fiziks Institute for NET/JRF, GATE, IIT-JAM, JEST, TIFR and GRE in PHYSICAL SCIENCES (c) 2

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1 Istitut f NT/JRF, GT, IIT-JM, JST, TIFR ad GR i PHYSICL SCINCS JST 5 Pat : Mak Qustis Q. cicula lp f adius R, cais a uifm li chag dsity. Th lctic fild, calculatd at a distac z dictly abv th ct f th lp, is maimum if z is qual t, R R R Q. Csid tw pit chags q ad q lcatd at th pits, R a ad a, spctivly. ssumig that th sum f th tw chags is cstat, what is th valu f f which th magitud f th lctstatic fc is maimum? Q. Csid a hamic scillat i th stat a, wh is th gud stat, a is th aisig pat ad is a cmpl umb. What is th pbability that th hamic scillat is i th -th igstat?! a! a! Q4. Th distac f a sta fm th ath is 4. 5 light yas, as masud fm th ath. Had ffic fiziks, H.N., G.F, Jia Saai, Na IIT, Hauz Khas, Nw Dlhi-6 Ph: / spac ship tavls fm ath t th sta at a cstat vlcity i 4. 5 yas, accdig t th clck th ship. Th spd f th spac ship i uits f th spd f light is, f z, y i, y!, y 4 y Q5. Giv a aalytic fucti, wh y C is a cstat, which f th fllwig latis is tu?, y y 4y C, y y C. y y 4y C, y y C ach ffic ad Istitut f Mathmatics, 8-/6, Jia Saai, Na IIT Hauz Khas, Nw Dlhi-6 mail: fiziks.physics@gmail.cm. If

ssumig that th sum f th tw chags is cstat, what is th valu f f which th magitud f th lctstatic fc is maimum? Q. Csid a hamic scillat i th stat a, wh is th gud stat, a is th aisig pat ad is a cmpl umb.

2 Istitut f NT/JRF, GT, IIT-JM, JST, TIFR ad GR i PHYSICL SCINCS Q6. F a systm i thmal quilibium with a hat bath at tmpatu T, which f th fllwig qualitis is cct? ( ) k T Q7. classical paticl with ttal gy mvs ud th ifluc f a pttial V, y y y y tim is qual t,. Th avag pttial gy, calculatd v a lg 5 Q8. If tw idal dic a lld c, what is th pbability f gttig at last 6? Q9. What is th maimum umb f tma f th fucti f P, ad P k is a abitay plymial f dg k? k k 6 k k k 4 4 wh Q, chai f mass M ad lgth L is suspdd vtically with its lw d tuchig a wighig scal. Th chai is lasd ad falls fly t th scal. Nglctig th siz f th idividual liks, what is th adig f th scal wh a lgth f th chai has fall? Mg L Mg L Mg L 4Mg L Had ffic fiziks, H.N., G.F, Jia Saai, Na IIT, Hauz Khas, Nw Dlhi-6 Ph: / ach ffic ad Istitut f Mathmatics, 8-/6, Jia Saai, Na IIT Hauz Khas, Nw Dlhi-6 mail: fiziks.physics@gmail.cm

6 6 6 5 5 6 Q9. What is th maimum umb f tma f th fucti f P, ad P k is a abitay plymial f dg k? k k 6 k k k 4 4 wh Q, chai f mass M ad lgth L is suspdd vtically with its lw d tuchig a wighig scal.

3 Istitut f NT/JRF, GT, IIT-JM, JST, TIFR ad GR i PHYSICL SCINCS Q. F -itactig Fmis i d dimsis, th dsity f stats D vais as d. Th Fmi gy F f a N paticl systm i will scal spctivly as, N, N /, N N /, N, N, ad dimsis / N, N, N Q. paticl f mass m mvs i N /, N, N dimsial pttial V Th act gud stat igfucti is such cstats. Th gud stat gy igvalu f this systm is,, which vaishs at ifiity. wh ad a m m m m Q. Csid a spi paticl chaactizd by th Hamiltia H S z. Ud a ptubati g H gs, th scd d ccti t th gud stat gy is giv by, g 4 4 g g Q4. Giv that ad a igstats f a Hamiltia with igvalus ad spctivly, what is th gy uctaity i th stat? Had ffic fiziks, H.N., G.F, Jia Saai, Na IIT, Hauz Khas, Nw Dlhi-6 Ph: / ach ffic ad Istitut f Mathmatics, 8-/6, Jia Saai, Na IIT Hauz Khas, Nw Dlhi-6 mail: fiziks.physics@gmail.cm

Th gud stat gy igvalu f this systm is,, which vaishs at ifiity. wh ad a m m m m Q. Csid a spi paticl chaactizd by th Hamiltia H S z.

