qdirr t F6,
fG, Q
t.
4ls
46.
A
L
is (where
constantswittt
ItErtrff qd ilTcdq q{ frqa fr{ fi
3ilq s *' sr;rqra t, Fr sftqtrd a?i
$rqfd trrdrcit sr q$dt
3. zls
l.
2.
3.
coshart
coshart
us
48.
,,i
^r"nonzero
'
r=cFl)
cosart coshEi
'sinhart corli
4.-
213
plane elecfiomagnetic wavc incident
normally on the surface of a material is
partially rcflected. Measrrnrents on the
standing wave in the regio in front of the
=o
then a possible choicri forthe gauge ftinction
ilcrlrlFf
cos[.i
coshl.i
'm dqr griT
e gffi
(t?F'
srdrqqifrq 6sr, dt lfr u dqr F{ur a
*' qr?r qReffi t fi*ar r qrfi fdfddur
otrar'tl
fr-aril?r n/2,
grirr ze,ttfr i/2
'
17
qii dr"r ?a g4d 6ur t
dIE-dr +qr
t. t6I
3. 4I'
il
gtrdt
t/,B),laln ,6 <rut 6tw' 6I frEEe
Rffiq 6r
arar t) W tr{
2. 8t
4. 2t
,
I
,i
i arethepcition, mcnentum and angular
(whereelp is dre lrcvi{ivita symbbl,T
morncmm rcspectiveb, and [r{, B }
reprm 6e Poisson bracket of and B)
simplifiesto
I
*i sgu{qt f daj$ Jrql rJsra
6,rdt
1.0
3. [email protected]
P
(f;, {)
2. (h i)'aei ar * r
1.
sl. w'
bl2 +lll2=
fdfr
1),
frnq tffi
sqiirur *' qfiqg,
dtrr p*
t tl
tM
H(q,p) =
il{ Ff{rrifi
m wilr
r. *er, *Yo,
l
2. zr-'
a1ji:pz
'z'
51. A rnechftal
'
l* ll
,.
$ ,. -fr
b;,
system
-9,
ffiiern dfi-Rfifdr rdffi t,i,t,i
q?i
and
2.
*Q'r'*Yp'
3.
f,.e+$0,
*tr*+Pn
I
Eg
!'
I
ry
I
^l
,.pf
t
s/55 CSr/14-€Blt-2A
a
r. *trr*Ye,
'*{o,{0,,ail
*tT e
!
** j
monrci&rmP becomes
qd +tdfq
\
i, arr"ril-.Ait €r A
nian in the new coordinite
Fnfl,,Iitrl
?rqT
I{ariiftonian H(q,p) =
muzq2. As
a rc$h of dre canonical hansformation
gqlerdcd by F(q,Q) =
the Hamilto-
50. aftil-d
tr?TQT:
0
dt E:- Ct
'
t.(fr frl), *cB' isrear
o (:p. f.),
t
"*n loi'+ lllz =
I
dfrd
il
3. |r, +{0,
LOzlr- *mo] p-z
4.
'- 2n-'z'
*,,*'*t
Ult=t
*^*
Ozpz
Let a ?nd P be cunphx numben. Which of
the following sets ofma$ices fonns a group
under matrix multiplication?
fl
'(;
, (p
qifrf;t
2.6
a. 7xf
l^rtt'tqffi-dil r1q,q1 :-; t
(fr ft.), at:'rqrmF6 tl
4' {!0. f'), *
r* }}
'*k''{P''
l'l'k=t
f sFFr dwt il Anr
tr{ (c5' WS ot ftrfq
The expression
3
4. 2l
f,*' a d{r
3Trqif
50.
t:
2.6
4. ixi
1.0
non-relativi$ic particle of'mass m and
charge e, moving witr a velocity d and
acceleration d, emlb radiatlon of intensity I.
What is the intensityofthe radiation emitted
by I particle of mass miL, elnrge 2e,
velocity ilZ mdueleration 2d?
