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[

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glreff 71r17 61:

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3. yi Ow 4' Tr rutpipf

4. ow ereE 4r ura rt Fr9T-7

2, .% .arr-? Tri e ?

I. 9 2. 14

3. 15 4. L7

3, cfw l vpior gram/ wig gnirf 4 4T-e7 cit4 Pew arrrr mr4727

rn mo t ?

PART A

1, In still air, fragrance, of a burning insert e stick by smelt by an observer quickest when the experiment is carried Out at

1. tow altitxre and high air temperature. 2. high 0,1t1tixtc and low,. air temperature. S. low altitude and low air telnperalure. 4. high altitude and high air temperature.

How thany squares arc there in this figure?

1. 9 2, 14

3. 15 4. 17

3. A MOtilitaill it4101 has 3 sections of di ifyrerd s !apes as shown. Viihat is the average slope in of rho snare Climb?

1. 1 2. (1/3) < 2,1.1 < (1/2.)

3. L < in N13 4. 01\13) < nr < 1

Which of the futlowing graphs shows the comeraration of a sugar solution as a function of the cumulative mown of sugar added in the process of preparing a saturated solution (the temperature remaining constant)?

4

7 : I

. -: I / E I

: kl

.. 1 il

•

: L•7 •7• 7-u•''' ...+A."'...-Neur;

.-

a 4

Cox

;A:n

!liC

k•n

4

S. There are sand-pile5 which ;',Ire geOalcteiCally similar

NH of diffeKenc heights. The ratio of the nias.ses of the sauf3 enmprisirkg two randomly chosen piles will be equal to the ratio of iii

L pile hethts, st.tuarc$ or the pile heights_

3, cubes of the pile 1162311..5 4. erii-Q-coot$ 1:4- the pile heights.

15, :Here are NM ideraical Iczss:els of volume 1.1 cfach, one empty, and 'le other containing a block of wriod of weight ► ir. The vessels az-e' 11= it Iled with water lip to the brim. The two arrangements are shoy..11 as A and II in the tisotec. If it &ask), of WaiCr is p 3-9J g is the accelearlion chic 10 gr5viry, then

1. A and .R have equal weights_ 2, A is heavier than B by act amount w. 3_ A is heavier than B by an amount Yfig - 1....

B is heavier than A by an amount Vpg — 11'.

7. if the father has blood gaup 0 and the mother has blood gioup AB, what am the possible blind groups of their children'2

• • • : ilvY • • •••••••

a

3

1, AD.

A !3

. AB,. A 2. A, B 3. A, 0

4_ B, AB

2. 1

9

o tia

• :

6

2

•••• •••••

. • 6V-T ?..rbfr;j • • 61.77

• ; .311.1/ .77. FR•172,4 .7q

•:17 ;7717 n7".:Q.,:e ;MT' ii

;

7 7.7-77774 !IL*.?,r rqr g e

-

77:

L.

I.

I ---- '

----- —•

----- •.

U

• • • 77.•

• A ;; iv,:e3Prif5 771.7?:Nee

4.1 .

5

8. MT .12-1.4.1rty eetr "P 32 S raft, q'w

ar-o? 3rjrffa go4461A1 L47 Win g z =15 S* )cr Z =16 )1 # v.r.44,4

vane

1. 0.4 TIJWC R:ff 1U17 Prirdd4 2, 22P WA */ nS 4571 e 7 3. 321:' ftOri )2.S a#Rek.. arila-46 g )

4. 4.).-r). r Wri TT39/7f ;rrra7

9, wpm' cr-43-4; Lin onfir? mum g! Ly r.r, 7.4mq 177#7 U-diq YirAgir 4517 # Te era vevi WURarAi uffo) PrFr 4ir 477 t .11 Tiliwt. 45777 22F zrzeo?

1, 27.47Pri 4r, r0 g I

2. weityPT 1140"r1 Wr# 4 7# TOT e ZFT ?illavrErrejir VPreir

zriteppe W-474 zwr Tivi war ereg e I mr-117 -.7717-4F E-7R nem t.

10. ev ,r1P2t #07 qe1 wren -

1. Tzi Trift %,r4,4]..4 Ny-t-F eiThr 2. TgZTFE4rkrifi77 2310V43- ffffTFT -frO: r

Wit .6-1PW .1t ir e 3_ Fait a, art-fa reeie 7ftuor 4. ??1"&" rfN7 r: 4? hifd-40q Rrear e

11. crW 0.001 Pr Wea W. A70 crtIV Pr," .17;' 4177. FaPJ-suffir( .ftr tAlwir e r ,3pry

FirPir marr vfi -F7

Plq F4-5 Twe. war/ mar

A . ritivi-/ qirS7 volor g ?

8, Nuclei of 321i aid aCCeitT2ted tt1TOU0.1. IhU 7.11 .ne potential difference enter a uniform, trmsvers..: magnetic 1161(2=15 for P arid Z = 16 for S). As they emerge from the rnagueLic . Feld

1. both nuclei orierge undefllecled. 2. '2P is deflected less than 32S- 3. 12 p i5 deflected more than 12 S.

4_ both are equally deflected,

9. A person chewing a bubble gum did DOI expn-icricu ear pain in a jet plant white landing whefeas a.nolher person not chewing -a gum had ear pain. The reason could

I. chewing pm is a pain killer 2. chewing equilibrates pressure Oil both .51Elcs of

the ear drum 3, chewing gum closes the ear dram 4. chew ing distracts the person

10,The rc..asoh why a lunar eclipse does DOI tICCLIT at every fill!. 11113015 is

1. 6-11-e position or the sun is noi favourable at 011 full moons.

2_ the orbital planes of the moon 21t14.1 that of the earth are inelined to each other by a small angle,

3, the shape of the earth is riot it perfect sphere. 4. the M0011 reflects only from one hennsphere.

11.A boy throws a stone vertically upwards will, a =pain initial velocity. Which of the following graphs depicts the velocity As a function or time, i if the acceleration due to gravity is assutned to he uniform) and constant?

lira) _ t om ••

2.

a.