4 Istitut f NT/JRF, GT, IIT-JM, JST, TIFR ad GR i PHYSICL SCINCS Q5. idal gas is cmpssd adiabatically fm a iitial vlum V t a fial vlum V ad a wk W is d th systm i dig s. Th fial pssu f th gas will b C C P V W V W V W V W V Q6. What is th aa f th iducibl illui z f th cystal stuctu as giv i th figu? Q7. paticl i thmal quilibium has ly pssibl stats with gis,, 6. If th systm is maitaid at a tmpatu paticl ca b appimatd t, T k, th th avag gy f th kt kt kt Had ffic fiziks, H.N., G.F, Jia Saai, Na IIT, Hauz Khas, Nw Dlhi-6 Ph: / ach ffic ad Istitut f Mathmatics, 8-/6, Jia Saai, Na IIT Hauz Khas, Nw Dlhi-6 mail: fiziks.physics@gmail.cm 4

What is th aa f th iducibl illui z f th cystal stuctu as giv i th figu? Q7. paticl i thmal quilibium has ly pssibl stats with gis,, 6.

5 Istitut f NT/JRF, GT, IIT-JM, JST, TIFR ad GR i PHYSICL SCINCS Q8. What is th vltag at th utput f th fllwig patial amplifi cicuit. [S i th k figu]? V mv V V Q9. Th gy diffc btw th p ad s lvls i Na is. V. Spi-bit cuplig splits th splittig f th p lvl is appimatly, Had ffic fiziks, H.N., G.F, Jia Saai, Na IIT, Hauz Khas, Nw Dlhi-6 Ph: / p lvl, sultig i tw missi lis diffig by V.V.V mv 6. Th Q. F a - dimsial hycmb lattic as shw i th figu, th fist agg spt ccus f th gazig agl whil swpig th agl fm. Th t agg spt is btaid at giv by si si si si si si si si Q. sphical shll f i ad ut adii a ad b, spctivly, is mad f a dilctic matial with fz plaizati P fm th its ct. Th lctic fild i th gi k ˆ,wh k is a cstat ad is th distac a b is, k k ˆ ˆ k ˆ k a ach ffic ad Istitut f Mathmatics, 8-/6, Jia Saai, Na IIT Hauz Khas, Nw Dlhi-6 mail: fiziks.physics@gmail.cm 5 99k R L Vut

Th Q. F a - dimsial hycmb lattic as shw i th figu, th fist agg spt ccus f th gazig agl whil swpig th agl fm. Th t agg spt is btaid at giv by si si si si si si si si Q.

6 Istitut f NT/JRF, GT, IIT-JM, JST, TIFR ad GR i PHYSICL SCINCS Q. Th lctstatic pttial du t a chag distibuti is giv by V wh ad a cstats Th ttal chag clsd withi a sph f adius, with its igi at is giv by, 8 4 Q. bik stutma ids isid a wll f fictilss sufac giv by z a y th acti f gavity actig i th gativ z dicti. g gzˆ maitai t b abl t id at a cstat hight z withut fallig dw? gz gz gz,ud What spd shuld h Th bik will t b abl t maitai a cstat hight, ispctiv f spd. Q4. paticl f mass m is cfid i a pttial wll giv by V f L/ ad V lswh. ptubig pttial H a L L has b applid t th systm. Lt th fist ad scd d cctis t th gud stat b spctivly. Which f th fllwig statmts is cct? ad ad ad ad Q5. Th ulli plymials sa dfid by, s fllwig latis is tu? s! s ad, s. Which f th! s! s s s! s s! Had ffic fiziks, H.N., G.F, Jia Saai, Na IIT, Hauz Khas, Nw Dlhi-6 Ph: / ach ffic ad Istitut f Mathmatics, 8-/6, Jia Saai, Na IIT Hauz Khas, Nw Dlhi-6 mail: fiziks.physics@gmail.cm 6

bik stutma ids isid a wll f fictilss sufac giv by z a y th acti f gavity actig i th gativ z dicti. g gzˆ maitai t b abl t id at a cstat hight z withut fallig dw?