2. 8r
l.- 161
qrfr,
6fdr
3. i0txi)
48. A
3. 4l
tttrftr
J
-!l
--
to' ?t h
l-
n
i0
I
, -t&. P:- l*
I
18
f* i
52. arfi
qrrfr
ry'
il6t r,1,o2,o3
= (o1,o2,o3),
ti qft a .Fr i nRffi f
EI
-4^z
t, at ilRg4o.fi
Id.d,i.al Fss gqrd h Os tr I t - 4.
ilFFff 3IqO
d;d $q{
l.
(a
qrfrnr
4t"r-*
o2*
$a?fin1
ruti""r.-ir
(x2
d
dimensions, the commutirror
(in
' thg following
'-"v."r'6
[ad,
t'#- t**
t ;iT
I bti' 6e
rus identitv
r.,e't*v
(a.D'
4. ldllrll
54.
d,'- ',i-:r
3.
I,H{H#H]X*T'
l' z=lil{I
avr
[email protected] tK ilr€r F5
0<d<zr*'RVs=Q
rfi[('rr
$'rcrch
Z.
z=rdrtr [email protected] tr{ ilrsr.fi$ aVr
0 s0 <Ztt *' 3idrdl 3lfr o *' fr('
z= 0$[ ffi' grdilfi
3. . z=lirrrr [email protected] tr{ ilr€r lt5 mr
53.
mir+
I fi,fu
z.1otr{ w
z=0,_z=lifrll [email protected] *{lrrotrf5
Considerthefirnction
-o
q
@
<
o).
The
are aslfollows:
l.
2.
f Q) =|to.1f
- r;
The function
/(x)
o
=
(rz
- r)f = 0
Xf*ffi
(;)'"-'
satisnes the differentiar equation
l'
"#*'#+
,2.- ,'#+
qFrrrt z= re.e (rt0, -po<0<-)
4.
tl
::'- .:
3. ,'#r*t**(r2-ty=g
-
f
^ 6 { [6., ]* ,^
:l:;:.
1ffi
StuEFr 6Tdr
i
-,d"i" rr" *o
arbitrary constant vectors in' three
):,
str6rq
,'
xfi+ + r)f =
"#+
1]/ ',#*u#*(rz - ry; = s
52. l*t d = (o1,c2,os), where o1,r,2,os are
matrixy
z=o.
'
4. Ftlilr
equat to
i=t
i_' t_
g' tnil?T f(x) =x;i.ffi$'"*'fuo
o3)
2. zi(axi).A
3. (a.Dr
the pauli
and a pole atz = 0'for all 0 other
than 0 < 0 <2r
branch points atz = 1 and z = o;
and a pole atz = 0 for all 0
branchpointsatz =0,
and
@2+ 1)/ = s
ztff+ (x2 - r)f =o
3. t'#+rff+(xr-t)f =a ;
4 ,,#_,#*(,,_1)f=0,
55. 6ril
rrM
it
f
fr'rmq|a
drrfr rre *.arw.
]fdr zrqr I $p1
3idzfdlq qrrr,
(gfir{ur *. Sfs), q6 mr rirlil (il{ qffi
drq sqra w viudf t} ildr$ rfi {16
$qT
rR
Tt
t
o" AtrEg il anf h
drrd *f 6qnr{
fi, grrr qs-r
*-
f*.gtid ,,
il
T1tr1
il
r
*r,
Tm,ry{
1rdt qd drrfr
*' ssnm s} ErdH
gt, q{ *, srter
"r,*
qra sI rfr, il_{ T6
r(fis<<r<<
q{'t
Rr)fr q$w
t a an 3
singilaritis of f.(z)
= tard z = oi and
< 0 < Zr
=
branch points at z =1 anil z
= o;
branch points
apole at z
atz
0 onlyfor 0
stSscsut{-58}F,28
r' ll'
19
W
f*
,w
56.
l.
trcrl
.J;
Jl. The probe Mangalywtwas
sent recently to
it.
