nucleus sample test paper 2013

7/30/2019 Nucleus Sample Test Paper 2013

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CODE : A PAGE NO. # 1

[PHYSICS]

Q.1 The dimensions of ba in the equation

P =bx

ta 2where P is pressure, x is distanceand

tistime,are:(A)[M2L T3] (B) [MT2](C) [LT3] (D) [ML3T1]

Q.2 A particlemoves withconstantaccelerationof3m/s2 along x axis. If its x-coordinates at t = 4 secis100mandvelocityatt=6secis15m/s.Itsx-coordinates at t = 6 sec would be(A) 54 m (B) 9 cm(C) 124 m (D) 134 m

Q.3 A man ofmassm slides downalong a ropewhichis connected to the ceiling of an elevator withdecelarationarelative to therope.Ifelevator isgoingupwards withan acceleration a relative tothe ground, thentension in the rope is

(A) mg (B) m(g + 2a)(C) m(g + a) (D) m(g + 3a)

Q.4 The pulley is given an acceleration a0

= 2m/s2

startingfromrest.Acableis connected toa blockA of mass50 kgas shown. Neglect the mass ofthe pulley. If = 0.3 between the block and thefloor, then the tension in the cable connected to

blockAis

a0

A

(A) 200 N (B) 250 N(C) 300 N (D) 350 N

Q.5 Power delivered toa bodyvaries as P = 3t2. Findout the changeinkineticenergyof thebodyfromt = 2 to t = 4 sec.(A) 12 J (B) 56 J(C) 24 J (D) 36 J

Q.1 lehdj.kP =bx

ta2

esa] tgk P nkc gS] x nwjh gS rFkk

t le; gS (b

adh foek gSA

(A)[M2L T3] (B) [MT2](C) [LT3] (D) [ML3T1]

Q.2 ,d d.k x-v{k ds vuqfn'k 3 m/s2 ds fu;r Roj.k ls

xfr djrk gSA ;fn t = 4 sec ij blds x-funsZ'kkad100m gS rFkk t=6sec ij osx15 m/s gSA t=6secij blds x-funsZ'kkad gksaxsA(A) 54 m (B) 9 cm(C) 124 m (D) 134 m

Q.3 m nzO;eku dk ,d vkneh ,d jLlh ij tks fd ,dfyV dh Nr ls tqM+h gS] jLlh ds lkis{k eanu a lsuhps dh vksj fQlyrk gSA ;fn fyV /kjkry ds lkis{ka Roj.k ls ij dh vksj tk jgh gS] rks jLlh esa ruko

gS &(A) mg (B) m(g + 2a)(C) m(g + a) (D) m(g + 3a)

Q.4 fojke ls izkjEHk ,d f?kjuh dks Roj.ka0= 2m/s2 fn;k

tkrk gSA ,d dscy n'kkZ;s vuqlkj 50 kg nzO;eku ds,d CykWdAls tqM+h gSA f?kjuh ds nzO;eku dks ux.;ekfu;sA ;fn CykWd rFkk Q'kZ ds e/; = 0.3 gS] rksCykWd Als tqM+h dscy esa ruko gS&

a0

A

(A) 200 N (B) 250 N(C) 300 N (D) 350 N

Q.5 ,d oLrq dks iznku dh tkus okyh 'kfDr P = 3t2 dsvuqlkj ifjofrZr gksrh gSA t = 2ls t =4 secrd oLrqdh xfrt tkZ esa ifjorZu Kkr dhft;sA

(A) 12 J (B) 56 J(C) 24 J (D) 36 J

NUCLEUS(11thPass) 2012

Select the correct alternative. Only one is correct. [813 = 243]

There is NEGATIVE marking.Foreach wrong answer1 mark will bededucted.


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Q.6 A particle of mass m isfixed to one end of a lightspring offorceconstant k and unstretchedlength. The system is rotated about the other end ofthe spring with an angular velocity in gravityfree space. The increase in length of thespring is

(A)m

k

2(B)

m

k m

2

2

(C)m

k m

2

2

(D) noneof these

Q.7 AmassmispulledoutwarduntilthestringoflengthLtowhichit isattachedmakesa90anglewiththe

vertical.Themassisreleasedfromrest andswingsthrough a circulararc.What is the tensionin thestringwhenthemass swings throughthebottomof the arc?(A)0(B)mg(C)2mg(D)3mg

Q.8 TwoparticlesAandBinitiallyatrest,movetowardseach other bymutual force of attraction.At the

instant when thespeed ofA is and the speed ofB is 2, the speed of the centre of mass of thesystemis(A)3 (B) (C) 1.5 (D)zero

Q.9 ParticleAmakes a elasticcollision with anotherstationary particle B. They fly apart in oppositedirectionswithequalvelocities.Theirmassratio is:

(A)

3

l(B)

2

l(C)

4

l(D)

3

l

Q.10 A picture is tobehungfromthe ceiling bymeansof twowires. Order the followingarrangementsof the wiresaccording to the tension force ofwireB, fromleast to greatest.

