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IAS Prelims 2009 PHYSICS I. A sphencal bod>· of densi ty p and radius r

IS movmg with l•eloca ty 1 in a medlum whose coeflicienl of viscosilj is 11 and density a . Which one of the rollowing gwes the retardatiOn F due to l'lscous drag? a. 67t!lfY

b. 4rrr1pgj3 c. ..f7tfcrg/3 d. 4~(p-C1)g/3 e. a

2. A particle moves under the effect of a force F = ex from x = 0 10 x = x1• Whl\lls the worJ... done m the process' I

a. ext b ex~ I 2

c. ex~ / 3

d. Zero e. b

3. Two planets of masses M1 and Ma have satelli tes of masses m1 and m:~

respecttrely. revohin~ around them at the same radius r. The 11enod of the fi rst sateUite (of mass m1) is twice as tl1at of tJ\e second. Which one of the following relations is com:Jct'' a. -IM, = M2 b 2M, = M2 c. M, =2Ml d. tntMt = mJMJ e. a

-1 . The amplitude of a damped harmonic oscillator in successive cycles decreases us a tn an anlhmetic progressiOn b in a geometl'lc progression c. linearly d. exponentially

"· b 5 A photon has enery) E. \Vhru is itS

relativistic mass? a. lYe b, E/c~

c. Zero d. ln linitr e. b

6. A particle is moving 11ith a constmt velocity par.illel to the axis of y and a velocity parallel tO the 3XIS Of X

proportional toy It "i ll descrlbe a a circle h. parnhola c. spiral d catenary e b

7 R is U1e mnge on u hori~:ontal plrme for n shot 11 i t.h the same velocitv a~ 1\\'o diiTerent angles of Jm~jection. ir h and h' be the greates t heights at1ained corresponding to these angles of prQjection, then 1vhat is R2 ecJualto? a hh' b. '.lhh' c I Ghh' d 1Shh' e, c

8. A particle ls executing SH1vl If tl1e displacement m rut\' instant is civen bv x = J cos 2t +4 sm 21.. 11 hm ts the- time pe;aod of the particle? 3 l.57 s b. 2 s c. 3.14 s d 5s e c

') A body of mass 2m is split in to two equal parts by an iotemaJ explosion which generates a kinetic energy E. Lf, after the explosion. the parts move 111 the same line as before. then whalts their relative speed?

fl .[IT';;

b. .J2E I m

c. .J4E I m d () e. c

l(l. A body is roll ing down an inclined plane with Mgle of inclination a and coeiTiclent of sliding friction ~~. What is the accelermJon of the body downwards along Ute pla11e'/ a 11gcose h. 11SSin9 www.examrace.com

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11.

12..

13.

14,

c, g( cosEl f.J,SinfJ)

d. g(sin6-~tcose) e. d A bouy of lllllSS m is released from a !wight equal to Ll1e ra<li.m; R of the earth. What will be the velodty of the body when it strikes the surface of the earth?-

a. /i,R b . ..j2gR

c. 2..{iR d. ..jgR/ 2

e. a A closed organ pipe and an open organ pipe of smne lengtlt are set into vibrations si.nm.ltaneously. The beat frequency is 4. Jf Ole length of each of !hem is doubled, rJten whatis the beat frequency? a 2 b. ,, •C. 6 d. s e. a Consider a satellite going around the earth in a circular qrbil at a height of 1R ltorn the surfuce of the earth.. where R is the radius of the earth. What is tl1e speed of the satellite'? a gR/ 3 b. (gR / 3)112 c. (gR/2.)V2 d. gR/2 e. b

A~-..-

j, •••• jo

----=:--------------------: - - - -:.:;?" s, -;;:::-----~

Two manometers are mounted on. a honzQnlll.l pipe canying water at the positions where the areas of cross-sections of tlte pipe are s1 ru1d S(l as shown in the fi.g11fe. Jfthe difference i:n '"ater column at th<ll'e cross-sections is h, what JS t.he volume of water flowing th.roltgh tlHi! pipe per unil time?

15

16.

17.

? 2gh a. .l'z I I ,Z Z

l $.2 - S;

h s2..}2.gh

o. (.~2-sl )../2ih 2g/i

d. slsl ~i ?: z 1 s:.t.- 31

e. d A clock i~ moving with a com1al1~spee(l v = c/2 along the x-ax:is with respect to an i.nertilll frame of reference F, c being: tl1e speed of light. It shows a ·time t = 0 when it. is crossing f.he origin. Wh.u1. is tile time shown by Ul.i$ moving olock when it has moved to a positinn x = c in frame. F? a. l s

I b. Jis c. 2 s

d . ..fSs e. iJ A p·meson of mass M at rest decays into two pions each ofl'est mass 1rt. What is tl1e speed of eithe< of these pious in teons of t.he speed oflighl c?

a. c(l- :::r b. c(l-4m7)

M 2

c:. c(l- 2m2)112 M2

d. c(l-2m2 ) M2

e. 'd.

Au object of smllll size and ma.ss m is altlldred to a spring of force constant .k 11xeclll1 one end and is rn1dergoing liney oscillatory motion. lf its maxinnun disvlacemenl from the point of equi1ibrium is xo, what il> its speed when it is at a disfil.nce of .xo/'1 irom Lhe eq11ilibtium poi.tlt'l a. XQ[3k /(4m)J 11" b . x.[klm] 1~ c. XQ[.IJ(2.m)f'~

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JS.