4.

11, VW e JIMA q 4000,..-ars 2T (p 2p) err' 47* 41" qr6 a,-140 dP4 eRY

ft6W T9 clt.ord.) tf I 00 ferg quilgs am' 37roff. Crq' ffrAn ITV d ad'

e w, Rler *

12.A rigid unifarM bar at a cerlain inass has WO bobs of the same size, but with different di:Lull:Les 0 and 2p suspended identically from iLS ends.

14.

tl A

- F77= ----

c C

a

C D d a

d b C

6

d dr 0"

1. 2d =

d = 2d'

2. d >2d'

4. d 2(1 1

When the bar iS kvct on a talcnim as shown iun the figure, d and d arc related by

1, 2d 7: if d > 2411 '

13. )1 I. A w./.1' ygra7 ftn. 0 oF oc. c-cio t 4.w Ihrff r 4 oh Q..5 a zir

# WM? , .151PT 3017F q'r NeEr t I Yerk1701Y

Wrr? aftk B BJ0 0' F,rw mre Aft t

1. BE" 2. AA .. .-. 2 BE'

3. (3) BR' 4. 44 = 02) B2'

14.

3. d = 2gt 4. Or 2d'

1, AA' w B8' 2. Akl= 2 Br

3. = (113) BB' 4_AA' = 0'2) BR'

13 ,Them am two Points A and on the equator at 10ngintiies ir and 5ITE. and two other poilus B and 8' on the same iongituks, respectively, but at latitude 6O S. The distances (along the tati.t ucio between the points A, A' and Br sr.e related by

r Ar? 77-47 k.rw TA. gml A .7 C -3ITTRY B 'poi ohrs4-6 4 adNg q311. .5icejaz g. B Pftz# * iNg7 cbg ,i4egfir Mr4-

1. A 7Ce7r--ir#Th-ve t 2. A 4' C 0.11 4 sffi'mv I 3. A C .1%0474 ffre# V'Ff7q g 4. A 0. LirrqJ al ,i)7 97 CO ga. 67

15, e.# w7 7ri

wmr 47'N u-eug- A, V#i E;riER a. Li;Rfl&I

h_ cif sr B. voq

C. Armin" ffk.-Tw-e Or ter D. remzur : d. l ,

2. 3, 4,

A a d

a d

h C

a

C

FC

b d C

1) ii

a b b

Water is flowing through a tithe as shoe, n. The cross-sectionai arcs at A and C arc equal, and greater than the crass-sectional area al B. If the flow is steady, that the pressure on the walls at B is

1. /C-5S than that at A and that at C. 2, more than that at A and that at C. 3. same as that at A and that at C. 4. more than that at A but less than that at C,

15, Match the two lists

Rms. Aiarerieg Product A. Limestone a. Porcelain. B. G um b. Glass C. Silica sand c, Plaster of Paris D. Cla • i d. Cement

3. 4.

A

a

7

•16. a-ter --.80,0(e 777F yei Ff7 el) 7"A7Vr

dug "C 7er *QT. err PreIfft;

1. ta crew, 5 4 ilad .417 wren. c'0 crud 13174- 41T7E- 40. "C rfir

4J'1 4576. I 3. crw. ?iv/ "C T J04111 .151 5,6 are I 4. 710 -,:.0aZ114 31 C fatioN. y-*-7 Et)777

17. Tw yo'rPrifi fr- 7/ arfitRy arp? * 6.0 *cikre S aeir NiNT vircn P rite

4 ;04 .ter 7 1 ..9 4to xift 46' 7 6 ao 7A, gat t.* rt. ziq. Tigunrt ?Or :

]. 2520.ks/3 41] 2. 42 fiiti

6. The l t dating method is rro t usually used for dating organic substances older than -80,000 years, because

1. such objects rarely contain carbon. 2. such objects accumulated "C after their formation. 3.. in those times there was no production of it. 4. ' mast of ' 1 C in the sample would have decayed.

7. A seismograph receives a S-wo.ve 60 s after it receives the P-wave. If the velocities of F- and S•waves are 7 ir.rm's and 6 kmfs respectively, than the distance of the seismic focus from the seismograph is

1. 25201.un

2. 42 km

3. 7070 km

4. 72 Iran

3. 7070 iWo 4. 72 JW, 4k,

18.'# w-d-fenf4w p .01d9 grA WV-MAW ?WO- t I P

apj evura# *-7 algid eV

1. 1/4

2. 3/4

3. 3

4, 2

lg., The decay of a radioactive isotope P produces a stable daughter isotope D. The ratio of rite miter of atoms of D to Ihe number of atoms of F after 2. hair lives would be

1. 114 2, 3/

3_ 3 4, 2

19. * irprcv./ oci.rpt ; 74 Tr? WOW' RE' lihr 4eard.) # e r MR') . .e•-s- A wg. Te;i1-

viroo t I om'-r? yvw To' Tr -Jr Pirq It *aw wEry PRI=11

1. firl

an zrE,72107 7 „Are gRuf4- 2 : .fir zregeiar sr -4t 07-fit

2. FA-.7 .31 ur aR-xf vita ilTiT 2 .-41Wr ;Prigifffui RFT qfilla`

3. Itrlaigr WON 7 3rat grYThire. firg 2 = alMr wrim tx arm 4Thf4:

4. 7= .1w 71174/7 NM Eir??Ja Ai'W 2 WORT V' Nat iiRgici;

20. um ?kJ/ ?7,p' to -4 # zr-erM CO3 4 1;777 ?PT/7 Oar 70.1" 341tt FPF.' MT 47 ..1 470 ZYPI1' 70 I:5W Smr).rn ier:rcigiu .t247.P

iff 47-4. krrJ EQ

1. w,feuzi gwrw /RFF 4/TUW 2. ura if Etrewl" Wif STY e 3, .0.2form ei:5 0.futgcsr14 .(c.1 ,lattrr

r•ijoeid 21.ir sYrrilarzu alrem ,763.-417

9, The scatter plots represent the values measured by two similar instruments. Point A ire the ti gers represents the true value. Which of the following is a correct description of the quaiity of these: measurements?