ftetirc
individual Eansisiors connected
is
If the only form of noise in each transistor
i7; nois", thon tlre equiv{9nt voltage noise
tpLr"f O"*tty for thi MOS transistor is
f . f/fV timesthatof aiingletransistor
2. 1r-l N? tiqnes that of a single transistor
3. w ti*". thatof a single transistor
4. Nz times ttat of a single transistor
57.
e*ptot" the ptanet Man. The inter-planetary
ttui"tto.y isappro*imately a half""'J"ftt"
Lttior" with the Ear$ (d the time of launch)'
Sun and Mars (at
of N
A large MOS Eansistor consists
in pqalle]'
fqffta m *' qif ifiul firlrd y(r) = alxl'
(c > o) t'sqrd f tl wrnsFffia f
rdt rrffiaqfiIo qrf Er (n = 0,1,2,"') f,
t #,"*il"' I *.E-v)' dn"
)o
n
,. [H("* )f'"
1.."\ - d(€ ]
dre probe reaches
a.tti""tion; formlng the major- -Tit'
n*ru*ipg that ihe ortis of Earth and tvlars
cirurlar with radii Rg and
"r"
ieipectively, the velocity (with respect
n","pptJ*i*ately
voyage
to"itre Sun) of the probe during its
(( R1v)
((
r
(
Rs
r
*t i" i, is at a distance
of
fto* tfte Sun, neglecting dre effect Earth
t.
llgH
ffi(*+) 4t "?d
')i.ru
t.ffi(,*gf"-il CPr)&"
ffist
and Mars, is
potential
57. Consider a particle of mass?r in the
qnergY
eigen'
The
a1a1, a
V(x)
) 0-
=.
.rot*t E,. (t =0,1,2,"'), in the WKB
7ilt
zcuffi
3.
ffi(n+!)
J-
''ffi{;
4'
56.
.&38&=-9'
ro'
@.{'tLrP\"\s ;
w G qr3fi'JT. EifuF{ f sniil{ lftifua r
qft
fi '
$6 eifrg-{ 3iffiffi tr et eifrs't
;#-;r*-r***"*m*t"
*#"H,l:'uH}-;*u
qt qr ffia trrd qr vo
iid Td rrn
,tg-dr
Fftd arar tr
fi
*w
or
qr3fi'3T. "rd".
*"tr{ rffar*ns1tl-gpfisrart, s?rqqra
{E ?5T r;5rnr sq 1/f Td t, d
grRE.{ fi Rq ga dlds {q- TqFEd ffiFr
6\fr ffi-d Ffa qr 6'fq s" t fi+s
trF cmar tz
r'+a EiRst 6r gmr fr
2.
t. UN gr t
'3.
lI T{r t"
Io+
L
r7rv'z
gar
4-' N' 5dr
:l
t
t
l. 6'60"
5'ol8:
'
'u,Lj} *,
{o''.+l){lJ
'L"u )cr-
+
2' s'l4o
4' t"'
\ol,
---"D
_
V- t-'
4L-'.
ta.'
\.
t'-
t-
;L
*_p "*-l'
r
rt
20
When laser light of waveleng& .1, falls. on a
metal scale with 1 mm engravingp at a grazing
angle of incidence, it is diftacbd to form a
vertical chain of diffraction spoc on a scroen
kept perpen{icular to ffre scale. If the
wavelength of the laser is increased by 200
Rg $qfuqfr Fnn
frp
(d /", t, &fi
qr
ffif { Sdtuo tr
sniil{
nm, the angle of the first-order diftaction spot
changes from 5o to
l. 6.60"
3. 5.0180
2.
4.
