Csir June 2011 Key Career Endover

8/3/2019 Csir June 2011 Key Career Endover

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16853Sr.No.BOOKLET CODE

' 2011(I)PNYSICAL SCIINCESTEST BOOKLETSUE.!ECI'CODE

i;l,51L-Jll{*inun Muk : 200Tine : 3:00 Hours

Roil No. ..,?. ,..:.--.'.9 ... . . .Narne ... l-k"..:. li*x: -il'- :"".dS/10 Tleil1-5BE-1A

lt

INSTRUC"TIONSYou have opted for English :s medilm of Question Pxpe' l iiis Test Booklet containssixty five (t0 Part'A'+z0 Part'B'+25 Parr 'C') M'.rltiole Ci:oice Cuestions (MCQs)'You are required to ansrrr a matimurn of 15, 20 and l0 (compulsory)+10 (out ofremaining li) questions from part'A' 'B' and 'C' resPectit/eiy [f more than requirednumber o1questions are an:wered, only first l5' 20 and l0+ !0 questions in Parts 'A' 'B'and 'C' respcctively, wil! be taken up for evaluaticnAnswer sheet has been provided separately. Before you start fitling up your paniculars,please cnsur e that the booktet contains requisite nuniber of pages and that these are notiom or mutilated. If it is so. you ntay request the In', igilator to change the booklet'Likewise- check thgansrcersieet cts#sheets for to$,L41 work tars$een apFnded{o thelest booklet-Write your Roll Ntl., Name, Your address and Serial Number o( this Test Booklet on theAnswer sheet in the space pnvided on the side I of Ansrver sheet. Also put yoursignatures in the space identified.

4.

answr shect.E."h q*rtl." in Part''.A' carries 2 marks. Part 'B' 3.5 marks and Part'C'5 marksrespeciirrely. Some questit'ns rn Part'C' have trvo sub-parts' A and B carrying 3 and ?ruik. "u.h. respectively (total 5 marks). There will bc negatir e rlarking @ 25% for eacliwrong answer.Below each question in Part'A','B' and C' four alternatives or responses are givenOnly one of tlrese airernativts is the'corect'' option to the Question- You have to find.for each question, the correli c:' lhe hest ansrver'Qardidaes-tqU-d-9c-p!!S9!:iglotlirirl-'.lq-qlr :.!tl!q!!-taa$ arel-Lablels-Ue--dlrSuClrfigdfujbls3lllUlu ie examinat j0r '.g. Canaidate should not r,;ritt a't1thlrg anyrvhere 'J\cepi cll rlirsrver sheet or sheets fortough 1vork.9. Afrer the test is (.'ver. you M!- '; lr;ry] -'rrr lle ansiie i -lreci (iJMR) i. the invigilator'10. tjse olcalculator ir, ii'l ler:rl:1:d.

1

i |av.: ' -riiled allthe information filledin hi ti: - :;rdidate.


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'a.l:

PARTA

l. A physiological disorder X ahvays leads tothl disorder Y. Houtcver, disorder Y mayoccur by itself. A population shows 47oincidence of disodr Y. Which of thefollowing inferencts is valid?l. 4% ofthe populdion suffers from both' x&YLZi Less thau 4% ofthe population sufFers

from XAt least 4% ofthe population suffersfrom XThere is no inciderrce of X irr the givenpopulation

Exposing an organism to a certain chemicalcan change nucleotide bases in a gene,causing mutation. ln one such tnutatedorganism if a protein had only 709lo of theprimary amino acid sequence, r.r'hiclr of thefollowing is likely?Mutation broke lhe proteinThe organism could not tnake aminoacidsMutation creatd a trminator codonThe gene was not transcribed

3.4.

t.2.j\g

l.2.