Fla

J . Fig.l good accuracy, good precision Fig. 2 good accuracy, good precisions

2. Fig.1 : poor accuracy, poor precision Fig. 2 good accuracy. poor precision

3. Fig.1 c poor aCC.ur2q., good precision Fig. 2 : poor accuracy, poor prceision

4. Fig.1 : poor accuracy, poor precision Fin. 2 : poor accuracy, good precision

0. Even though the concentration of CO, is the same at sea level and at high altitude, the photosynthetic raw i higher in a Owl grown at sea level than in a plant (of the same species) gown at high 5iiiictidc- The reason for this is

I. light intensity is more al sea level. 2, temperature is lower at higher altitude. 3, atmospheric pressure is higher at sea level. 4_ relative humidity is higher ail Sea LCVel.

r z d

2 I - -r -••••• 1-

• 4 E- L.

8

21.. = 5 0 Yikirirt eFF rff RE7 .Q„i? R.q77 Utr .

7 7 2.

3. 4. 2i .--3 ). )k

I 2

22...31nt-r. .4=1 2 4 6 R;;+` g .

1,3 6 9/.

I. (1. 4, 9) 2. (.0, 7, 7)

3- (0, 1, 13). 4, (0., 0, lz .-)

23.. I 2 L'ii:x"

•- 1)(2 - 2)

1, - , • ' I - ..

2 4 8

4. 2i -1-3)+ 5k.

22, The eig(greahleS of the matrix A =

( 1

2

„. 3

2

4

6

3

6

are

23. The first icrms in 1h Laure.nt 5eries for

-1)(z-2)

in iibc- region I S I v 2 and around ,r= 1 is

1_ (1.4.9) 2 (0, 1, 7)

3. (0, 1. 13) 4. (O. 0. 14)

L. • ( 1 -h(1-z i -;

-II, I 2 4 ,

z z - z - .1. 2c: -1)+50-, -1) 2 1-7(z-l)

-• +._._

z • • (1 - z) 2 (i

3. [1+ 1 1-LK] +.1 +1 -1-....1 z - z

4_ 2(z-1)+50-1Y +7(z - 1)' +....

2. 1- . z

24. .6:q74-rkt TIT O uR. eu raw 711 . 24, radioaclive decay cif a coain malerial Va Oz11,-V Mir Qie# sIrdqr.6-.1 N.FIEFF1

g FPI* AiNya L.-T4 yeg4 AlTe) •}i, +b

(.1w/a 0-)? 0.4:t ?

SatiEfics Pilissort statistic with a mean rate of A per second. What should be the minimum

of counting (in seconds) so that the ieialiye error is Ics than 1%?

I. EQ0/2.. 2. 1.0 4 /2. 2

3_ 10 4 .2 4. 1/A

1. 1001..1. 2. 10' .1 ...Z 2

3. 10' Lei. 4.

PART B

2 1. A vector pa:rwinliculair to any vqcior Shat lies on ihc plane defined byx -F y z is

9

ulkgiT wq- 2= x+iy cw c iK f (Ow viecraz 'FT

ii(x,y)=.3..-!.-1 -(x 2 r j(z.)4tg 2

Newrow t?reT .61

25.. Let u(x„y)=x+(x l .3".1 ) be the zeal part of an

funttial f (2) of the complex variable

= x+ 1V The imaginary part of f(z) is

Lw y fly 2. .x.y

1. '-F

3. }I

2. xy

4. 3. y

26.. FA. y(x), ar"dvia. 0 u 2,7 cf-6

.ch cif WFq Wir 31Yr'i I'd 714J

11 2 y 114;7'04 Sill -I-COSX -4'Y =4X

die dx 2 w-far t x N/2 77 1:15.0/dIc zFr

Yft. Z1- I

▪ aROF-Ir

efirrce? e I 4_ 407 amitrm. 0 1

27, 4. t'iv .WW: 2 wor-1 2ir 3 irgik. 4t.r 1741'3 • 4 Yrii;q. IT .0( o?.0 w"fe PY r9F

Porn') krorri rft Tr

t

•

WA.1 PRITUF 47' e

26. Let y (x) be a continuous MI thilatiOn in the range

0 and 2n. 5atisf .ying the inhomogencouE differentia] equation:

x dx

ILY =.cil( X --)

▪

T110 IT 2

value of dy/dx at the point x = 412

1. i5 continuo:v.5 2. 1)13 a discontinuity of 3 3, has a discontinuity of 1.03. 4. has a discontinuity Of 1

27. A bail is pickod at random from one of two tort&s that contain 2 black and 3 while and 3 blan.k and 4 white balls rasped:iv*. Vrrhat is the probability that it is white?

1. 34/7.11. 2, 41/70

3. 3.6170 4, 29170

28. cw OFfi -2.1 06. Liar 4)0.1 Utd7 Ocrflf .0L ffA preIT unrr e P'1 / 4'. 4 447 .I'Z7 fl OW) 28. glArfenr-rreSt ArV 457 47E017 rce te e?

E . 4170 2. 4 V70

3. 3 6.17.0 1. 29/70

bolo of a stippic pcnduittni, whkh undergoes small oscillations, i.s immersed in water. }Which of the following fag Tres best rcpmenls akc phase space diagram for the i.xndutum?

4, 4. lP

P

rp

1 r

F

3. 3-

2.

29. r # 9 k Up e. =re ? t > re .07-4p2. e Tti

•.:E0 0.8 .0 4* .0147 gxr p-ey c = 3 x

10117t0 Pia 41- 3rh-rg viiir iewer. eFf tre7it k eNclicfe FY777

29. TWO events. separated by a (spatial) distance 9 x LCI.9 rn, are simultaneous in ono inertial fra.-r&. The time interval between these two events in a frame moving with a constant speed 0. c (where the siJeccl of light c 74 3 x LOP mis) is

1_ 450 * 2_ 40 3. 20 * 4. 0 A,

1. 60 s

3. 20s

2. s

4. 0 s

30. 4"ft crx a-14.ttri M40471 VF7 wz-m- t

- - V (x) ,fir

;564)9 epi-,irk

30. if ihe Lagrangian of a Rani* wing in one

dimensions is given by L= v(x). the 2x

Hamiltonian is

1. -41' V(x) 2. -2x

-1-1/(x)

1 • 3. x

2 + Fq

2x 2 x) 4, V(x)

1.