I

A B

II

A B

cm cm

III

A B

cm

(A) I, II, III

(B) III, I, II(C) I and II ties, then III(D) II, I, III

Q.6 m nzO;eku dk ,d d.k cy fu;rkadkrFkk fcuk f[kaphyEckbZ dh ,d gYdh fLizax ds ,d fljs ij yxk gqvkgSA fudk; dks xq:Ro eqDr vkdk'k esa fLizax ds nwljs fljsds lkis{k dks.kh; osx ls ?kqek;k tkrk gSA fLizax dhyEckbZ esa o`f) gS &

(A)m

k

2(B)

m

k m

2

2

(C)m

k m

2

2

(D) buesa ls dksbZ ugha

Q.7 ,dm nzO;eku dks L yEckbZ dh Mksjh ftlls ;g tqM+kgS] ds /oZ ls 90 dk dks.k cukus rd ckgj dh vksj[khapk tkrk gSA nzO;eku dks fojke ls eqDr fd;k tkrkgS rFkk ;g ,d o`kh; pki ij xfr djrk gSA nzO;ekuds pki ds iSans ls xqtjrs le; Mksjh esa ruko D;k gS \(A) 0(B)mg(C)2mg(D)3mg

Q.8 nks d.k A oB tks izkjEHk esa fojke ij gSa] vU;ksU;vkd"kZ.k cy }kjk ,d&nwljs dh vksj xfr djrs gSaA ml

{k.k ij tc A dh pky gS rFkk B dh pky 2 gS]fudk; ds nzO;eku dsUnz dh pky gS(A)3 (B)(C) 1.5 (D) 'kwU;

Q.9 d.kA,d vU; fLFkj d.kBls izR;kLFk VDdj djrk gSAVDdj ds i'pkr~ nksuks d.k cjkcj osxksa ls foijhr fn'kkvksa esa,d&nwljs ls nwj xfr djrs gSaA mudk nzO;eku vuqikr gS &

(A)

3

l(B)

2

l(C)

4

l(D)

3

l

Q.10 ,d rLohj dks nks rkjksa dh lgk;rk ls Nr ls yVdkukgSA rkjksa dh fuEu O;oLFkkvksa dks rkjB ds ruko cy dsvuqlkj fuEure ls vf/kdre ds e esa O;ofLFkr dhft;sA

I

A B

II

A B

cm cm

III

A B

cm

(A) I, II, III(B) III, I, II

(C) I oII leku] fQjIII(D) II, I, III


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Q.11 A uniform thin bar of mass 6m and length 2lisbent to make a regular hexagon. Its moment ofinertia aboutanaxis passingthroughthecentre ofmass andperpendicularto the planeofhexagonis

(A)5

92ml (B) 6ml2 (C) 4ml2 (D)

1

122ml

Q.12 Two blocks each of the mass m are attached totheendsofa masslessrod which pivotsasshownin figure. Initiallythe rodisheld in the horizontal

position and then released. Calculate the nettorque onthis system.

m m

l1

l2

y

x

z

(A) (m2g m1g) k

(B) (m1g m2g)k

(C) (m1g + m2g)k

(D)(m1g + m2g)k

Q.13 A uniformsoliddiscisimpartedanangularveloc-ityand placedona rough horizontal surfacesuchthat its plane isvertical.(A) It will continuetorotateat the sameplace tillits rotationceases

(B)Iftheangularvelocityis clockwiseitwill movetotheleft(C)Iftheangularvelocityisanti-clockwiseitwillmovetotheleft(D)Frictionwill act opposite to thedirection ofmotionofthe disc

Q.14 A mass on the end of a spring executes simpleharmonicmotionaboutanequilibriumpositionwithanamplitudeA.Its speed as itpasses through theequilibrium position is v. If extended to 2Aand

released, the speed of themass passing throughtheequilibriumpositionwillbe(A) v/2 (B) v (C) 4v (D) 2v