3. Tlre speed ofa car increases evcr) rnitrrtte asshorvn in the followingTable. The speed atthe end of the l9'h minute would be

Time(minutes)

Speed0n/sec)

1.5z 3.03. 4.5

21 36.025 3't .5

26.528.027.028.5

4. lf Va6 is applied to the circuit shown, theoutput would be

I ---tN--F--^",--1""'

l.1.J.g lo pg4pg4 tngl0 mg

5. Water is dripping out of a tinl' hole at the bottonlofthree flasks whose base diaureter is the same,and are initially filled to the sanre height, asshown

Which is the correct comparison of therate of hll of the volume of rvater in thethree flasks?l. A fastest B slowest2. B fastest, A slowest\JZA fastest, C slou,est4., C fastest, B slowest

6. A reference material is required to be pteparedwith 4 ppnr calcium. J'lre antount of CaCO;(molecular neight = 100) required to prepare1000 g of such a reference material is


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--a''-l'l itn rdirdra '".' ____]

The normal boiling point ol a solvent(whose vapour pressure curve is shou'n inthe figure) on a planet rvhose ncrmalatmospheric pressure is 3 bar, is aboutl. 100 K2. 273K:,*:' qoor,4. l00K

8. llow many o bonds are presctlt in tirelollowing molecule?llC=CCH=CHCHTl.' 42.6t-z:' tol. 13

9. The reason for the hardness ol dianll:rd isV extended covatent bcnding2. layered structure3., formation ofcage structures,{. formationoftubularstructures

10. The acidity ofnormal rain rvatei is due tol. soliy' co,3. NOI4.,, NO

I l. A ball is dropped from a height ll above thesurt'ace of the earth. lgnoring air drag' thecurve that best represents its variation ofacceleration is

.ll.l Ipl /0ll /9l ,/a L-,'3.t

l'!te cumulatrve proiiis oi a cotnpanysincc its inception arc shown in thediagrant. Il thc trct woitlt of tlte{iompany at the end o i '1"' 1e ar is 99crores, the principal it nad started rvithwas'1. 9.9 cicr:s2. 9i c:o"esV(/90 cmre :;4. 11.0 crore:

13. Diahctic p:iietrts ai,: ad"'ised a lowglyeatiilic irir:< rjr::- fh: reascn forthrs isi . Thf ) reqL:tis | :ss ,:ei-t-'-'il)r'} a'.c thanltralthy in


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l4.Standing on a polished stone floor one feelscolder than on a rough floor of the samestone. This is because

Thermal conductivlty of the stonedepends on the surface smoothnessSpecific heat of the stone changes bypolishing it3. The temperature ol the polrshed floor isig)ver than that olthe rough lloor\jy'fherc is greater heal loss front lhe solesof the feet when in contact rvith thepolished floor than with the rottgh floor

15. Popular use of which ofthe followingfertilizers increases the acidity of soil?l. Potassium Nitrate2./ Urea1--}:dmmonium sulphate4. Superphosphate of limc

16. If the almospheric concentratior']dioxide is doubled and there ateconditicns of water. n'.rtrients,temi'erature, rvhat rvould happen to waterrequirement of plants'.)l. [t decreases inrlrall] ior J shorl lime

and then retums to thc original value2. It increases3. [t decreases.-,y'n increases initially lor a shorl time- and then retums to thc original value17.

lncreasingdepth

The graph represents the depth profrle oftemperaFJrc in the open ocean; in whichregion this is likely to be prevalent?

t. Tropical region2. quatrial region\3:-Polar region4. Sub-tropical region18, Glucose rnolecules difluse across a cell 'of dianreler ri in time r. If the cell

diameter is tnplet!. the difl'usion timewouldl. increase to 9r2. decrease to ri33. inctrasc to 3r\-4.4 dcrcas to ./9

19. Identify the figure rvhich depicts a firstorder rac{ion.

of carbonfavourable

1.

3

l. alpha2. elctron3. ggaitronVA1'iasrna

I

];l?E6

2

?

0 3

66

2c

I

Oll!456 23r56

20. Which of the lollowing particles hasthe largest range in a given mediumif their initial energies are the same?

.:

tI


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PART B


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27. The el.rcttr,i.:i- :-.ltential /(.r,1) in free spacein a re":ri:r -.., qalc ai'le charge densityp is zero isgi,-et 't',' " ..,.;; . '..i'1 : 4e" + /(x) - 3yt .. Givenihai ihe .-{-r..., rr,r:',e:rt ofrhe electric field, { , and.Lt ,':e';,,:r,: ,. ' .: crigin, /(x) is

'r . ,, .i.i . ,,, ' ,- 3.r.2. 1:. - "' ..i6,r-/.,;' ,;;

?z!.I,rt d ::r:,"1 il b,: r'',,c Cistinct tluee- dimensional.?- erio" ':. , '::>rnponentofb that ispcipirtrli.ir ',r'..' :: rr is giVen by'..( -'-'t.::- ''

i.