4. +, v (x) 2x

--1-i x) x

31. 4Fr PriF .0'ropf kr4.7. Nr7 tfetft ret

`7qJ. NW. .71E4r wsr e 07-r. "W AR-41 N".17 .rn

+74 v Via # eff4W )27g it ...clew TM)" Trnard. frq%, gr'77 7FA '-41:7 #07

3L A horizonrai circular platform rotatcs wit.r9. a eonslant angular velocity n. directed vertically, ipwardS. A person seated at the centre nhonis bullet of mass harimatilly w Wet speck] v The aCCCIOralion of the bullet, in 12w erferclie frame or the shooter. is

10

-e

I. Rive TP2 4? 2v1 I 2. 070 s 3. vor 4Tif vr2 1 4. uv457 mir vS2 ;

32. ;fir

:4=1:0 x F +41 7 ! we tV /kV 2

fi7Ter yaw 4./cx t

2..

4--

-F

30 F

33. 70- ifr7yq70,27 qw V7-4-To ..3Jtmrizr Offqffrf

e en* 4 tetronqo ffOr Atgr Eral7 Pe MIMEO pfr .3/7;

wrir-4 veur t 1 re,Oze et5 H 40 rir4r-mr

1_ ~kr Rft eh* 2. 3A- / 2 ilth'WerOfft 1 yr I' 2 a; ft 4. 1r tATIMY tt4

3."

+ Pt +n) 2

3 2. ±n 2

4. ±- 2

1, 0

3. t 2

(r) +n +n)

11

I . 21,0 to his right 2. MI to his left 3. vi2 to his right

1.42 to his left

32. The magnetic field corresponding to the vector potential.

- 1 - 10 _ A =-FKF-I--r

2

where F is a constant wog, is

1, fr 2. -F 30 7

4.F- Or 4

31 An electromagnetic wave is incident on a water-air interface. The phasic of the perpendicular corapownt of the electric held. £^ , Of the reflected wave into the water is found to remain the 5.Zirne for all angles of incidence. The photo of the Ettagnetie field H

1, does not change 2. changes by 37r/ 2 3. changes by 7r!2 4, changes by ;I

34. ikri. .01;yr ti,re I zir wrff er,err, FIT R 34444 a‘yraer # .0q7

34. The magnetic tictd at a distance R from a king straight wire carrying a steady current I is proportional to

JR 2, fie

3. I2/R2

4, f/R

L

2. ijR 2

3, PIR3

4. 1/R

35. gum- Wz7 Tr-q-A-ur 4c:clr cr4F 35. The component along an arbitrary direction M. with direction cosines (tux , rrx „nr ), of the spin of a

ag falivn , Antoi 2 ,,,obittt (11„ny,m.)g,

err qffirrir : spin - pamicie is maguroi. The result is

2:filt•p 2. 2ih (sp ) L 2e1J.ip

S. px

2. 11171 rp y iv/

4. p.r) 3. 2th 4 . 2 -

39. •Comider s:..., stem of nor-interacting particks obeying th dispersion relation

E -= .4 , wherc is 'be encrgy. k L. the wavevector, s is an inie_17,er . and A ri con srAnt, c.iintsity o L sw.cs. lye (6) pi.....,ponioEi.n1 r.o

.LIFR71■ 7-?? mi-wc4:1 ytiri; 67 sr:For;

co, A .51,1 ii771 77.q77. 8

7,r A va7 .tkFt Frq7,r (c)

a'jgrir # .1 •

1. e. 6 2. c'

3. e r r 4.

12

36. m AVPIM M a Riffq qciv e sit?

ed-7 4r r'l g 1 1PiV WIT Urai .171i

1471.2 11 ?

.86 - 2ma

L.

2.

3.

4.

1 , . r. , 0 1 7

qs =

=

r 2 ) 3:%2 - a

- a

2 -

a y I Z -

L 1TX . 5.7ry

S ift -Mil-Sin a a

72rx 5:111- sin - sin

6.7z

a

-

. 4x .

sin

Sir) -Sin -51n 21 --

a rr a

2;Ty sin -sin -sin s i n

u ) a

36. A panicic.. o[ mass nit is i17 a cubic box of size a . The potential inside the box (05x<a, 05y<a, f):<a.)iszefoand

infinite outside.. If the perticic is in an cigcnst3.te of

energy E-14ll , kt5 wavefunction is 2nrai

f . 3.'2

1 2 ry -1. 3.7rx 5.7 6;12 L 4..• - • sin sick -.-- sin

,.. a a

al a

( 2 :,..2

. i.../ ---2

sin '.2-.r

sin 'iry

sin 3.1e3

a a a a

3, v = I -2 sin ei2rxsin

.re..}.. sin

2ze2

., a a a a

= ..!

2 sin y grx sir, 2iry sin

3::r.7 4. y.., - -•-n - --

a a a a

37. Rir t ?#04' Ftlifilaw ftqw )1 (0 ,341Wrerma, r,'7377) at K ir, Pile.

7P717 erOT 1 r -

r/i= -I ffi „ .., NF:1 v211 TV L . 2 .r. 15 +

x'1:7•76.tiPiN -T Mir :

L H it L. I.,

3. 1! /

4, 1.2 7 Jr.,

37. Let w w., denote: the (if a Hamiltonian lot a spherically symmetric potential

V (r) , The 94:•et-unction

I r = -4 Wr.1-1 1- 416 V? I:1 iS an

ei•erifimeiion only 01

1. are. L , 2. orki L,

3. H and 12 4. LI and T._

fet .14;4

3& r conirmtizior r x 3 , o' 1 i • J

•3. An LED operates as 1.5 v and $ rnA in forward bi25...V.sumi.n, an .C1 0..4 external efficiency of the LED, how many photims of emitted per S4CCH1142

1. 5-0 2, 1_5 3_ 10t6

4. 2.5 101*.