Q.15 A system isshownin the figure. The timeperiodfor small oscillationsof the two blockswillbe

(A)k

m32 (B)

k2

m32

(C)k4

m32 (D)

k8

m32

Q.11 6m nzO;eku o2lyEckbZ dh ,d le:i iryh NM+ dkseksM+dj ,d le"kV~Hkqt cuk;k tkrk gSA nzO;eku dsUnz

ls xqtjrs rFkk "kV~Hkqt ds ry ds yEcor~ v{k ds lkis{ktM+Ro vk?kw.kZ gS &

(A)5

92ml (B) 6ml2 (C) 4ml2 (D)

1

122ml

Q.12 nks CykWd ftlesa ls izR;sd dk nzO;eku m gS] fp= esan'kkZ;s vuqlkj dhyfdr ,d nzO;ekughu NM+ ds fljksaij tqM+s gSaA izkjEHk esa NM+ {kSfrt fLFkfr esa j[kh tkrh gS

rFkk fQj eqDr dh tkrh gSA bl fudk; ij dqycy&vk?kw.kZ dh x.kuk dhft;sA

m m

l1

l2

y

x

z

(A) (m2g m

1g)

k

(B) (m1g m2g)k

(C)(m1g + m2g)k

(D) (m1g + m2g)k

Q.13 ,d le:i Bksl pdrh dks dks.kh; osx iznku fd;ktkrk gS rFkk ,d [kqjnjh {kSfrt lrg ij bl izdkj

j[kk tkrk gS fd bldk ry /okZ/kj gksrk gSA(A) ;g blds ?kw.kZu :dus rd mlh LFkku ij yxkrkj?kw.kZu djrh jgsxhA

(B) ;fn dks.kh; osx nf{k.kkorZ gS] rks ;g cka;h vksjxfr djsxhA(C) ;fn dks.kh; osx okekorZ gS] rks ;g cka;h vksj xfrdjsxhA(D)?k"kZ.k pdrh dh xfr dh fn'kk ds foijhr dk;Z djsxkA

Q.14 ,d fLizax ds fljs ij ,d nzO;eku lkE; fLFkfr dslkis{k vk;ke Als ljy vkorZ xfr djrk gSA bldslkE;koLFkk ls xqtjrs le; bldh pkyv gSA ;fn bls2Ard ys tkdj NksM+k tk;s rks lkE; fLFkfr ls xqtjrs

le; nzO;eku dh pky gksxhA(A) v/2 (B) v (C) 4v (D) 2v

Q.15 ,d fudk; fp= esa nkkZ;k x;k gSA nksuksa CykWdksa ds vYinksyuksa ds fy;s vkorZdky gksxkA

(A)k

m32 (B)

k2

m32

(C)k4m32 (D)

k8m32


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Q.16 Anaddition of24kgf to the tension ofsonometerwire of fixed length increases its fundamentalfrequency3 fold.Then theoriginal tension in thestringis(A) 27 kgf (B) 18 kgf (C) 9 kgf (D) 3 kgf

Q.17 In the experiment for the determination of thespeed ofsound inair using the resonance columnmethod, thelengthoftheaircolumnthatresonatesinthefundamental mode, witha tuningforkis0.1m. When this length is changed to 0.35 m, thesame tuningforkresonateswiththefirst overtone.Theendcorrectionis:(A) 0.025 m (B) 0.012 m(C) 0.05 m (D) 0.024 m

Q.18 Wavelengths of two notes in air are 1m and

1164

1m.Eachnoteproduces1beat/swithathird

note of a fixed frequency. The speed of sound inairis(A) 330 m/s (B) 340 m/s(C) 350 m/s (D) 328 m/s

Q.19 Ifa steel bandweretofit snuglyaround theEarth'sequator at 25C, but then was heated to 45C,how high above the Earth would the band be(assumeequal everywhere)?