.,, : .:j::,. . ,r .:tic wave is propagating in alossles: i, .,' -: " 'fire electric field is given byL. ,,01i;|"-(,.J1')l]'.,!iiei.i : i: , t , .,g.:,:ri Dilight in vacuum, Eo, lairQ i.;,,,' ,'ir-:ii::1I:r end i and Zare unit'.lcii:,is ,..: .r,::.'ir,. .:- aiid z-axes. The relative^.irelcr:i., ,',r.:i;ltiitt oi the medium, a, and thea:(rnci:i t" I l ,-

\.r/, ' ri .':r; .'l

-. . -.--:::

).j

:.'r -:-.

i-11.t

t'i

, A particle of unit mass moves in a.hpotential i/(-r)=d.rr -ri, rvhere a andx'l, r.rc positive constants. The angulartiequer'cy of small oscillations about thei.ninirniim of the potential is

.iBb/s'jB" tb. Consider the 'Lransition of liquid r,r,'ater tostearl as rvaler boils at a temperature ci

I 00"C under a pressure of l atmosphere.Which onc of the follorving quantitresdces uot cl'lange discontinuousiy at thetrarrsiiion?yV4*cibbs fie; energy,. llhe inte raal energy,i. 'I he enirc;p;,j+. i h: sp;cific vllume,1, iv'rr,'h .:' rhe tbtlo\vilg matnces rs an/'/' el-'m.:nt of th,: grr.;up S{/(2)?

\-r

,' 't i\rll i. 1l '//.r1_tl_.--/:\-{ I '-ii -Fi .i 1i1.; r-l lJ ,Il:lr

,.lliJ-^-lI:t:i./. )

i-.\


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33. Circularly polarized light with intensity d isincident normally on a glass pdsm as shown inthe figure. The index olrefraction ofglass is 1'5'The intensity 1 of light energing from theprisrn is

1. I^'41 o.eol"3. 0.9? 1,,4. 0.8810

34. The Hamiltonian of arr elction in a constantnragnetic field B is gn etr by- i! = ltci'E where pis a positive constont aud o =(q'o",or)denotesthc Pauli matriccs. y71 r4 = 18 !h and I be the2x2 unit matrir. lhcrr the'operaroret""'simpliltes to

t. t'cos9!)/.^ i6 lJ^,,-r'{ lcos(tt + - slna'l3. t6 I]l sin rr.r t + --'- cosr'i,/IJi6E

,lsirtlatl + -- cos rr{rtii35. The l{amiitonian ol a syitem rvith n degrees of

freedonr is given b; tl (q,,...,q,,;p,,...,p";r).with an er:plicit det'';n''lence cn ihe time : 'Which oi rhe lblloi''rrig is coneci?

Difle:c'rt fhasI'. ri rle\'1.):iL-s cannotinter:ect each oilter.2. li always tepieselllii thc lotai energ) oitile system :rnd i-' il ctll.lsisnt of dre mction'

3. The equatiirns 4 =dH 16P,,F,=- 0H ldq,uenot valid since Hjras explicit time dePendence.$ nnv initial volumc element in phasespace remains unchanged in magnitudeundgv t ime evclution.

Consider the digital circuit shou'n belowin which thc in1lot C is always high(l) .

{hish)The tnrth table for lhe circuit can bewritten as

i6. Il ot+ --- stn -)-The cntries in thearei. 101 1i2.''1)10!)3.. llil4. 10i0,

Z column (vertically)

4.

. A cavity contains blackbody radiation inequilibrium at temperature f. Thespecific heat per unit volume ofthephoton gas in the cavity is ofthe formC, = yTt ,where I is a constant' Thecavity is expanded to tr+'ice its originalvolunle and then allorved to equilibiate atrhe sanre temperaturc I. 'fhe newintcrna! energy per unit volume is1. lyT'2. t1T'''- :t ,'' /1

A B Z0 00 In1 I

i?''