-NW

lx

VI =

1, - 0,33 V - 0,50 V

3, - 1.00 V

4_ -0.25 V

13

N tir #1.4, wy. Ow cenif tl'Or? e ?

1. N 2, Pr' - 9/2

3. ihkr(N-1-1)/2 4, N

41_ wErTie cw 477 .Q.E9,A arme7 Fgrifiy,,r

F Ni,7 In. [ac,V

.w-10 z,,zu ze ice rKa'rfrohr Free TIEN'', 1 itTi 4 vf-d-ft I

L -3

NA. T 2

2, -ANik T

3. Ark 87 In [ay (417)' : J , isiiit ur

4. N47- 1.n [(AV/V( 57)51

42. .W-F F.7.114 mica ever r

zEkvirV ; r PO VD T?' t7I 1K

40, The number always in which. N idenlieg bosons can be distributed in two eeeru levels, is

I. N + I 2_ NOV -1)/2

3. N +0/2 4_ N

41. The free anew oral of N particles in. a

vulumu V and at a ieraperonoe r i5

F = N knT ln[abit (ion' Air],

3 eck. is a COnStarlit and ke cicncies the 11133Lansinn wilS11@r1.1. The itTICTual energy Dr the KaS is

L N T

2.

2 8

iNkDr

Nk.,1 7 - In [ ao .r7 it.D.TY 7N] -;

In [ 0,3PRk lo Tr

42_ h, thet)p-arnp circuit E'1.01%11 in the 1ignrc.17,elew, the in ]Tuil voltage v i is 1 V. the value of che cvuEplat VD

K I Vg.

1K

J.

1. - 0_33 V 2_ - 0.50 V

3, - 1.1)1) V 4, - 0_25 V

43. F.7141T 7 ..51E*151T7

Mr+rrl T.Y 1.5 V F 5 rnA 1 g 31.

0'1 CI aryznr 80% .71;0 0. ;RI 4,6%.,:r. Thror? 93k 4.1

L 10 14 2. 1.5

3. 0.S 10 16 4. 2,5 x 1e

1K,

14

44, N rift?. 4. tftrn7 h f = 35c2 /t ic

= 1000Q Tiff *we mfatheo RL = 100052., z'ke7. gra Wira :

j"- vo

0

1

1. - 35 +35 2. 35 - 35 3. 35 w- 0.97 4. 0.95 zr- 35

3. F patia q -340-araT ).0.) laVqq1 icOVIt ft if 4.Z'ffe) Tel h

=61.474‘ cry e .ww: j, II 7

thirn 3.1%* :

JI

5 I.

f if

1=1

WaYdiraf-n"

Fwg-,1i: Ma) alazO• NE:rcf. tpg 7 7'21-057*

,7,75-q7Tu F.rom

774 rr qu

4, The transistor in the giver] circuit has k re = 35n

and 't ic = IOCIOrd. If the load resistance RL

10000, the voltage and current gain are respectively,

1. — 35 i 35 2. 35 a - 35 3. 35 T- 0.97 4. 0_98 71 — 35

45, The experirocntedly measured transmission sp.actra oirma I, insulator and semiconductor Nu flints or shown in the figure. It can be inferrod that I , I F and III correspond, fespectively, to

1. insulator, sernica.nductor and metal st. micoricluctor, metal aid insulator

semicuatitmor and insu later 4 - insulator, metal and semiconductor

TO

fril

ram

ic.ip

(1,5

1 5

LIPTc

46. .111 707.15.iu 3177 rr A =

r07 ie •

0

n3

1%. j'12

– 1r3

0

fl,

n2

- n i

0

1. 0,

3. 0.. I 4-i.,

the ,componthis of a unit VI2C[01, are

f,

3, 0, 1+1, -1-i

47. 14. 1. # 74. t&ifst r arf st ?

1. Linn — +In Phr nr

1± 3, Urn ( .... -1n .111.7) 111 1.1

47. Which orthe folio-veil-1g limits exists?

. lim ri —1 +1n N ) .14 or.t

3. Lim i In 44.1 Ni

wr-r n11 , nr q. n3 m9r-0 FriiThr 40 ,f4., 4 4` SerdZifEtr4C

1

4.

- n

0, t , –1

0, 0,

n2

0

n3 0 - - ra, where n, , n and Ph 2Ire

– n2 ni 0

7, 0, 1, –1

4_ 0, 0, 0

2. limn 2,-1 ( -In ?1r 1'

A'

4. Urn

2. (E— -In .A.7) .14 —F=

4_ limn R

46. The eiprivaktes of the antisymmeric matrix., A.=

48.f7w 44-41. # argu -74i Nriv 7-47 .311r 'n' 3f4r zrrd't MW–ZOW 4 n ;P4' t A* I Trdt 1, 2 .3/* 4rgt 2, 3P-4 N .11,/ m) f 014a*.

77,14.re 7Fir .rW Sr4 Mirari &UT urn e zir wrinir oft uprft .5r4h- at pp- V? Ohit1.4. wr4 Awn) 771r SiVT 7.7 1F2 WIT 2

16

2N 1 1.

3 2.

3. N

N (PI +1) 4.

2 2

2

48. A bag contains many balls, each with a nuinher painled. 0ii it. There arc exactly n balls which have the number .P2 (namely one ball with I two bags with 2., and GO Oil until N bal Is with Non them). Ann expeTiinerit COOSists Of choosing a ball at random, rintinE the number on it and remaking it to the bag. if the experiment is repeated a lark.,re number of times, the average value of the number will tend to

1. 2N +1 2

Pi +1 .

I 49. - cosi- et/

9 2

- R2 . 2R

i/R 2. -a-/R

49. The value of the integrali

cosCOS - idr is - 2R)

4. 2.1r/R

1. -2k/R

2. = %IR

Qrryi►y Irl, IFI t

1 . I r l 'PI

2.