19.

20.

2t.

d. xoJk/(3m)j c. a 'll•e followiJ18 C<tualioM represent transverse wave~ :

z1 = A cos (kx-c~t) Zl - A cos (IQc I WI)

ZJ - A cos (1,1'-f~t) Which une of th,, followintt combinations represents a wave travt:ling m a direction making an angle 45" \\'ith the positive ~ and positive y axC!l? a. z1 Zl b. z, • 7.1

c. Zz + z.~

d. z, • z~ 7.j

e. b

A S()here of radius r and denJ~ity p iJf dropped under gravity through a nuid of vis~:osiry 11· lf' th., average aecc:l~;ro~tion is half of initial acccl~~·mion. wlwt is the lime requir<ld to attain terminal velocity? a. 4pr2/(C}J1) • , b. 9pr"/( 4 f))

c. 4p•·2/(311) d. pr2111 e. a

A rod at rest in nn inertial .fi'amc:: of reference r: Is of t.mgt]l I and inclined to the x-axi~ by an 11Dgle-of 45°. \Vhat is lhe l~;ngU• of lltis rod ios observed from 3 Jramo F' which is moving will• velocity v in the x-direction will1 respect to frame F?

a. / I ''1 J''! \ 'l

l

\/" I ' Jill d. 'l' -, 2c"

.:. d

A con vox lens mnk.:s tbe n;al imugo of a J>Oinl s-i tuated on tJ1c optic nr<is. [f the upper-hau· pM1 of the len~ is painted with

22

2i

black colour. what wiJl happen to the image? a. The image will be disp laced downw:ll'(l b. The image will he dispi;H:ed upward c. The image will be displaced on the

optic a.xi~

d. The image will not be displaced e. d A telescope uses a paraholic reflector so U13t it can completely climinat<> a. chromatic aberration b. •pherical aberration c. astigmatism

d. distortion e. b At n point P. a diMance L from a point sourceoflighllhe intert.~ity is measured to be [. An aperture is now introdu.:ed belween the source and the point P such thllt it sblocks all Fresnul zones cx~cpt the central zone. What is the intens ity at P now'l a, 41 b. 2J 1!. [12

d. 114

e. a 24. Jn a Michelson in terferometer, shnrp

circulru- .fi·ingC! are observed. A very thin plate will1 optical thickness e<JU3l to twenty wavelengths of the light heing us"'.l is inserted into one of th¢ interfcrcm1cter amts. \\ihat is ll1e number of bright fringes Uun cross fhe ficiJ of vic:11 ? a. 10 b. 20 c. 40 d. 80 e. c

25. \\'ben a Orin g lass wedg.: or rc(racli\'U index l.-5 is illuminated by the \U\elcn!!lh of light 60()() A. the fringes of equa I thickness are observed with a fringe spacing of l mm. WhGt is the angle of wedge in radian'/ ~. l • l O"" b. 2 10 ~ c. 4 · 10"' d. 6 x 1 0 ~1

c. b

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26. .Keeping tltt: widiJ1 of tmn~mission grating the same, tile number of line.~ is incrensed. Which one of ll1c following will happ~11 in the dittraction patlem? a. Tlu.: di.ilfa..:tion p11tlt:m \1 ill remain

llllchang~;;d

b. 1l1e principal ma)(ima "ill incre;~se in height and their width will increase

c" The principal maxima will dei:rease in height and tll..:ir width will decrease

d. l1u: principal maxima \\ill increase: in height bull heir '' idtl1 will decrease

e. h 27. The re.solutioo of an object being obsen ed

using a microscope I\ iU improve, if light of a. lllghcr Ircqu~:ncy i~ used b. lower frequency i.s used c. plane polarization is used d. higl1er intensity is used e. a

2R. A very ~mall source of light is ohserved with " microscope. An>und the sharply focu~ett image. circul.1r fringe~ are ohser:ved. Thuse diffraction rringes :m: due to '" Frosn"l diJ'fraclion only b. Fraunholer diffraction only c. both Fresnel 11nd Frmmhofer

diffractions d. neitll~:r Fn.:socl nor Fr.mnhofcr

tlil1hct ion e. a

29. 1\ quarter-wave plote is placed on a , ltiny coin. On the top of the tJUDrtcr-wave pbte. a linear polari1.er IS pl3ced. When the polario~:cr is rota led ~~ itb rcspo:cl to tb.: quarter"wave plato:, l11c coin appears to darken and tl1en again bc<!omcs shiny. What is tile Dngle between the axis of lhe quartcr-w11vc plalc and lhat of pularizcr wl1en t11e coin appcars darkest?