5.140
52lo
qrfr ffi' t'fi-Rrfi 3nr** qfdrfi * silraw{qr
aqr glrr 3dfrd 3rirFn fi dtT qtrdt frr
(,?fitrkT dtrq hI,) = col0) +crtl)
t ccdrro
?T?r[ cr 3rqt t 3itt r8 *cf = 1;1cs *'ffi
qro t'R(' k) 3rri
3tnaarT
u
l. (r)=F , ,o=Lfi
{qr
frH Tqd *da+r sfr p
urEr
l.
fnp
2.
fap >
6Tdr
2. ttl:.,rlF-.,
t
co=l
Let
t;
{mo,
co=i1
l{) = col0)*crll)
-4fet:F,
,. (r)=F,
(rJ =
F,
mrar
t
t' frq, a {s vrsr fr;eg{ t
s'{ f a* olar t aqr B d*d aht
fnp < fu
4.
fuFw fut fftT qlfrd srdr
hq, A d*d st fu€{
fnp > fp
qrfta
Ril ffdr
mrar
aen g fs_
cs and c1
1) be a linear
(w.here
are constants widr cfr + 4
=
combination of the wavefunctions
of thp
ground and fhst excited $ates of the onediminsional harmonic mcillator. For what
value of cs is the gxpectation value (r) a
maximum?
qfrr
3.
.11f
t
fr{6r"r fu6a{ *'sq
60.
.
fu * frq, A:d*d d qrnm 6IA
t6dr t iln Bri*'iT st ffia{ ffit
fdar
1
3. (r) = l-!znar' co=E
4. (r) =
t frq, A {g qrr6,, fu€t qii e
6 6q-6or ftE{ t,sq f srff +ri t
1;o
t
t
f 6Fr 6{?il t
Consider a Low Pass (LP) and rHigh pass
(IIP) fi lter with cut-off frequencies
and
respeCivrly,
connected
in series or in
f1p,
fp
parallel configurations as shown in the
Figures A adB below.
co=E1
co=
':
1
i
L
'1
co=G u
1,
4. o) =.F, co=i1
-
b
*tJ*$'
aw /,
e) ^K\
(B)
,t)
t'
I
t,,l
i
21
$
l.
filter and B acts as a Band Reject filter
'
2. Forfry" ) fw,A stops the signal from
passing through ard B'passes the signal
withoutfiftering
For f6p fw,A acb as a Band Pass
3.
filter and B.pasestre signal without
filtering
4. For fr, ) fi,p,A passes the signal
withoirt filtering and B acts as a Band
If
now thc. same process is. canied out
adiabatically and irreversibly; and Tj is the
+
temperatre .of
equilibratddrn
,i=Tz
F
''
I
61.
si, i = L,2,...,N
(S1= *l) EfiI q?5' frf atq T f rm' argq
E"€r. etd a f rer ffi tl fiffirq 6t
tffffifi t rr = -Nttst I qrur 6i) >i
ilfrq?
r. f,n nz
3.
A
2. 2ln2
4. iVln2
#nz
collection IV
minimum value of
value (Si)
t.
]rv
2l?
ffi
2tn2
4.
3. |lnz
IV
ln2
t{fram Tffiofq sffi'qr (dr{r d{
(1q, rts $rqtrd r, t r, irir Elqrfi: fdg{a
drfr t T6 arq 4 t r, ilm" tffrd et$ tt
qfq q€f sfr-qr @a: qd staffifi!ff{d:
fi Eildf t aqr Eri['ir6 srqrcRtd F m
1ro
r; t dI
l. Ti=f,
3: Tl=TzebJ
arq
ti> r,
2.
fl=w.
a
gas expards adiabatically from
volume V1 toV2 by aquasi-static reversible
prooess, it cools from temperature TrIo Tz.
62. Wh€n
ttir"-fls*-',,,.F
..
ill J+
- .---')
-
t,t.l
'
t
.,
.!3
rl
<)
')
-.
f
ffi
L NF.
3. Znlt
t
2: nlB
4.0
63. A randomwalkeq
'
takes a step of unit length
in th" positit a dhection with probability 2/3
and a step drmit length in the negative
direction widr probabitity 1/3, The mean
displacerned ofthe'walker after n steps is
1.
2.. nlB
nl3
3. 2nl3
,/o
64.sq.