(Take : for steel to be 12 106/C)(A) 1.028km (B) 1.536km(C) 2.062 km (D) Noneof these

Q.20 Suppose objectC is in thermal equilibrium withobject A and with object B. The zeroth law ofthermodynamicsstates:(A) thatC will always be in thermal equilibriumwith bothAand B(B) thatC must transfer energyto bothA and B

(C) thatAis inthermal equilibrium withB(D) thatAcannot beinthermalequilibriumwith B

Q.16 fuf'pr yEckbZ ds Lojekih rkj ds ruko ij 24 kgfyxkus ij bldh ewy vkofk3 xquk gks tkrh gS] rks Mksjhesa okLrfod ruko gSA(A) 27 kgf (B) 18 kgf (C) 9 kgf (D) 3 kgf

Q.17 vuqukn LrEHk fof/k dk iz;ksx djds ok;q esa /ofu dhpky Kkr djus ds iz;ksx esa] ok;q LrEHk dh og yEckbZtks ,d Lofj= f}Hkqt ds lkFk ewy fo|k esa vuqukfnrgksrh gS] 0.1 m gSA tc bl yEckbZ dks ifjofrZr dj0.35 m dj fn;k tkrk gS] rks ogh Lofj= f}Hkqt izFkevf/kLojd ds lkFk vuqukfnr gksrk gSA vUR; la'kks/kugSA(A) 0.025 m (B) 0.012 m(C) 0.05 m (D) 0.024 m

Q.18 ok;q esa nks Lojksa dh rjaxnS/;Z 1m rFkk 1

164

1m gSA

izR;sd Loj ,d fuf'pr vko`fk ds ,d r`rh; Loj dslkFk1 [email protected] mRiUu djrk gSA ok;q esa /ofudh pky gS &(A) 330 m/s (B) 340 m/s(C) 350 m/s (D) 328 m/s

Q.19 ;fn ,d LVhy ds NYys dks 25C ij i`Foh dh Hkwe/;js[kk ds pkjksa vksj lVkdj O;ofLFkr fd;k tkrk gSysfdu fQj bls 45Crd xeZ fd;k tkrk gS] rks NYykiFoh ds fdruk ij gks tk;sxk \ (ekuk lHkh txg ijl eku gS) (fyft;s % LVhy dk = 12 106/C)(A) 1.028km (B) 1.536km(C) 2.062 km (D) buesa ls dksbZ ugha

Q.20 ekuk fd oLrq C, oLrq ArFkk oLrq B ds lkFk rkih;lkE;koLFkk esa gSA "ekxfrdh dk 'kwU; fu;e crkrk gS fd(A) C lnk oLrq AoB ds lkFk rkih; lkE;koLFkk esagksrh gSA(B) C,Ao B nksuksa dks tkZ LFkkukUrfjr djsxhA(C) A, B ds lkFk rkih; lkE;koLFkk esa gksrh gSA

(D)A,B ds lkFk rkih; lkE;koLFkk esa ugha gks ldrhA


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Q.21 For a temperature differenceT=20C,oneslabof material conducts 10 W/m2, another of sameshapeconducts20W/m2.Whatistherateofheatflow per m2 of surface area when the slabs are

placedside by side with same T=20C.

T = 20C

10 W/m2

T = 20C

20 W/m2

T = 20C

(A)10W/m2 (B) 30W/m2

(C)3

20W/m2 (D) noneof these

Q.22 The quantitykT

pV represents

(A) massof the gas(B)kinetic energyof thegas(C)numberofmolecules in the gas(D) numberofmoles of the gas

Q.23 How much heatmustbesupplied toa mixture of10gmhydrogenand40gmofHetoincreasethetemperature by50Cif theyare kept in a closedvessel

(A) 2500 cal (B) 2750 cal(C) 2000 cal (D) None

Q.24 Whichofthefollowinggraphscorrectlyshowsthechange in internal energy of an ideal gas with

pressurefor theisobaric, isochoricand isothermalprocesses.

(A) (B)

(C) (D)

Q.21 rkikUrjT = 20C ds fy, ,d inkFkZ dh ifV~Vdk10W/m2 dk pkyu djrh gSA leku vkd`fr dh nwljhifV~Vdk20W/m2 dk pkyu djrh gSA tc nksuksa IysVksadh lrgksa dks vkil esa tksM+ fn;k tk, rks leku

rkikUrj izfr m2 i`"B {ks=Qy ds fy, "ek izokg dhnj D;k gksxh \

T = 20C

10 W/m2

T = 20C

20 W/m2

T = 20C

(A) 10 W/m2 (B) 30 W/m2

(C)3

20W/m2 (D) buesa ls dksbZ ugha

Q.22 jkf'k kT

pV

n'kkZrh gS&(A) xSl ds nzO;eku dks(B) xSl dh xfrt tkZ dks(C) xSl esa v.kqvksa dh la[;k dks(D) xSl ds eksyksa dh la[;k dks