30.

a. 1809

b. 90~

c. 45° d. 0° e. c" Wllllt IS thc: dimension of tl1c quantity 'specific rotntion '? a" tvll-1. b. M-1l?

c. NfL d. Jld1L~T

e. b 31. /\ s ignal of 100 mW is i•tiwhxl into :1

fiber. n.e outconting signal from lhc: other end i$ of 10 mW. What is the loss'/ a. 10 dB b. 20 dl3 c. 100 dB d. 1000 dl3 e. a

32 n.e longitudinal chroma! ic abemtjoo depends on which one of the following ? a. Dispersive power of the luns only b. ?. lean focallenglh nfthe lens only c. Both (a) and (b) d. ~eith er (a) nor (b) e. c

33. \\'hat i~ the additional pha~e ditference caused. if a thin transparent plate of tlllckncss 8 tun and refractive indc!t 1.4 is introduced ;cross one ot' the bo::nns in a Young's doub le-~Jit experiment? !ThD wavelengtll of light (in 11ir) used is 4000 AJ a. Sn b. 11.211 c, 611 d. None ofthe above e. d

34. What is the total angular width of the central ma~imum in diffraction due to a single slit? :s. lh b. 2sin 1

( /./(1 )

c. 2cos- 1(A.Ia) d. a?,

e. b 35. A right circularly polarized lisht 1s

incident normally on a quarter· 1\a~c plate. The output will be

36.

a. lin<larly polarized light b. right cin:ularly polarized light c. left circularly polari~ed light d. unpolarizt:d light e. a A rc.:U!ngular coil is ro1atinjl i11 a liJliform magnetic field R. The e.m,t: induced in the coil is max1mum when tlte plant: of the coil

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37.

3!!.

39.

40.

4J .

a. iS" paraltelto .B b. makes an nngl.:. 30° wiUt B c, makes an angle 45° with J3 d. is pc-Tp<mdiculnr to B e. a A disc tota!<;;S at 300 r.p.m. A v~~rinbltl

fo-rce is appJjed to it and the speed is reduced according to lhe bw o, - -2vl revolutions pet· square minute, whet·e w is in r.p.m. What i.q the expre;;sion for revolutions f) as a function of time I"! a. 9=150i 1-e-21)

b. €1=150(1- c")

c. t·\: 150i I <-e ~) d. 9= I SOi 1- e -ll)

e. a A rigid insulateil box Is divided jnto two parts wilh a pa,·Htion, One pad is occupied by I !,>m mole of ideal gas at temp<:ralltre T1 and the other by 2 gm n1oles of tlie ~ame ideal gas at temperature T'z, Wheo Ute partition is removed, what is the final etlllllibrium tc.'rnpc:tauu>e of lhe mixture? ~ . T=(T1 +T~)I2

b. T =-(21',+1'2)/3 c. T"(T1 +2T~/3 d. Cannot be determined due to

insutlicicnt <lat.1 c. •.

11te relation J rdS = J pdV is va lid for

a. any process b. any cycle c, ~ny revet:s ible process d. ~n_y adiabatic process e. d Consider an ideal gas 11<ith molar specific heat Cv : 3R/2. lt m at temperature To and has a volume Vo. If it is adiabatically compressed lo volume V11 12, then what is the fmal temper;~ lure? a.. zt-1To b 2·r'r • . !)

c. 2YTo d. 2To e. h wltere y is the ratio between opecifio heats What is the maximum amount of work lbat can be done by extracting I. J of heat energy from 11 boll y :tt temperature 127 •c w,ill1an environment at temjlerature 27 •c?

42

43.

44.

45.

46.

a. 1/8 J b. l/4 J c. l/2 .r il. 3!4 J e. h What is the change in tmltopy wh<:n 100 gm of water is heated from 27 °(' to 87"C? [Talre specific heat of wate1· to be constant, 4.J 85 Jl(gm K)]

a. 25lt0 J/K b. 4 18.5 ln(S) JIK c. 418.5 ln(6) J/K. d. 4 18.5 In( 1.2) J/K

e. d Whal is the change in entropy of one gram mole of an ideal gas wht:n j[ ""xpands isotheml.ally ·fi·om volume V 1 to volume V2? a" R(Va-Vil b. R(V;JVJ) c. Rln(V 1 V1J d. Rln(WVJl e. d

A blackbody \\' iUt -surf«ce nrel! A and ten:tperaturc 127 °C emil~ a.n amo1tlll of radiation E J/5. What 1s the radiation emitted by another blackbody wiUt surface a!'ea 2A and temperature 3 27 °C'? a, l0.125E b. 3li ~. 4-.5E d. 6.75E e, ~

The 1'1\diation enlitted pt!r 110it w'aveleqglb per mtit time hy a blackbody at temperature T has maxmmm at wavelength 'J. •• Wb~t is tho wnwlength at which Ute radiation emitted per unit wavelength per unit lime by this blac.k­body ~t t.;mperat\l.t'e 2'1' is maxim11Jn? /1 . 2/.. b. 4/..

c. ~J2

d. JJ4 e. c The r<:)ot-meatt·~quare ve1ocity of otle molecule al 300 K is four times that of Mother molecule, If i.be (J.TSt molecule is hydrogen, tlten which one of the following may be the oUter molecule? a, Heliuni www.examrace.com

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47.

48.

49.