50. The Poissrm bracket i r l. [PI} has the value

L . I rl I P I

3. Ar/R 4_ 2)0

1 . 3 4.

3. 3 4.

51. 747- .Q &&,' .11,4,14 13"77.7 V(X) = (X2 - 2) Wffl qW t4iTtackfir tre;FT Cr? gl-cee 49% 4

wcs rd-r Xer 7i" -Tc-{ g ..1.1CtiP100 Recucir-f reW r (4017 Oct UOZLF zr776' ) th

1 - 61)". .Apro f4F = fr.rw s5i147. .770 47 rpitzrf

2 .5-67 UzT 04.11:0 co = 2 it wei rrre;r rrft rf

3. ow 4,4 zaq ceirereo Eta

4. ,717.■ TM' 3174:4177 47 uieo w ' :R 1-4,r(

51. Consider the motion of a Classical particle in a one dimensional double-welt potential l f A z .F. (,x) -4

k ) = xd - 2) If the pamele is disptitecd infinitesimally from the minimum on the

x-axis (and friction is neglected), then

1. the particle will =mat simple harmonic. mcition in the right well with an insular frequency

= 2. the particle will execute simple harilKinic motion. in the right well with an angular freclumey

3_ the particle wilt switch between the right and left wells ‘. the painlicle will approach the bolt= of the right well and settle there

52. iirw vr,;.. Ar d toe'rroe-Y x I 0.8 4'0 6,5 00 MR-MT' # tie tf, TR• Fre9K4 .4'177 45T VIV WiZrerii * ?

6.50 09 2. COO Zilb. 3. 5_75. R13 4. 5.00 go

52. What is the paper lima trilariel between Ehc OCCUMICS Of two. event i 6 in case inertial frame the events are sepamted by 7,5 x 10* irt and occur 5.5 s spare'

I. 6.50i s 2. 6.001 s 1 5.75 s 4._ 5.00 s

SI Le•i.R43v, Z- -kW 4 C1.7 S VW Wfrt rl .7e'rf # efia, ;7W pa- OW i7W il-f3To

V erl- r R V (r)={ 6 a ga'tir4F FY* gr 0. are,(R 07'Ly Ref?. vcet? -0,.I PIM 2V,I, qv' 91-MM

0 aft r ›R

ORrir .11727.. a' efri t... --1.4.,GOziTfrri 4 .3.tPc...r-0 0 gralzfq &you

. orf# 1r4.‘ # 'ATLI a.gd? * 2_ ar,41 V.44. 37717 4-0711 .r

3. .f ry 4. WO. RI A:0'

A frex particle described by a plane wave and urrovia.g in the positive E•direction undergoes scattering by a potential

Vt. if r

if r >R

rf rc, is changed to 2V0. , keeping 11.411

Born appmxirrialion,

the differential scailerilig cross•scclirm, in the

L irielease-s to four Limas the original. value 2. increases to twice the original value

3_ rl..mrexs.N.to bathe original value decreases to one fourth the original value

21.1 lx1 a 54. ,,.zu-.1e4hr RFP V (.r). ;.1.r. .4T1P1J-2.4d arfitra7)-ft Mt.

l* 4k > a

.1 7

NiU ipix) = - xi jie cw ft-07 topocil

'NWT'

wecil g I 0?...rd i4o-rdve 3:Werf 771

S.1 07 RCIli2--151:VH-2A

3 eHer

18

NT' .3ir 2 Sh" 2, .—, 3. 4 :ma" Sind 4med

54, A \ t! ational caErulattimi c1011c w.11 10.7raz1]:.D.-1.1 wayt...tuictiou v.e(x) = —(2.12)

4a'' av!. %veil

t .c

awry is 1.1c.

5 1.1t 3IF 2 • • 7 . - 4_ 1 ).?2a• / r 5.11?..1 iI

S5, 47'4

97k.' #; 0 1: 1. 9 Te'Er

0 7.1.1t

.rr 417q '5 151; .4 • =or .t.;.rov :10 VIM? mad/:

1.1"Fr "

_ Ole

iJkir Iv% einr.--kiiniensiun Is 211 E11.4

I r.:,

() ir

211YR:".

th'slk!w ;' east 0:21: b4412 1-d. 1:kizential i R

3. 20.7 7

4. '•"

215ffe,F1 tr o 0) t0.371' 4' 4;, ,..1 e . .

h _

1. 0 .e.J

ih . 3. 4_ - sin

i El 0 F....0 ao

7 2_

;SeNi

SIO7ROi2-5A 2 B

- 20

- 20

19

56. Which of the following is a self-adjoint operator in the spherical polar coordinate system.

(..r, 61: 0?

dr 6 a 1 2. —

3, —

dfa — 4. - ih sin 0' -2-

si

-

nz0 69 .in 0 DO

57. ,(43 zisS. w .mhe *

I. lExBI" 2. 1E1' - 1 13 I 2 3 . ! Er + 1Er IEnBr

57. Which of the following quantifies is Lorentz invariant?

2. 1 F-1 2

1E1' +10' 4. IEr

SR. El6f cr ev-pg Rq..?...f ABC $ Rgr, vArre 3:74Ti u - 2Q Tti u.tr4

4 4p?Tar-4r- P?TlIer. r rr mot trp• ,3iNbY e

1. +2.2Q 2. .iZedQ) 3. - aQ. 4. 0

58. Charges. Q Q and. - 2Q are plziced on the vcruces of an equilateral triangle ABC or side,s of tkength J.S shown in the figure

-n ic dole mament o f this cal figuraciou of charges, irrcspw-ive of ih6 choke oforigin. is

i. 2aQ r 2. 3. -vrifig .1 4. 0

20

59, 2 ,T r r .§.-RrAT .3.77:0C: nr * 49F-7 .o.# rrig FiZsr ieT4,.. A —L

zat m pe

717-Ffrg Mr r

3 ynx y

r -

3, 3nrxz

4 04?

r5

59. -Elie 3 t tc r potentiai A due tO a magnetic monwnt 111 at a porn! r is .stvert by

111 xr , , A In 3S rtirectc.d alnng the reis.iive ..r-axis, the ..r.ewnporient or th.c. magnetic

Flint r

3m y r -, 3 arxy I_

' r_

? _

,F.