@f+rqfifrqtffi
3TrE{6H,=(l
H'
z.
qrfrffi
f
for which the mean
rnz
4. ri=T
qrrdrft tril?Fr ftnn
$tr+,ar zF?. {tq (rqr6'ffi m uc'
6q7r aqr rnfuftr 1/3 t' flrrr ?ilrldffi
ifit ('i5'aaq dmr tl n
Enn Effi
m,{fff t' G qnrtltf .ff etsq F{qrrd
of
non-interacting spins
Sr, i= L,z,...,N, (S1= *l) is kept in an
extemal magnetic fieldB at a temperature T.
has
2.. Ti>T,
.ri=r,W)'
e?5'
:
The Hamiltonian of the system is
ff = -pBXrSi. Wbat should b€ the
c2.
63.
rffifagrfuit
fi frq # 6r efnirfi aFr rqr 6tdl
61.
3.
filter
Reject
the gas when it
\
i
il-"il{rr6
l0 10\
= elt
0
r I 1retr << 1)
\o 1' ol'
t qtrFa
dtfi 6, qnwrT rrrsrT Edt sffdwtrr+ ard
Eo=2triil{srh
1.
2.
e,-Ze
-e.Ze
.F,
j
t4. *2e
3. te
))
'
64. Ttr Hmibnian
H6 for a three-state
quanhrm i5r$ern is given by the
<-
mafiix , !
(t o 0\
flo=10
- Z 01.
;*-'L"
\oorl
When pettirbed
$
+)2
H' =
e
fiiil
where e (( 1, .the resulting shift iir the
erierry eigcnvalue Eo=2 is
l. €,-b'
3. te.
.
i;
,/'
-e,Ze
'F
lze
j{
,J J=10,,1
( t
.
''
22
qH snilur 3Fa $ird [email protected]) = -b d(r) il6i
b>o
sat mnur qtwsr EFila
o. < x< c fiftt
0o) =[,rcosrf, -
65.
t
0
,
l.
,iw
sJ.2
qra t:
m,b2
J'
**
F.fiffi
65.
.
The
grud
$ate energy of the attractive
de lta fi mctkn' potential
whcrc D >'0, calculated with the variational
trial fimction
-a
for
t 0,
TUII6
t:
'."[(#)'*(#J'l
n r|+d
^'?i1;;
l/(r) = 'h 6(r)'
o(r)
- = fncosfi'
72
92
rlBq{ Eflt{r$g 6r Tsfdffi drfir wrt q,ri
rHt t qzvt t'rsq tr sffi{d tr rt
alG;qfr q{rilT fi fuqr 4 ?r?n 6{ Tf,}fti
q fr tuvr.a il rtat h fifi FeE w
s{ir rFT ard?fi, frFrd lliTi tt ss ft6* *
3ralq1,
*'urqqffid fi ildl t d rror
)b2
2mb2
^
'''' rt*
[email protected]
^{
--ffi
2.
4.
68
.
,.m
,l+d
\
n."ffi
< x < a'
otherwise,
ls
-I
^{
--
2mb2
}P
/
r,h2
--zl2P-
=g,
mb2
-ffi
4:
66. hrdl ;[fro, fmrfld
zl A iffi tffit
B
67. Considor the crystal structure of sodium
drlorlde which is modeled as a set of
touching spheres. Each sodium atom has a
radius r, and each chlorine atom has.a
radius 12. The centes of the spheres form a
.simple cubic lattice. The packing ftadtion of
:w
rDz
A-asAzn
riqr ,l arn gTrier
- o'
(22
tris system is
,."[(#)'*(#)']
:A)z
'n zn fi+fi
':.71r6p
a"Z2
_M
.
't
A
'."ffi
tl
MeV,asrr = 24MeVd{t ac = 0.75 tvtev
A --TL6 .gfir \1i5, ilfrlfi, 6T 31.q6 ft5q
{qflfrfi qiqlul 6r z t:
5
2.
t'
':*
66.
ntmberl
and charge Z ) is
t
B.=oyA-asA2l!
strfi *s rdnff t' Ert tr ffi
ffi t ('ifi'fi wra q-a Tiwdr t aqr
ryt m EhcqifEnqr +irrar tr d_?[qr
enrnrt f v{ms$fi fr ilE s!ilS *,,,qril
trRifi Sr grnr f.'c-frqtT fr srffrspit fi
fq qfirfi ;r'dt Rrrifi sTrrrr tr 'ffi
gt
D
(mass
liven by
(22 A)2 o"Z2
- or^ff_M
.