50.

b. Boron c. Oxygen d. Cutbon dioxide e. c

v-CoTJSider the figure given above. W11en a system is taken from state A to state B along the path ACB, 80 J l'f heat tlCIW.l' into Lhe systt'lll and Lite system does 30 J o.f work How much heat woUld flow into the system if the system is tuken from state A t() slate 8 along the patft AOB and the system does I 0 J of wotk? a. 301 b. 40 J c. 50 J d. 60 J e. d Wlmt is the approx.irnate root- mean speed of line smoke patliclt~ of mass 10'11 kg a1 2TC? [k = 1 . 38 " !O~' JIK] a. 2.0 • 10'2 mls b. 2.7 ' l0'2 m/s c. 3.5 < 10'2 m/s d. 4.4 ' 10'2 m/s e. c ln a ga.• eon.sisting ofr1 molet;tile~, 1Vbatls the number of mol<:cular collisions occun:ing per second? (whore pis the colli!iion rate) a. np b. np/2 c. 2np d. n(:rL- l)p/2 e. d '111e MaxweU lilermod)/JUliTlicall'elalion

(as) :c( .:P ~ arr r ur"'

can be derived from which one of the following relations? a. dU =dQ - PdV b. dH = dU I pdV ~ Vdp c. dF = dU - TdS - SdT d. dG = dH-TdS-SdT

e. c 5j . Vihat is the kinetic energy of a molecule of

a diatomic gas at STP? a. kT1'2 b. kT c JkT/2 d. 5KT/2 e. d

52. A Camol engjne wo.rki ng between 300 K and 600 K has a work output of 800 3 per cycle. What is the amount of heat energy SUl)plied 1o the engine from the source in eaclt cycle? a. 800 J b. 1600 J c, 3200 J d. 6400 J e. b

53. A positron is projected into a unifOTm magnetic field wi1h its. velocity ved.or making an ~e of 79° with the field. What is the trajectory oftlte positron_? ~ Circll' b. Parabolu o. Sb:aight line cL Helix e. d

54.. Three identical charges each of ma~nitude q are placed at th:e com~rs of.an equilateral triangle of side a. V/hatJ.s the magnibtde of force ou each cl:iarge?

a. P-=- q l I ( 4m-0a!) b. F = $q1 1( 4rr&na1)

c. F=l 1(2'm:0a1

)

d. F = JJ1;l I ( 8m;0a1

)

e. b 55. Consider a spherically symmetric charge

distribution wilh dert!<ity p(r) = pO to( r < R -where pis constant =0 forr ~ R What is the rna~ tude of the elecb:ic field at r = RJ2? a . poRI(6SiJ)

b. pnRJ(3f.O) c. pol( 4neoR) tl po/( 4neoR~ e. a

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56. A spl1ere of radi U>' R ts made· liP of unifoOtJJy distdbuted positive chm-ge. A1 a di.s.llulce r from the centre inside the sphere, tl1e electric field is propmtional to whiclt one of the followirtg?

57.

58.

59.

a. r -2

b. I ·I

c. 1'

cL The eleclric field does not depend on r e, c What is the eleclric flux through eaeh of the fi1ces of a cube of side t m, if a charge q coulomb .is placed at the point of intersection of its diagonals? a. q/~ b. 6q/Sto c. q/(6so)

d. q/(3so) e. c A piece of clielectric 0f thiokness slightly less than Ute ~eparu1jon ]Jetween 'll1e plal:es of a Charged and isolated parallel•plate condensey is Ulllerled partly between the plates. CM$ider l:he follo\Ving statements: 1. T11e ••mergy stored u1 the ct\!ldertser

door eases~ 2. The fi·ee charge density on fue

conden.~er plat~>s decrenses. Wl\icl1 of the sb;ttemen(S g[vep above illlare COITecl?

a. l only b. 2 only c, Bo1l1 I and 2 d. Neitlter 1 nor 2 e. a A capacitor CQnsists of two parallel plates each of area A and I<epM!led by a distlmce d. If it is connected l>y a battety of voltage Vl what is tl1e final charge stored on each plate? a. (&oAfd)V b. (f>oA/(2d)JY

c. (2soA/d)V d. (4s.-)\/d)V

e. a Copper and iron wires of same length artd diamet:er ru·e i 11 series and connected across a battery, The resistivity of corJf?er is about one- sixth of that of irorL lf E1 and E2 are the elecl:cic fields in tile copper and iron

6 1.

6'2 .

63.

wires re:;pectively, then whid1 one of the following is correct? a. Et < E~ b . E1 =E~ "' 0 c. E, > E2 d. E1 = E,. = 0, because eleclric field

cannot e;ds~ l:u metals

' ' I ' - . ~ ' ' • > • I

f) fl '~'-+

The vru:ia1ion of magTietization with lentpera.tw·e (T) of a magnetic material 1~ shown in the figu:re. ru ihe temperature increases, tllemagnetization drops down to zero at Curie lempl'rattrre 9. Above Curie t:emperature, 1/7, (where ;<. IS the susceptibili1?') increases lirtearly with tetnperature. What would be the nature of magnetic ntflterial ~ a. F'etTOJTtHgnetism b . Pru'alllagnetism c. FerriJnagnetism d. AntlfetTomagneti sm e. a*

For engi.ne.ering applicatiom (electric motors, loll<h~peakers, etc.), the magnetic rnal.erinls with high ct1ercivity, triglt remanence and large hysteresis loss are desirable, These materials are -.;ategorlzed as a. ltard magnetic materials b. Boft magnetic materials c_ normal u\ag;neuc materials d. Nru1e of the above e a A resistor has stripes tllat read green.. blue, brow11 and silv~r. \Vlm.t IS its n()minal resist'ailce and tolet'ance? a, 56 Cl ± 5% b. 560 L) ::t l 0% c_ 560.Q± 5%

d. 5600 Q :t- I 0% e. b•

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lf a shod magnet is moved along Lhe axis of a coil with c(lflstimt velocity, the variation of induced e.m.f (E) witl1 tinJEl (t) is best represel\ted as whiclt on<' of tlte fall l'wing? a

i E

l~

b.