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38. Let p,,( x) (where n =0,1.2,...) be a polynomialofdegree n with real coefficients, defined in the4

interval 2 S n ! 4. \f I p"g)p"(x) dx = 6 "^,then

2. pu (*)= I6 anri p, 1x) = .,[(3 + x ;rl:t. n,G)= iand p,tx1={ir-:-.rrrlT3. p,'(r)=t and a(x)={;(3-r)

./' r lTv+1 7r, (r) =-tand p,(.r)= ri;tl -..t39. If the perturbation H' = 4.r , where a is a

constant; is added to the infinite square v''ellpotential[0for 0


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i443. A particle in one dimension moves under the

influence ofa potential Y(xJ-a75, where a is areai constant. For large n the quantized energylevel{depindsonnas:

2.J.

_/

146. Consider a system or .,,' .,. : . r ..! spins, each ofwhich hr: r'.,i;...:iI magnetic moment cf ir:^.r ..:. i.I Hamiltonian of this svs,, !i' . . - . .. . .III nragne c tletd H ls *:.' ) .l:,'II wlrgre p, rs tlrr' rraEn.-i , .": . a l| ,'n spin. The magnetir;r, r.i:. i . : : :I _.I tcmperature I rsII , --L 1t-r1I k"rl_i , ,l"",nipsl_{L_ii 'l \r,rl p'iI| . .(ult\i t rslnhl -- I| . (.r,riIi-| -a t,,u\i \4 r' annhl /" Ii l.k'r jII| !7. Considerthe matrir .1 ' = . ::i 11 ' I

.,t( o" - n'E - tta'3r' 6/5Ln-E - n1'2

44. The Lagrangian ofaparticle of charge e and massn in applied electric and niagretic fields is givenl-by L = _ mi: + eA.i - eQ, where ,J and y' arc')the vector and scalu potentiais conesponding tothe magnetic and electric fields, respectiveiy.Which of the following statements is correct?

7.

1. The canonically conjugale momentum of theparticle is given by p = pfThe Hamiltonian of the par{icle is gilenu (-by H =-+-A.D+eA2m3. I remains unchanged under a gauget! anslomtation of tlre norcutitls

, , Vl .ndei a gauge trausfonlalion of tliepotentials, I changes b.y the roral timederivative of a function of F and l'-{5. A static, spherically syrnmetric charge distributicl

nis given by p(r)=" ,-" ivhere I and K aretpositive constants. The electrostatic potentiaicorresponding to this charge distribution varieswith r as1. re'.,^'"/. !e-r'r-l_KtJ. , t'-

13 t-{l*e-"')?'\ |

i.. The eigenvalues oi'rlf ai-I. 0,1,2o,,z1o,o,s3. r;1, I4. -1, i,3

E. The exponential of il.l s:irlpiif;'' ' .(1is the 3-r3 identity :;r:,:ii-,r ;A'='-[?i."e" =i+M+-l-:ieq =l +33 ltieM =(e -t\ i,4

3.4.


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qye'48. A resistance is measured by passing a currentthrough it and measuring the resulting voltagedrop. If the voltrneter and the ammeter haveuncertainties of3% and 4%, respectively, then

A, The uncertainty inlhe value of theresistance is

,41r.ou2. 3.5%3. 5.0%4. 12.0%B. The uncertainty in the computed value ofthe power dissipated in the resistance is4*2.5o/o3. lt%4. 9%.

49. In a system consisting oltwo spin I particleslabeled t and 2. let.S"' =!d"'and2Stt' = -d"'denote rhe corrcsponding spin2operators. Here 6 =( o,,o, ,o" ) and. o,,o",o. are the three Pauli matrices.A. In the standard basis the matrices for the

operators Sj')Sf') una Sj')Slt) u." respecrively,

t. h'(t o'l rr'(-r o)+lo -rJ'+[o t)''''+('r:) +[; :)r0o0-i) foo o -r)3. r'lo o i ol r'lo o -r ol-ltttlo -i o ol'+lo i o ol\, o o oJ l, o o o)foloo) fo-,oo)

a. a,lr o o ola'li o o ol,rlooo-ii'+lo o o rl[o o r o.J [o o r oJ

B. Thjse two operators satisfy the relation .r. {sj'rsj'r, sl,sl',} -5{r)5iztyz" {sj')sf), sa)sPt}= or. [sj',sf), sj',sj',] - is(')s{')l. [Sj')Sj'), S(')S'('])] = 0