..
where' a,
= 16 irt V, as = 16 MeV,
'MeV
os)ru = 2f
and a, = 0.ZS MeV, then
the Z for'tlrc most stable isobar for a nucleus
withA F.216'is
.f/'L
:
6s. El
72
If trc binding'eaergr B of a nucleus
ti+d
"J (rr+rryr
ilil A a6i' av = !6MeV, a, = !6
l. 6t
:
q{ ER€ srsqr +t qtnrfi dFrErd fi
.q{6rt irFr. rfr ffira f'ga ron $rBd
arqt
.
ilnr
l()
t-
i
$'!
ir
:l
lI os
lr
I
!
\,, \
.
.
\*\
.t: \
\
1
1
'ft\
io j
r'l
tt
il
$
23
r.
Efd$mhrmdffi yqrt *'Rq 12,
qrg srdr w dw qil* Rq 13
t
z.
*'sq tr
af,cwmiqffi dffi .rdlf fi Rq r, drn
s{er tra
T<t{ fr frq 13 *' sq
t
fr
3. dtdt 6ts r{rfi * Rq r t,w f
4. ffii 6ts r{rfi fi Rq fi 13 sq f
70. qfr vo EFvraqm ry 4r ,'-dt ?frtr;r FK
6r :Et 6r srm sdErdl {ijtr
-+(n+l)'h&,,t6t r" = o.oo1t iil
dil-arat wit fir Fo dwr wnrrr t:
l.
crlntalline solidg one of
which has a siryle cubic shucture, and the
other has 'a tctragonal stucfure. The
effective spring constant between atoms in
the cdirection b half the effective spring
constant betwn atoms in the a and D
directions. At lo\il temperatur6s, the
behavior of the lattice contribution to the
specific heat will depnd as a frrnction of
src* t dE w $Srq A-* Eer
JqRtr { w'$furil+ itirq qfi grK
fdsg-dqm
l.
1.0 nm
l.
3.
3ffdfffi
* 3iat t
f
tl
h
v6'T{{
4. s
il
w:Fqt 3iilrfr Eattdr t, il
strqrirfr fr {flrur ffi fi 3rfrd d'
tt
2. 0.1nm
4. l0nm
tS
rrcamqa +'t
t
f{ Trffi t
69. An atomic tansition lP in a magnetic
field I Tesla drorvs Tneman splitting. Given
that the Bqhr'magneton' lrn =9.27x10-24
J/T, and tlp rravelength conesponding to
the transition b 250 nrn, the separation in
the Zeeman spccfral lines is approximately
'0.1
nm
0.01 nm
.
l0 nm
1.0 nm
tr
qrffd $trdr6
hcle Er !m-d
micfi-o
tfutarfi S EqFqRr t,ti {ffirq
qHf Trrrq qr fret{ afr Sl
3. fr;q-ffrRr trffE idqr Fsfr+:rur
.?x1'+A2d= o dtikd t, ;r6i n
ErrreTrr
0.01nm
qfff, 6{ar
q6ori:
rS
l.
3.
750
71. sqd
z.
fr
2.
4:
t.
air' E{€tq
tsnfr
-r"
3.250
fd f vfr
q{firurrffi s'iiEur tP - ffi Fdcr6
Eefrdr t t aF ffida pa=927xl1'24 !ll,
aefi :itrTsr t d4d dirrtE* 25onm t, d]
ffi rftr
750
levels possible is approximately
500
1000
- 4. it forbotr*tidt
l tFsr *,
1000
(n + |)' nr *itf,
xe = 0.001, the total nupber of enerry
diatomic molecule is
temperahre T c
l. T2 for thctetragural solid, but as f3
for the sirnple cubic sblid
2. T for thetehagonal solid and as ?3 for
the simplecubic solid
3. T forbodrsolids
69.
zfi
70. If the lcading anharmonic correction to the
energf'of the r-th vibrational level of a
68. Consider two
''
2.