F.3 n_tr 3,4' - .2..y) :,. 4.

5 r

field, at

60. (fa' err On' wit. rzi at, .7 = 26)r urg rtrAmR1f rr e iffiwyry r offla

4hto,?) we IN` 0 ,mr ► x =e- im"L Z rremce r ArrfoiErwe

(x 2x 2 Z 2. ,J± + xli2

on. A sysicni has tvea normal moats of ribralion, with fmclucncics co, and = 26), What is the

probability that al temperature 7 , the system has an cruergy less than 4irm, ?

fln the following x= and Z is the partition function of the system]

L . x4 : (A: 4- 2 ..( 7 1/2 2, x:1"2 x +;(1Z

3. :lc' , 1.2.1;20

4.

61. 745 ATT547 4F7 gwr4Fr .114, wwirm 7ra-tek 41'7 if 457f7 46" 57 ;'). WROP(GT

= trmb (I'vf -F 1-1-) uft it me .7.7 1-J r.4.41. mg* ( =.11.1(11 = 0 T

$.r.5rwr7 evr .

1 •

-

2.

4.

1. T I -M 2(0))

3.

I - .1d 2 (0)

7.

21

1. ] - (0) 1- 114' (0)

2. T - (1- ,1.6. 0)) 7`-

(0) 1- M i (0) 3. 4.

T +

61. The Inapctizarian au fertcouwet, as a function of the tempertaure I and the magnetic 7

field H , is described by the equation 1 = tanh +-). in these units, the zero-field T T

magnetic susceptibility in terms of MO) tikei (lir = 0) is given by

62. g.,IN He cii*Fft tar YV 2.17 K aztr 774r t, ffPFT .994. 474-4 1.1e

6;ip-f Iry 044 He 4 Ter ruin 777 wry Urqx(F7 z17 dt77 #61ft leFri 2

elm/ 0-ei

L 2.17 mK I 23.7 ruK 3. 211.7 111( 4. 2.17 p.K

62, Bole condensation occurs in liquid 1-Te4 kept at ambient pressure at 2.17 K. At which

temperature veih Bose condensation occur in He' in gascsous state, the density of which is 1000

times smaller than that of Liquid lie (As-stimec that it is a perfect Bose gas.)

1. 2.17 ntK 2_ 2E7 rriK 3. 21.7 pK. 4. 2.17 ja,K

63. qw .0E7 A.)%-eff or rprel At?' &AT RaRW P7t MaNY 20' celpfm , 710 2T To- iiv21,1 mut Oax.1 tri.• Tet erpwrirms aii4 frig urzt 14.a7ur 1;f1E9` Ter* 7-47 170 ;

1. 2 2. 4

3. 8 4. 16

63, Consider black body radiation contained in a cavity whose walls are at tempirrature T The radialiom is in cquilibrium with the walls attic cavity. lithe temperature of the walls is increased to 2 T and the radiation is allowed to come to equilibrium at the new temperature, the entropy of the radiation increases by a factor of

1. 2 2. 4

3. 8 4. 16

22

64. .eNr 7f2', 4..met Tv II 4. '1C1 0 ;en.' el0.?

OC:.% 4.•FT; is A.,B=1:C,D=ft E,F=1 wiG=0

777 LL ; B =0; C, D= E, F=0 u G = 1)

A — 8 T)57_ ct, 4--1

I. Cr, 3. 0.0 ], I

64- The output, 0, or [kw given circuit in caws I and where

C:asy1 ; A.B=1;C,D=0:E.F-tandG=0 Cag! A,B — 0; D = F,".„ F -= and = I are. resr›miveiy

I , 1, 0

c - o

2. 0, 1 3_ 0, 0 4. L,

D=1r7.41 4;4 Cry ...7.77177 rfra tr.1:11%iro7 1000 ITA7 P:117 Fra7Tf -4/0 ‹7777

arF41,tq L7rger kPoi[P , TT, 3 itfr it:sizirrf STage77217 riviip. 2 54 1 O R' .ukt.

,71; 41.9 t. .47)7',' Eri9: V1197 7 ,=17 RIM' .0 Dv* :

Nrfa'rc;4 .9711 ;:1•) ;Rag. Ziolcerir Fu" riR3 C47)17

2. 3.0 x 7 0..16Y E0 -5° 4. 0,5 x 11?c 7

65- A wsisiance. strain gauge ;s fastened to a steel rmixtre ..and subjected to a stress of 1000 kgim 2 . 1r locicir is 3 <md the modulus. of vlasticity u fsttt I is

I 0.1 " then the fractional ckunge ir, mista.nce of the strain due To Iltc applied sire:is is

(Now; The gouge Factor i5 clothied as the tatiG of the fractional change in resistance Om fracthyrial (;:kailge in lerwh.)

1. 2. 3.0 A I II -

3. 0.1 foe HT" 4_ 0.5

1 . 7, 2 and A=IV

3. f- 0 and t=I V

2. 7=1. and 05 74 51 V

4. 7=2 and .71 = V

1_ 1.851 2. 1 .286 4. 1.035 3. L .046

3. 1.046 4. 1.03& I . 1..85 I 2. i .2136

3. 3 ah2 5 -,

4_ -a Tr- 2

]. - h7 2. -fie 2 2

23

66, 37-47 1 V 7 aver fa vw vocr ETD', .441ri tIZ ..1kTirt Rhur sing' Tiu 7:k uF 457-et

pt, Tor wq 1424) 4FI3irif Mani ft-074 07# g I zAl Vitff LoAP4 alrfr 77 anzekFir RreAl effr t