I g l.,.----1-----'>-

i

J .

e. b

B

. I D I

p Q

A haltel)' is connected between points P and Q such that a current J flows from P to Q. From point A to point C, H1e· CLtn·ent flows througlt two circular arcs ABC and ADC as shown in tlte figure above. The me ADC makes an angle 90" at the certtre. The entire circle is made up of' t.he s!ln1e wi:re. What is the magnetic induction at tbe ·centre of the circle ofr'ddins r?

66.

67.

68.

69.

;1, p.oli(2J) b. ~Li!l/(4r)

c. J)J~l1(8r)

d 0 e. d A rectan!2;Ular frrune of wi:re is mo\'ing with con;fant velooit;y in a TJon-unifo~ magttetic field which is pe1pendicular to flte plane of the frame. Considt:tr the following statements: 1. The role of tl1e sides of the 'frame,

pruall.el to th.e direction of velocity, is only to '(lrovide a closea path.

2. J ottle heating takes .I) lace in the fi:ame. Which of t.he statements gjven abPveis{are correct? a. 1 oDly b . 2on1y c. Bolli I and 2 cl Neither 1 nor 2 e. c Wluch one of tlte following .>tatemerfis' is not correct'? ln an LCR circuit at resonance a. tl1e inlpeoonce i:s purely resistive b. the current is ma:x:iJ.nUJII and irr phase

,.,jfiLIJ)e applitld 'Voltage c. quality fuctor of the circuit is

rn axi n111m d. voltage acros.q the inductance is equal

to voltllge across the capacitance bul oul of phase

e. c In a series LCR circuit;. the resonant frequency is I 000 Hz. The hall' power points are obtained at fi:'llquf)ncies 950 Hz mtd I 050 Hz. Wlmt are the quali1y fa.ctor and bandwidth of the circlllt· respectively? ·a. 100, JOO Hz b, 10. 100 llz c. 10, 10 Uz d. 100. 10Hz e. b There is a phase change of 1300 when an eleciiO!Tiagnetic wave is a. reflected fi·om a derLqer roediwn b. reflected from a rarer mediwn c. transmitted to a denser mediwn d. l;ransmitted to a rarer medium e. a

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70. [n a Van <le Graaff accelerator, charge is always transfen·ed from the in.ner shell of radius r to the mottlr slu~H of r:•diu~ R(r<<R). 'fhe charge is tfan.<>f<:~'red.

because a. irrespective of potentials, the charge is

always transfQtTed whenever two metallic bodies make electric contact

b. irrcspcctivll of the <JUantity of char~e on the outer shell, U1e potentia I of the iuner shell is higl1er tha.n tl1at of the outer shell

c. lbe outor ~hell has l~rger ch.,rge• holding capacity (capacitance)

d. swface charge tlensity is high~T on the innersheU

e. b 71. Consider Ute following statements m

respect of a cyclotron: L ln a 50 MeV proton cyclotron with

uniJorm magnetic .fit:lJ. the cyclo1ron fi·equency ut 10 MeV energy is equal to the cyclotron frequency of the same proton at 50 MeV energy.

2. Relativistical.ly movmg pa1ticle has highc.:r mass than its rest mass.

Which of the statcmcn1li given 1obove is/are correct? a. I otily b. 2 Ollly c. Both 1 und 2 d. Neither 1 nor 2

"· b 72 Two particle,; 11•ith charg¢! <11 ~nd q2

(both positive) are it1itially at J'll~t at a distance d al t - 0 and ure released. What i.s the ir totill kino:tic en'T!,'Y when they are at a distance 3d (taking otily coulombic forces it1to accounO? a. <)1q2 i (127lSQd)

b. q,q2 /(67l~t)d) o. q 1 q2 /( 4n&(){l) d. qoq2 /(3nsod) e. b

73. A posilronium atom is made up of one electron and one positron. \Vltat os tl1e ground-state energy of )>ositr·ottium ato.tn? ~. · 6.8 e\1 b. 6.~ eV c. B .GeV d. -13.6 eV

e. a 74. ProJection of angular momcnhln:i of a 2p

electron on the z-axis has va!u~

a. ,fih1(21T ),O,-J2h l (2tr)

b. h t (211').0,h 1(2r.)

c. hI (211' ),0, - hI (:br)

d. h,O, - h

e. c 75. Consider U1e following stat~mcnts m

respect ofZe.:man el~ect: L Atoms art: plac..,d m weak clectJiu

tiel d. 2. Atoms are placed in weak magnetic

field. Which of the ~tatements given a hove is/nr" correct?

a. I onl.y b. 2 only c. Both 1 and 2 d. Neither 1 nor 2 e. b

76, X·rays of ~vaveleogU1 />, art; incident on a crystal and the. second-ord~'1· rellection from the crystal is oh~erved at an angle 45~. Wlt~t ~~ the latfice const.1nl of t:be crystal?

"· /~,. b. 2?. c. IJ -J2 d . .Jn . e. c:

77. Consider the following statement~ in re~pec! nfMoseley law of X-ray speciJ·a: I. Plot of squlll:.e root of the frequency of

K" line and atomic number is a straight line.