In the absence of an applied torque a rigidbody with three distinct principal momentsofinertia given by 1,, 1" and 1, isrotating freely about a fixed point inside thebody. The Euler equations for thecomponotts of its angular velocity(a, ar, oJr) are, I._1. 1..1.0,,=?oray a2=

-(o,o)r.T, I,. I._Lar= J-;J a, a,I.

A The equilibrium points in (ot, @2, @r)space arel. (1,-1,0), (-1,0, l) and (0, -1, l) .2. (1, 1,0), (1,0, l)and(0, t, l)w*(,o,ol, (0, l, o) and (0, o, 1)4. (l,l,l), (-1,-1,-l) and (0, 0, 0)

B. The constants of motion aret. ai + ai + al, and l,at, + I,a4 + I,a,y.{4ai+ I,al + I.at] andIiai+Iiai+riol, 3. I{)i + I,al + I,atl and

q+@2+@3a. ai +ai+atl, andIiai+Iiai+tial


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Choose rny l0 of the remainingquestions

51. The radius of a $Cu nucleus is measured tobe 4.8x l0-r3cm.A. The radius of a ]lMg nucleus can be

estimated to be1.2.86x10-rrcm2.5.2x10-trcm

,,.{ 3.6*lo-"cm4. 8.6x10-r3cmB. The root-mean-square (rms) energy ofa

nucleon in a nucleus of atomic number I inits ground statc varies as:I. AO'32. At't\X A-ttt4. A:ltl

52. The character table of C..,,. the group ofsymmetries ofan equilaleral triangle is givenbelow

r@l flIt" zltllc" I I bJL: 1 6t, c2q I l tl

In the above (,Cr,( denote the three classes ofCr,, containing 1,3 and 2elements respectively,and y-{'l , ,(t) uo| rPl are the characters ofthetluee irreducible representations pto), J'(t) un4f(t)-of Cr".A. The entries a.&,cand d in this table are,

respectively,l. 2, l, -1,0r;2,- -1,7,0,-l3. -1, 1, 0,-l4. -1, I, l, -l

l6

ItcM,M,,lv{ -

B. The reducible representation f of C','with character Z =(4,0,1) decomposesinto its irreducible representations;(o), p('), f(t) as1. 2p(o)* 2p(t)2. p(o)a 3p(t)3. f(o)+ p(') * 1-i:)4. 2rPl

Consider rhe decay process T- +7r- +vtin the rest lrame of the r- . The masses ofthe t- . t- and 1,, are M , , M, andzero respectively.A. The energy of z- is

(u; - u1)"'2M,

Mi + Mj)c'

B. The velocity of z is1.

3.

V:_v):M)+Ml

5s. cdkci0,-ra{

"-/'{

4.

A,

Mi + w;)c

4.

2M

MM


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Light ofwavelength 660 nm and power of 1 mWis incident on a semiconductor photodiode with arabsorbrng layer ofthickness of (h +)lm .A. Ifthe absorption coefficient at this wavelengthis l0ncm-r and if l% power is lost onreflection at th surface, the power absorbedwill bel. 750pW2. 6751tWva/zsostw4. 225pWB. The generated photo-cunent for a quantumefficiency of unity will be

l. 360FA2. 400pA

"-*Anpe4. l20FA55. Consider the energy level diagram (as shown inthe figure below) ofa typical three level rubylaser system with l.6x l0r' Chromium ions percubic centimeter. All the atoms excited by the0.4pm radiation decay rapidly to level E,

which has a liletime r=3ms.