7 Istitut f NT/JRF, GT, IIT-JM, JST, TIFR ad GR i PHYSICL SCINCS Q6. Th ski dpth f a mtal is dpdt th cductivity f th mtal ad th agula fqucy f th icidt fild. F a mtal f high cductivity, which f th fllwig latis is cct? (ssum that pmittivity f th mdium.), wh is th lctical d d d Q7. Th blackbdy at a tmpatu f 6 K mits a adiati whs itsity spctum paks at d 6 m. If th tmpatu is ducd t K, th spctum will pak at, m m mm mm Q8. Th wavlgth f d hlium- las i ai is i glass that has a factiv id f. 5? Icass by a fact f Dcass by a fact f. 5 Rmais th sam Dcass by a fact f What happs t its fqucy Q9. Which f th fllwig citd stats f a hydg atm has th highst liftim? p s s p Q. Th Lagagia f a paticl is giv by L q qq. Which f th fllwig statmts is tu? This is a f paticl Th paticl is picig vlcity dpdt dampig Th paticl is cutig simpl hamic mti Th paticl is ud cstat acclati. Had ffic fiziks, H.N., G.F, Jia Saai, Na IIT, Hauz Khas, Nw Dlhi-6 Ph: / ach ffic ad Istitut f Mathmatics, 8-/6, Jia Saai, Na IIT Hauz Khas, Nw Dlhi-6 mail: fiziks.physics@gmail.cm 7

If th tmpatu is ducd t K, th spctum will pak at, m m mm mm Q8. Th wavlgth f d hlium- las i ai is i glass that has a factiv id f. 5? Icass by a fact f Dcass by a fact f.

8 Istitut f NT/JRF, GT, IIT-JM, JST, TIFR ad GR i PHYSICL SCINCS Q. paticl mvig ud th ifluc f a pttial,t. If th wavfucti chags t,t gy t th iitial kitic gy will b, k V has a wavfucti, th ati f th avag fial kitic Q. Hw is yu wight affctd if th ath suddly dubls i adius, mass maiig th sam? Icass by a fact f 4 Icass by a fact f Dcass by a fact f 4 Dcass by a fact f Q. Th appimat fc td a pfctly flctig mi by a icidt las bam f pw mw at mal icidc is N N 9 N 5 N Q4. Which f th fllwig statmts is tu f th gis f th tms f th cab atm i th gud stat lctic cfiguati s s p? P D S P S D P F S P F D Q5. Th tpy-tmpatu diagam f tw Cat gis, ad, a shw i th figu 4. Th fficicis f th gis a ad spctivly. Which f th fllwig qualitis is cct? S T Had ffic fiziks, H.N., G.F, Jia Saai, Na IIT, Hauz Khas, Nw Dlhi-6 Ph: / ach ffic ad Istitut f Mathmatics, 8-/6, Jia Saai, Na IIT Hauz Khas, Nw Dlhi-6 mail: fiziks.physics@gmail.cm 8

Icass by a fact f 4 Icass by a fact f Dcass by a fact f 4 Dcass by a fact f Q. Th appimat fc td a pfctly flctig mi by a icidt las bam f pw mw at mal icidc is N N 9 N 5 N Q4.

9 Istitut f NT/JRF, GT, IIT-JM, JST, TIFR ad GR i PHYSICL SCINCS Q6. Th fc vltag f a aalg t digital cvt is V. Th smallst vltag stp that th cvt ca cd usig a -bit cvt is,.4v.4mv.4v.4v Q7. spig f fc cstat k is sttchd by. It taks twic as much wk t sttch a scd spig by. Th fc cstat f th scd spig is, k k 4 k 8 k Q8. Which f th fllwig pssis psts a lctic fild du t a tim vayig magtic fild? Kˆ yyˆ zzˆ Kˆ yyˆ zzˆ Kˆ yyˆ Kyyˆ yˆ zzˆ Q9. I Millika s il dp pimt th lctic chag culd b witt as.5 k,wh is a fucti f all pimtal paamts with gligibl. If th viscsity f ai is tak t b.4% lw tha th actual valu, what wuld b th i th calculatd valu f?.5%.7%.6%.4% ka, wh ad a Q4. Giv th tight bidig dispsi lati k si cstats ad a is th lattic paamt. What is th gup vlcity f a lct at th scd illui z buday? Q4. Th ttal umb f h a Na ad a h Cl is p uit cll f NaCl is, Q4. if a Hamiltia H is giv as H i thmal stats, th igvalus f H a i i a h, wh ad a Had ffic fiziks, H.N., G.F, Jia Saai, Na IIT, Hauz Khas, Nw Dlhi-6 Ph: / ach ffic ad Istitut f Mathmatics, 8-/6, Jia Saai, Na IIT Hauz Khas, Nw Dlhi-6 mail: fiziks.physics@gmail.cm 9