2. Plot of square .root of the ftequenC}' of La line and atomic numbeJ· is a straight line.

Which of the statements given above is/are correct? a, 1 only b. 2 only c. Bo!h 1 and 2 d. Neither I nor 2 e. c:

78. \Vhicb one of the following is correct in respect of an electron a.nd a proton l1aving same de Drogue wavelength of2A? www.examrace.com

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79.

80.

8L

82.

S3.

a. Both have same kinetic energy b . The kinetic eot:rgy of proton is mote

than th~t of electron o. Both have same velocity d. Both have same momentum e. 11 A. particle of energy E is incident ·from the lett on a potential step of height Vn at x = 0. ITE < Vr., what is the wave Junction in the rt:gion x "" 0? a. C exp( -jrot + kx) b. C exp( -iwt 1 ~J

c. (' exp(ic.)t- ikx) d. C exp(-iolt- kx)

~. d Approximately how m any h~lf-lite periods n1ust elapse, if the activity of a radioactive isotope sample is to he reduced to 0004 of the original value? a. 3 b. 5 c, 8 d. 60 e. c Cons ider the foUowing m r"sp<o:cl of

ba.ry6llll 1. They interact strongly.

2. TI1ey interact weakly. 3. They possess integral Rpin. 4. They possess half-integntl spin. Which of the above are correct'!

a. J and 3 b. 1 and 4 e. 2 and 3

d. 2~nd 4 e. b Wh~o.'ll a neutron is converted into a proton

:1. only an electron is produced b. ont: electron and a ne;:utrino are

produced c. one electron and an anti-neutrino are

produced d. cme electron and a ph()lon are produced

e. c In ~ photoelec.tric effect experiment, tlte rn3xifl)um energy of U1e emitted e lectrons

i~ leV for incoming r~diation <rffrequency vO ami 3eV to r incoming radiation of

85.

86.

87.

frequency 3vol2. What i.~ the maximum ent:rgy of tb.., ck:clrons emitted for

incoining radiation ofJrequency 9vo/4? a, 8 e.V

b. 6 c.V

c. 45 eV d. 3 eV e. b

For a helium atomic iou will1 one electron nnd nuclear charge 2q where q is the

charge of a proton. what is the energy. of the .l;tale witl1 princip:1l quantum number n =41 a. - 27.2eV b. - 13. (leV

c. 6.8eV d. - 3.4 eV <:. d Cons ider a particle in nne-dimensiona l h()x

between :o:: = 0 and x = a: V(X) - 0

= r-:(1

fot for

0 •- x "' a x s O orx ~ 11

When it is in the grmmd slate. what is the prollilbility U1at it will he found in tbe

regiolt (a/4) < x < pa/4)2 a. l/2

b. ( 112) • ( l htl

c. ( 1/ 4) ' (2/7t)

d. ( ] 14) ··(l 111)

e. b

i\ particle of mass m is In a harmonic oscillator potential V(.v) = 2A;..?. Given th:1t

~1(x) ~ Aexp(-a.~) ls an eigen function of

~n~:rgy. What ill lht: value of tht: coruit~nt a'? 11, b(k /m) 11a I (27t)

b. h(2k /m)h)112 /(211)

~. n(mk) Ill; h

d. 2n(mk) 112/ II

e. d A paJtkle with energy V .)2 coming in .from the left encounters a potential -3V v/2

nt x = 0: V(x) = O :fi>r x < a

= -3V 1/2 for -t ~ a What is the transmis•<ion coefricient'?

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88.

S9.

90.

l a. -

2

b. 2

3 4

c, 9

d, 8

9 "· ('

The h~lf-tiJe of a dec.1yirtg11ucleus is r 1r1.

What fractiotl of the ot-iginal nuclei will l1ave dc;ca yed in a time of 3; tlz'}

1 ~.

8

h. 7 -R ~

-' c. 4

cl . ~

-' !)

e. b For \\•hiuh de<.-ay scheme of tlte otigin·al nucleus arc the original nucleus and the £inaJ nucleus isotopes?

a. Two gamma decays b. An alpha decay fo llowed hy two heta

decays c. A beL<'l decay followed by an alpha

decay d. A bela decay followed by neutron

emission e, ~

CoMider the J'lss ion process of doxay 236A ~ IA4B + S9C + 30 lf the approxitnate binding energy per t1ucleon i~ 7 MeV for A. 8 MeV forB and 8 MeV for C, what i~ the energy released in the decay of one tlucleus of A'l

a . 236MtN

b. 4'3 MeV c. 226MeV d. 2 12MeV e. d

91. '!l1e dec.:ry of A-+ p I 7( lllfOugh strong interaction i~ forbidden, because the process violates a. cl1arge conserfalioJt

b. angular momentum conservn.tion t.l'. pari1 y conservation d. str:1ngeness c,onservat~on

"· d 92. Match List-! with List-II Md sel~>et the

93,

94.

95,

correct answer using the code given below the. Lists l.i~t 1 A. Electromagnetic interaction

B. Weak (nuclear) interaction C. Strong (nuclear) interaction List Jl I . Hadrons '2. Photons 3. Leptons Cod~:

A II. 1 b. c. 2 d. 2

e. d

B c 2 3 " -' 2

' .)