1. .f = 2.40 4r7f=1 V 1 7= f„ 0 5 A 5 1 V

3, 7=. 0 u A =1V 4, 7. 4 = v 2

66- C(1111Sider a sinusoidal. waveform of amplitude I V and Frequency swung from.. aiiaitrny

initial time, the waveform is sampled at intervals or I 42fo. If the corresponding Fourier

5rxvrum peaks at a frequency fand ais amplitu.de A , ih

67. 12:C160 wr WM; JRRIktfor 3.M2 -#071ta-1 77 tjt waft C 160r77 3.673 7:640 •1 rR. .7,r`Nr .3.rprf 7h1 317;7ff

67. 'fhc first absorpLiOrr sfncinurk is at 3.842 ern -3 while that c4 is sa 3.673 em 1 . The ratio of their mainents of inertia is

68. ?;11 qmpg 7-4-A97-4%-ri ar-qh- remri H T t1 L.S Rat 77FT L a S WPM' Irr4eq /1;.`

reg LI cap Ly 4,.iv.Pq 91\7 e go 2 p w 'I 4:1. etw Rran g

1. - ezh 2 2. 1 -air

, 3. 3a h' 4. -5 oh`

2 2 2 68. The spiii ,orbit interaction in an atom is given by if = a L•..8 , where L and denote the orbital

and spin angular momenta. respectively, or the electron_ The splittilw hetwei..-n the levels 1)5:2

and 21t.,. is

24

69. or. I Jr = 0 ,314-ana# t;t. ara WVIEslar FilT31.7ir # ?tuff ever kVF ke rtf44 g&

]..6K 104 A ors rr alfq u-e-47 &H A T e j zfit Tff MT ISO A. 4. ffirrf tae

f 1 .3:m-6.7 g - u747 8. 2 PM • - kr AA? wr u.277;'.37 ym,t4 ..te J

s

1, 2 2. 3/2

3- 1 4. 1/2

69. 'the spcctra I line con-espiinding1Q 4171 atomic tfansition from J! I to J. 0 gams splits LrL a

mapetic fictd of 1 kG into three componems separated by L6 K L CO A. I r the zero field spectral

lint curesponds Lu 18.49 A, what is liheg•facior corresponding to the J. I Sim? {You may LISC.

}ne: — 42 x10 4 cm.) p0

1. 2 2. 312

3. ] 4, 112

70_ Taw L eV .0 mvut Fait; 1200 K 300

K .716,':111 4 OW49". F57417-47eir A -erm xywr n (1 20I3 K ),41(300 K) mprir

1. exp{-30) 2. cxp( -15) exp( I 5) 4. exp(30}

70- 1111,.... Ciwra .required 10 create a !Vice vacancy iii a Chita! is equal ty ] eV. The rallio of the number densities of vaeancieS ( 200 K )in POO K) when the crystal is at equilibrium at 1200 K and 300 K, respectively, is approxiimately

1. ex pf -30) 2. il.xp(-15) I exp(15) 4. exp (30

71. .ijhr W77-17n. t'17' Titt7E7 U'.9w7 4V 2 (*) C4.1r2, (3 — a - cos kia - cos.k,e2 MUT e xas ynt-t :

L. u„af 2. \i'Troua J.

7l . The diSpMiOu reIBLECIM of phonons in a solid is given by

6) 2 (k).= (a - cosh. , a cckfik. cr — c05k,cr),

'Me veioeiLy of the phonons at large wave Icnoh is

co 0

b y ÷2kg g z — 2kg ) 2.

Yo2 ( I + 1 1. vo ce ic,,,

25

72. L 04447 4,7470 , 41.Y1 UM */ (.x) =1,91X -F L ffirl Trd crov crgueq 40 rif

ff/4 1 ot cid-e1 X e' ?Arm 6-,=--;2 mei u'r r

Jorif R-4.7 r(x)=vo colsxm7.rza g Rep g, 2.4 1,a7 ree5 dgfo vo-, op, eb7mifiu ,9r-jurz no') LT-701 Fi0 47:17 ?

1. voleg ic: ( . 2 ]

, ..2 +.2kg g ,

3. VG,2 (g., —ex We:. 4.. -F Cr )

72. Consider an electron in a box of length L with periodic boundary condition ctf (x)=y, (x L)

it • If •f the electron is in the crfk (x )= —, e with energy sj, = —.62k2

, what is the correction to its 2tu

crirrgY. to second order of perturbscioa theory. when it is subjected to a weak periodic potential V (x) Vc, cos gx „ where g is an integral multiple of the 2g/LI

3. V: (g.t )14 4. .V.:/k +e x )

73. 2Ci.; P b errziO P Xr1-4217. t57 7-0-0171 WriAM vrviO, ti;17* 017 Neff

Jr? = e r04 rrezt umo-a. ammo .ard747 eso..of .cibera * ..Wt uirel vc.r

Tcrft, ar4req e;

E2 E3 2. M2 7 P3 3_ E2 ■I M3 4. M2 ar M3

The ground state of 2L7 Pb nucleus has spin.parity = —3- while the first excited state has

P 5- J =..1 The eteettonni..gietie radiation emitted when the nuclens makes a transition from the

first excited state to the ground state ore

1. E2 and F.3 2, M2 and E3 3. E2 and M3 4. M2 and Ki

1, EN31

4. firn ii 7.91 ,0 2

26

74. MR. crm41 e - A . i4 t p —> +.,2• T

c —>

1 A: guR., C! r?Er-e 2, A: Y-471, 13! R#F 7 C: 1 r1

3_ A! I ;r4F,B: .q.)1:r.019-req, 4 C 4, A; rridcl, 13! .19 1 5277774T C:

71, L17e dcmtriam irtitrft Liens 1.111dCel.y:11.0 the rallov..ing processes

—>

E, -hp' —5 , IC +K .

F. Z. p

are

L . Strong, electrevaoeue and C; wrak

3. A: wcak AEA C: stron5i

2. A: a.112.1 .1g., B! weg fad C; wwk

4. A: weak, B: .clectromagnecie aril C.! wok.

75. Int eqdf. -f nen R:Pa. -.11) 10 - = 77127 UR. T.7. 0701 4;:v1"-7r eirzr

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