Q.23 10 gm gkbMkstu rFkk 40 gm ghfy;e ds feJ.k dksfdruh "ek nh tk, fd mldk rki 50C c


6/18


Q.25 Three objectsA,B and C all individuallyfloatontop of water.Aand B have identical massesanddensitiesbut different shapeswhileBand C haveidentical sizes andshapesbut C has lessmassanddensitythanB.Ifthreeidentical weightsare thentied to the objects and all three are pulled

completelybeneaththesurfaceofthewater,whichobject will displacethegreatest volumeofwater?(A) objectA only(B) objectC only(C) objectsAand B only(D)Allthree displaceequal volumesofwater

Q.26 Thediagramshowsapipeofuniformcrosssectioninwhich wateris flowing. The directions of flowand the volume flow rates (in cm3/s) are shownfor variousportionsof the pipe. The direction of

flow and the volume flow rate in the portionmarkedAare:

(A) and3cm3/s (B) and7cm3/s

(C) and 11 cm3/s (D) and15 cm3/s

Q.27 Youstand ona platformata train station and listentoa train hornasthe train approachesthe station ata constantvelocity.While thetrainapproaches, but

before it arrives, you hear:(A) increasing intensityand smaller than naturalfrequency(B) increasing intensity and larger than naturalfrequency

(C) decreasing intensity and smaller than naturalfrequency(D) decreasing intensity and larger than naturalfrequency

Q.25 rhu oLrq;sa A, BoClHkh vyx&vyx :i ls ty dhlrg ij rSjrh gSaA Ao B ds nzO;eku leku gSa ysfduvkd`fr fHkUu gS tcfd B o C ds vkdkj rFkk vkd`fr,dleku gSa] fdUrq C dk nzO;eku o ?kuRoBls de gSA;fn fQj rhu ,dleku Hkkjksa dks oLrqvksa ls ck/kk tkrkgS rFkk rhuksa ty lrg ds uhps iw.kZ:i ls f[kap tkrh

gSa] dkSulh oLrq ty ds vf/kdre vk;ru dks foLFkkfirdjsxh \(A) dsoy oLrq A(B) dsoy oLrq C(C) dsoy oLrq AoB(D)rhuksa ty ds cjkcj vk;ru dks foLFkkfir djsxhA

Q.26 fp= esa le:i vuqizLFk dkV dk ,d ikbi n'kkZ;k x;kgS ftlesa ikuh cg jgk gSA ikbi ds fofHkUu Hkkxksa esaizokg dh fn'kk ,oa vk;ru izokg dh nj (cm3/s esa )

n'kkZ;h x;h gSA A }kjk vafdr Hkkx esa izokg dh fn'kk,oa vk;ru izokg dh nj gksxhA

(A) rFkk3 cm3/s (B) rFkk7 cm3/s

(C) rFkk11 cm3/s (D) rFkk15 cm3/s

Q.27 vki ,d Vsu LVs'ku ds IysVQkeZ ij [kM+s gSa rFkk ,dfu;r osx ls Vsu ds LVs'ku dh vksj vkus ij Vsu dk gkuZ

lqurs gSaA tc V su vk jgh gS rks blds igqpus ls iwoZvkidks lqukbZ nsxhA(A) c


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[CHEMISTRY]

Q.28 Statement-I : Probabilitydensityof electron atnucleus in1sorbital is zero.

Statement-II : Numberofsphericalnodes for5porbital is 3.

Statement-III : There are noplanar nodes for 5s

aswell as 2zd5 orbital.

Statement-IV : De-brogliewavelengthofanelectronmovingwithspeedequalto thatofelectroninfirst orbit

ofhydrogenisgivenby 6.13

150.