3 l

The C<)mpton wavelengt·h {rf an electron is ~hnut 0.024 A is .~caUered at an ang_Je 90'1

by :m electron initial.ly at rest., what is the Mgle ntwhich Ute electron comes out? a. - 45" b, - tan'1 2 c. 60'1

d . tan' 1 (-112)

e. d Wl1en reverse voltage acros~ silicon diode i.~ changed from 4 V to S V, what happens to depletimt layer? a. II decreases

b. II incr~ases c, It is unaffected d. It may increase. or decrease

e. a In n-typc semiconductor when all donor stales are filled, then tile net cllarge denoity i.n the dooor $lates becomes n. l

b. > I

c. ·-=-l. b ut not zero d. 0 e. d

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96.

98.

99.

Two identical Zener diodes baving

s.pecification 12 V_ 2. W are connected in 4

series. lfbreakdo\Vn voltage oJ' e~ch ·diode is 5 V then what is tlte breakdown voltage

in the seric;s combination of the diodes?

~' 2.5 v b. SV c. iOV

d. 12V c. (' Consider Ute foltowing truth table

lnpujs 0 110'111 A B £' X

()

()

0

()

1

1

0

( )

l

1

I

(I

I

lJ

1 ()

l

0

0

0

()

1

Wlwt is t he simplified Boolean expre~sion for Ute output X in leans of inputs A, B and C?

a. AIJTA BC

b. AB ~ABC

c. if B+ ABC

d. iii3+ABC

" · d A BJ'J' having current <tmplilication factor 0.99 is used in a common- base mode. If the lmtd resistan ce is 4.5 kQ and dynamic resistance of the emitter ju~1ctinn is 500, then what is tbe vo·ltage gain 'I a. (!9.1 IY. 79.1 c. 69. 1

d. 59.1 e, a lu an n-t.ypt: st:miconduclor, tbe Fenn.i level lies 0,3 eV below the conduct·ion band al :\00 K. if the temp erature 1s

increa~ed lo 3~0 K. where does the new position of the Fermi luvcllic? a. 055 eV below the conduction band

b. 0.44 eV below the conduction band

u-. 0.33 <JV below the conduction band d. 0.27 eV below the conduction band e. d•

tOO. Til(: built-in potential ofp·n .iuaction diode is ~ fuucti<m of a. ten1perature

b. biased volt.1ge

c. doping densil y d. All oftlw above e. d

101. 1.<• Cll mf,lde, the input characteristic of a BJT is llie variation of a, lB versus V Bll at constant V a;

b. lc ver~us Vf's at constant Vae c. Ic vers us V em at constant lA

d. IB verw~ V c;s at constant V Bli

e, b

I 02. AJ \ 'el'Y bjgll .frequencies. mica capacitors a.re used, because a . mica hilS high resistivity at these

frG'tlucncics

b , the additional energy for the reversal ofpn~1icles of the dielectric ill a.c .. fieJII

is small c. the retention of charge by mica t fl

negligible d. leakage Jon in mic.a does no! exist

e. a 103. A pru·ticl~;~ or mass m and charge q is at rest

at t 0 iJt ~ unifom1 elecu·ic field E in Ute x­dlrectlon and 1s releast:d , lf lh!! parliclt:

moves through a distance of 5 m b~;twCtm

t= 1s and t=2 s- what is the m~gnitude of E'l a, !Om/(3q) b. m/q c. 3.m/( lOq) d. q /m e. a

104. CoD!l id~r a circular charge loop wilh radius r and total charge Q lying in the x;~plane w ith centre al tlte origin. \Vhat is the magnitude of the force acting on a point cb:1rge qat :1 point (0, 0, z)? ... . a. <fQ1(4nso(r" +z.") ]

b. qQ/[4neo(r~ ~-'.?)r] c~ qQ~(4n8()(? 1<:

2)

312] www.examrace.com

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105.

106.

107.

108.

a, c

l.n sPherical wavefronts, the amplitude of the disturbance iR proporliortal to {Where r is tlte radiu~ of the wave-front) II. T

b. r l c. ? r d.

., r~

e. b

100 fl

·r~- ~~--~2-n-~--~----~ ·

IS V 1t- )2 V S RL

0·315 w >

[n tJte above circu:i~ what is the range over whidh the load resi~tance can be varied? a. 298.6 Q :;; Rt < ro b. 303.7 Q s R1 < oo only c. 408.2 ~"2 1> R.i. < oo ani y d. 428.6 Q $R.i. < 00 only e. d-InS tem-Ger1ach e:;.;perimem., one finds file $pin (i.e., total angular momentum) of the charged atom due to $l)litting on the screen. Consider the following statements: ]. The splittLng is due t.o magnetic Held

gradient. 2. The charged atom must travel

perpendi.:ular to the field gradient so thai splitting occurs.