A. Assuming that there is no radiation ofwavelength 0.7pn present in the pumpingcycle and that the pumping rate is R atoms percm3, the population density in the level N,builds up as:l. N,(t)=Rs1s'l'-1;\2i N,1l;=P7(l-e")3. N,(/)= J.e-"-"')T4. Nr0)=Rt

E3Et-2El

lelrl1-5BE-2

t7B. The minimum pump power required

(per olbic centimeter) to bring thesystern to transparency, i.e., zero gain, is-/4. tJ2 kW2. 264kW3. 0.76kW4. 1.32 kW

The magretic field of the lnE , mode of arectanguhr.waveguide of dimensionsaxb as $own in the figure is given byH,= Hocg(0.3'trx) cos (0.4ay), wherex and y re in crn

A. The dirnensions of the waveguide arc4a=3.33cm, b:2.5}cm

2. a=0.40cm, 6.= 0.30cm3. a=0.80cm, D = 0.60cm4. a=1.66 cm,6:1.25cm

R The emire range of frequencies / forwhich the IE,, mode will propagale is1. 6.0GIIZ


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A. The lattice constant is*y'a.ool2. 4.5643. 4.00A4. 2.s64

B. The sine ofthe anglecorresponding to (l ll)reflection is

L Jtl4-z


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A. The Wigrer-Seitz cell has an arei ofl. 2az

E^ r,lJ r2. -a-t3. 6'Ea'\xe"

B, The Bravais lattice for this array is a

l. iectangular lattice with basisvectors d, and d-,2. rectangular lattice with basisvectors c:r and c-23. hexagonal lattice with basis

.,,vectors d, and d,n ,X hexagonal lattice with basisvectors 6, and 6,61. Two gravitating bodies A and B with masses

m, and m, , respectively, are moving in circularorbit. Assume that m6, >> mrardlel the radius ofthe orbit of body Abe R".If the bodyl is losingmass adiabarically, its orbital radius 1,, isproportional tol. llm^z. tl n',3.^"a. ^'"

62. A time varying signal Z,circuit with output sigrralhgure below.

is fed to an op-amp/o as shown in the

L

The circuit implements a

l. high pass filter with cutofffrequency 16l'lz2. tigh pass filter with cutofffrquency 100 Hz.p,/to* pass filter with cutofffiquency 16 tlz4. low pass filter with cutoffiequency 100 HzConsider an ideal Bose gas in ihreedimensions with the energy-momentumrelation e cc p" with s > 0. The range ofs for which this system may undergo aBose-Einstein condensation at a non-zcro -emperature is

\J/1


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2065. The Hamiltonian of a particle of unit mass movingin the ry -plane is given to be:-- I IH = xp, - yp, -: r' + il' in suitable units. Theinitial values are given to be (x(0), y(0))= (l,t)

and (2,(0),r,(0,)=(+, ;) Duringrhe morion,the curves traced out by the particles in the ry -plane and the p,pr-plane are

.h*#. straight lines2. gstraight line and a hyperbola respectively92:-a hyperbola and an ellipse, respectively4. both hyperbolas


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CAREER ENDEAVOURlnstitute for NETJRF/GATE & IITJAM ExamsPHYSTCAL SCTENCES (JUNE - 2011, BOOKLET IBI)

l. (2)2. (3)3. (4)4. (3)s. (3)6. (4)7. (3)8. (3)e. (l)10. (2)ll. (4)12. (3)13. (3)14. (4)ls. (3)16. (4)17. (3)18. (4)te. (2)20. (4)

21. (3)22. (2)23. (r)24. (4)2s. (1)26. (3)27. (4)28. (1)29. (l',)30. (3)31. (1)32. (2)33. (2)34. (2\3s. (4)36. (2)37. (4)38. (4)3e. (1)40. (3)

ANSWER KEY4r. (2)42. (t\43. (1)44. (4)4s. (2)46. (4)47_a. (2\47_b. (t')48_a. (1)48_b. (1)49-a. (2)49_b. (2',)50_a. (3)s0_b. (2)51_a. (3)sl_b. (3)52 a.(2)s2_b. ( )s3_a. (2)s3_b. (2)

54 a (3)s4_b (3)5s_a (2)ss_b (1)s6_a (1)s6_b (4)s7 a (r)s7_b (2)58_a (r)s8_b ( )s9 a (1)se_b (2)60_a (a)60_b (4)61.( )62. (3)63. (1)64. (l)6s. (3)

Note: The institute shall not be responsible for any printing error/mistake in the publication.

Csir June 2011 Key Career Endover

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