4.
500
3.
;
71.
A suitercorducting
ring carries
a
steady
cunent in the presarce of a magnetic fieb E
nonnal to tlre plane of the rirtg. Identifr the
incorrcct $atement.
l.'
-'f4.
2.
iJ
The.flux passingthrough the supercorductor is quantized in units of
lvle
Thecurent and 0re magnetic field in the
srprconductor are time independent.
"1
'h
24
3.
The currcnt density/and
by Sre e4uationf,
4.
x/+
F
aie relatee
sitifisr
3" drlT
strfr
ttd'a rqgq $
fr {lq
ltffit
H'="3".30 t fr ildI t r
Tririrur-ni$FuT
Fqffiqr
ar*r
l.
3.
tR qra loo mwcm2 il q
AzE = 0,
where A is aconstant
The superconductor shows an en€rgt, gap
which is proportional to fte transition
tempeiatuie of the superconductor
u agstra ry
f lffi
h'qftunfr
6tdl
ssrr
gs
:Ff,t Tat €ffi
t:
2.
4.
lon"
oilL2
2ah2
lahz
2.
gRr.
l.
2,
3.
4.
4. f,"h'
Zt. 116 ffid a,ri fi R(' fr flr etfdt SI
. l.
L
3.
1.
1.25
x
10e eV
1.25x
1012 eV
1.25.x
tr05 eV
108 eV
12Sx
o.s
Bega
v
o.s irfi
0.?
t
42.0to26..2
24.0to16.8
.
21.0 to 10.5
16.8 to 10.5
fia
tnr qfrqnfi rK Rmt:
gw
t/&
oufr
(r) P+-n*e++v"
(ii) Ao- p+*e++v"
(iii) fi+ - e+*v"
(rv) no -y* f
ohz
F Fnfr 6ffr ffi{:
ffi
f
74. The power deni,s.ity of sunlight incident.on a
solar cell is lffi mWcnf'. Its short circuit
cunent densrty is.30 mA/cm2 and the open
circuit voltage is 0.7 V.If fie fill factor of the
solar cell fureases from 0.8 to 0.5 then the
perceirtage efficierrcy will decrease from
2ah2
56 3lidfffi dr+dr t qr nfr, trs{F grdqrclr
fr€Iotd S Sildld diffi t rfiFhd ffi
ari il f*rh mq Ftq*a 6I Fqt sl ffi t
qtr
' .2. 24.0t 16.8 irm
3. 21.0t r0.5 iffi
+. 16.8* r0.5 ilfi
pven by H' = aie . 3o. As a result of this
interactioq thecnerry levels split by an
amount
3.
t
qfr st{ td $r ry{rir
T"i"
qedT t, al sfren ertrf,r Etfi
l. 42:0t 26.2 d6
dre ground state of the Hydrogen atom is
2.
30 mA"lcm2
aqr gdr qtr
il
72. Tte effective spin-spin interaction betrveeir
elec&on spin 3, and the proton splo 3" in
.the
r. ion''
ts w $TqRd qfnonr 4t
24. $fi'ilt{ (ntrt)
fi
Rru lqtrtrd
*
+ta+rnil affia
2.
(ii)lT{rfiv)
(ildan(ii)
r. tTfr(iD
3. (i)drr(iv)
75.
4.
Considerdre four processes
,(i)
1n+e+ +v"
.ftii) A9 - p+ + e+ +v"
.(iii) r+ -e+*ve.
p+
(iv) ro
+y+ f
Whish ofttre above is/are forbidden for free
tr deep inelasic scattering electrons are
'scattered
offprotons todetermine if a proiton
has 4y. internal structure. The enerry of the
elecbon for.this must be at least
particles?
l.
3.
only
?.
4.
(ii)
(Dand(iv)
(Dand (iD,
I
l. 1.25x 10eeV
2. I.25 x
.1, L.zS x
4. L.25 x
(ii) and (iv)
.51
1012 eV
106 eV
108 eg
i
r
I
I
I
\
`