Whiclt of 1he statements giveu a\xwe isiare corred? a. I only b. 2 only c. Both l and 2 d. Neither 1 nor2 e. c Which one of the fullowing is correct about wave-particular duality? a Wave-particular duality l1olds for

matter particles but not for light . b. W11ve-partiole duality holds fe>r Jiglrl

but nol for m atter particles c. Wave-particle duality holds for

electrons but not p1'otons d. Wave-particle duality nolds for light as

we.ll as fc•r matter particles e. d

109. A whistle of frequency 540 l:lz roMes m a circle of ramus 2 m at an artgnlar ~peed of 15 rad/t: . What are the lowest and the ltigh<?st frequendes respectively lteard lry R

listener, a long distance away at rest with respect to the centre of the cixcle? (Speed of gound = 330 ruls) a. 495 tlz, 505 Hz b. 490Hz, 505 Hz o. 495 Hz, 594 Hr. d.. 490 H;1., 594 H7, e. c

110. The principal quann1m number 11

characterizes the allowed ener.gy levels of hydmgen at®J. In which oftl1e following tran!lttions, the emitte<l photon has the sh01test wavelength'/ a. n = 2ton = l

b. n =3 ton=l c. n =4 ton =3 d. n = 5 ton = 4 o;.. a

ll L A rectangular block of mass 5 kg is kept on n hotizontal surface, Tile cooeflicienl of friction betweell 1i1e block and the surface is 0.2. If a, force of 20 N is applied to the block at an angle of30°with the horizontal plane, whll1 is tlte force or friction on the block? (Take g= iO m/s~) a. 5N b. lO N c-. l2N d. 20N e. c

Ll2. 1:n a typical phase transition (such as oondensalion), which one of the JoUt,wi.ng remains unchanged? a. Internal <~llo:ttgy b. Enthalpy e. Helmltol lz free euergy d. Gibbs free energy e. d

J I 3. T11e electric fielll associated with a propagating electromagnetic wave IS

described by the "quution E = Eosin(4r. x LO' .x-1. 2n x I 01 ~t) where xis in rueter and tin second. What is tlte wavelength? a. lO.s m

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b. 5xl0 m c. 5 x l(r7 rn

d. 10'1 IT1

e. c

I 14. Whnl is llu: r~tio of moment of incrti:• of a thin rod about an :rx i~ U1rough midpoint ~nd perpendicular to its length and that abo\Jt an lt.'<is through one end and perpendicular to its length? a. 114 b. 113 c. l 2 d. I e. a

115. \\'hat i~ tho number of electrons in an atom m \\ hich oil tl1c states 1\ itb princip~l quantum numbers n - 1. 2.. :< and the angular mom.:nturn quantum numbers I =

0, 1 st.1t.;.~ will1 principal quantum number n = 4 are "filled'! ll. 10 b. Ill c. 30 d. 36 e. d

116. Assertion (A): When an ultrasonic wav" is passed thmugh :m oil pol, it tan heat a glnss rod to :1 high temperature:. Reason (R): The temperature of tJu~ oil tncreases due to high frequency oscillations. a. .Both A nnd R :rre individunllv true and

R is U1e correct explanation of A b. Both A and R are individually true but

R is 1101 ll1c corrcet C:'!planation of A c. .\ is true but R is f:t lse

d. A i~ fal~e but R is true e. a

117. Asser tion (A): Oilfusion is tbo phenomenon of movement of molecules from regions nf higher molecular densitv to regions of low~or molecular density. ' Reason (R): The mtl.'lll lrcc path of lho: molecules of a gus depends on the number of mole-cules per unit volume nnd tbc sizu ofU1e moleeol.:~. ~ . Both A nnd Rare individual ly tme and

R is the correct cxplnnnlion of A b. 1:3vth A and R ~re irH.lividu;slly true b11t

R is ll tJI the cnrreot explanation of A c. A is true but R is false

d. A i~ fal8e but R i$ true

e. b liS. Ass11rtiuu tA): A source of light c:1n be

temporaUy coherent but spa tially incoherent and vice vers~ . Reason (R): Spatii!loohel"''fH:c dcptmds on lhe angular size of the source nnd tcmp01-al coherence on the mono-chromnticitv. 111c two are therefore not dependent o~ each ulher. a. Botb A ami R are individually true nnd

R is the t:orreet l::'(plan3tion of A b. Both A and R are individually true but

R is 1101 the correct e'<planation of ,\ "· A is lrut: but R is false

d. A i.~ false but R is true

e. a 119. Assertion (A): The p~rticle nuturc of light

is prevalent in the photodcctric effect and the wave nature is es•ential to describe it~

int~o:rfllr~>'ltcc: elleot. Reason (R): Th~ ~pp:srent p3rndox. leading to the dttal nature of lighL may be resolved in a prob;lbilistic desCJiptiotl of a p:~rticle, where ull) WiiV(l pl:syN Ulc mill of :1

probability amplitude, a+ 6oth A and Rare indiv.ichw llv lnt~ and

R is U1c correct explanation oi· A b. Bolli A and Rare individually tru.: hut

R is !1af ll1e cotTect explan<~ti~n of A c. A is true but R is false

d. A i.s fn l~e but R is true

e. b

120. Asser tion (A): A nuclt:ar Cission is initiated b}' llte c.apture of thermal neutron by a heavy nucleus and involve.~ release of abuut200 :\leV per fission. Reason (R): The energy relea~e occurs because the smaller fission-product nuclei are more tigbily bound by about I MeV per ouclton than i11e original heavy nucleus. a. Both A and Rare 1ndividuallv tn1e and

R is the correct e.'<planat ion oi· A b. Both A and Rare ;ndividually true but

R is n ot the correct explanation of A c. A is true but .R is false

d. A is false butR is true e. a

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