Kˆ yyˆ zzˆ Kˆ yyˆ zzˆ Kˆ yyˆ Kyyˆ yˆ zzˆ Q9. I Millika s il dp pimt th lctic chag culd b witt as.5 k,wh is a fucti f all pimtal paamts with gligibl. If th viscsity f ai is tak t b.

10 Istitut f NT/JRF, GT, IIT-JM, JST, TIFR ad GR i PHYSICL SCINCS Q4. Th stabl uclus that has th adius f 89 Os uclus is, Li 6 4 O H Q44. chagd paticl is lasd at tim t, fm th igi i th psc f uifm static lctic ad magtic filds giv by yˆ ad zˆ spctivly. Which f th fllwig statmts is tu f t? Th paticl mvs alg th -ais. Th paticl mvs i a cicula bit. Th paticl mvs i th, y pla. paticl mvs i th y, z pla Q45. Csid th difftial quati G kg fllwig statmts is tu? th G ad G is ctiuus at G a ctiuus at. but G G is disctiuus at. Th ctiuity pptis f 99 Q46. Th sum m m is t. Gad is qual t m 9 4 N ; wh k is a cstat. Which G at dpds th valu f k Q47. Lt b th wavlgth f icidt light. Th diffacti patt f a cicula aptu f dimsi will tasfm fm Fsl t Fauhf gim if th sc distac z is, z z z z Had ffic fiziks, H.N., G.F, Jia Saai, Na IIT, Hauz Khas, Nw Dlhi-6 Ph: / ach ffic ad Istitut f Mathmatics, 8-/6, Jia Saai, Na IIT Hauz Khas, Nw Dlhi-6 mail: fiziks.physics@gmail.cm

Th paticl mvs i a cicula bit. Th paticl mvs i th, y pla. paticl mvs i th y, z pla Q45. Csid th difftial quati G kg fllwig statmts is tu? th G ad G is ctiuus at G a ctiuus at. but G G is disctiuus at.

11 Istitut f NT/JRF, GT, IIT-JM, JST, TIFR ad GR i PHYSICL SCINCS Q48. F th lgic cicuit shw i figu 5, th quid iput cditi, C mak th utput X is,, t,,,, XOR U,,,, Q49. Th acti is fbidd bcaus, C U U XNOR ND X lpt umb is t csvd lia mmtum is t csvd agula mmtum is t csvd chag is t csvd Q5. lcts f mass m i a thi, lg wi at a tmpatu T fllw a -dimsial Mawllia vlcity distibuti. Th mst pbabl spd f ths lcts is, kt m kt m 8kT m. Had ffic fiziks, H.N., G.F, Jia Saai, Na IIT, Hauz Khas, Nw Dlhi-6 Ph: / ach ffic ad Istitut f Mathmatics, 8-/6, Jia Saai, Na IIT Hauz Khas, Nw Dlhi-6 mail: fiziks.physics@gmail.cm

Th acti is fbidd bcaus, C U U XNOR ND X lpt umb is t csvd lia mmtum is t csvd agula mmtum is t csvd chag is t csvd Q5.

fiziks Institute for NET/JRF, GATE, IIT JAM, JEST, TIFR and GRE in PHYSICAL SCIENCES NUCLEAR AND PARTICLE PHYSICS NET/JRF (JUNE-2011)

fiziks Institute for NET/JRF, GATE, IIT JAM, JEST, TIFR and GRE in PHYSICAL SCIENCES NUCLEAR AND PARTICLE PHYSICS NET/JRF (JUNE-2011) Institut fo NET/JRF, GTE, IIT JM, JEST, TIFR and GRE in PHYSICL SCIENCES Had offic fiziks, H.No., G.F, Jia Saai, Na IIT, Hauz Khas, Nw Dlhi 6 Phon: 6865455/9 98745498 NUCLER ND PRTICLE PHYSICS NET/JRF