Identify thecorrect set ofTrue (T)andFalse (F)statements.(A) FTTT (B)TTTT

(C) FTFF (D)None of thegiven options

Q.29 Calculate the % ionic character forABmoleculewhere theinternucleardistance betweenAandBis1.27andexperimentalvalueofdipolemomentis1.03D.(A) 83 % (B) 17 %(C) 10 % (D) 85 %

Q.30 IUPAC name ofCH2CN

COOHis

(A)2-Carboxycyclohexyl ethanenitrile(B)2-Cyanomethylcyclohexane-1-carboxylicacid(C)2-Cyanomethylcyclohexylmethanoicacid(D)Noneofthese

Q.31 How many atomic orbitals wil l haveenergy lying

between 10 s to 11 s orbital in a multi-electronatom.(A) 0 (B) 5(C) 35 (D) 32

Q.32 Which ofthe followinghas largest insize?(A)Li+ (aq) (B) Na+ (aq)(C) K+ (aq) (D) Cs+ (aq)

Q.28 dFku&I : 1s d{kd esa ukfHkd ij bysDVkWu dkkf;drk ?kuRo 'kwU; gksrk gSA

dFku&II : 5p d{kd ds fy;s xksyh; uksMksa dhla[;k 3 gksrh gSA

dFku&III : 5s rFkk 2z

d5 d{kd ds fy;s

leryh; uksM ugha gksrs gSAdFku&IV : gkbMkstu ds Fke d{k esa mifLFkr

bysDVkWu dh pky ds cjkcj pky lsxfreku bysDVkWu dh Mh&czksXyh

rjaxnS/;Z 6.13

150}kjk nh tkrh gSA

l R; (T) rFkk vl R; (F) dFkukas dk lgh leqPp;igpkfu;sA

(A) FTTT (B) TTTT(C) FTFF (D) fn;s x;s fodYiksa esa ls dksbZ ugha

Q.29 AB v.kq ds fy, %vk;fud y{k.k Kkr djks] tgk ArFkkB ds e/; vUrZukfHkdh; nwjh 1.27 rFkk f}/kzqovk?kw.kZ dk izk;ksfxd eku1.03 D gSA(A) 83 % (B) 17 %(C) 10 % (D) 85 %

Q.30

CH2CN

COOHdk IUPAC uke gS&

(A) 2-dkcksZDlhlkbDyksgsfDly ,Fksu ukbVkby(B) 2-lk;uksesfFky lkbDyksgsDlsu -1-dkcksZfDlfydvEy(C) 2-lk;uksesfFkylkbDyksgsfDly esFksuksbd vEy(D) buesa ls dksbZ ugha

Q.31 ,d cgq&bysDVkWu ijek.kq esa fdrus ijekf.o; d{kdks

dh tkZ 10 s o 11 s d{kd ds e/; dh gksxh&(A) 0 (B) 5(C) 35 (D) 32

Q.32 fuEu esa ls fdldk vkdkj lcls cM+k gksxk\(A) Li+ (aq) (B) Na+ (aq)(C) K+ (aq) (D) Cs+ (aq)


8/18


Q.33 Degreeofunsaturation forN

N

N

N

is

(A) 2 (B) 4

(C) 3 (D) 5

Q.34 For a gaseous reaction,A + 2B 3C + 4D

if atequilibrium total 100 moles are present in a10lit.rigidcontainer and whenA& Bare taken ina molar ratio of 1 : 2, the volume % of productswas 70%. Calculate the value of equilibriumconstant KC.(A) 33 43 (B) 33 44

(C) 633

1043 (D) 43

6

4310

Q.35 WhichofthefollowinggivesH2 gasonhydrolysis?(A) Ca (B) CaH2(C) Both (D) None of these

Q.36 Relation between and

is

(A) Chainisomer (B) Positional isomer(C) Conformer (D) Metamer

Q.37 10molesofethanol havingvolume50mlismixedwith1moleofwaterhavingvolume18mltoforma solution,what wouldbemolarityof thesolutionifdensityofthesolution is0.956 gm/ml.

(A) 100068

10 (B) 1000

68

1

(C) 2 (D) 20

Q.38 Boron has highest melting point among the 13th

group due to(A)highermolecularweight(B)Giantcovalent molecular structure(C)Lowest volume(D)Noneofthese

Q.33N

N

N

N

ds vlar`Irrk dh dksfV gS&

(A) 2 (B) 4

(C) 3 (D) 5

Q.34 ,d xSlh; vfHkf;kA + 2B 3C + 4D ds fy;s]

;fn lkE;koLFkk ij10 yhVj n`


9/18


Q.39 NumberofHwhichcanbereplacedbyDeuteriumby OD and D2O (excess) for followingcompound.

O

)excess(OD/OD 2

(A) 9 (B) 10(C) 11 (D) 12

Q.40 A hypothetical atom obeyingBohr's theory wasfound to havepotential energyvaryingasP.E.=

3r

K3

where"K"isapositiveconstantand"r"istheradiusof Bohr's orbit.Whichof the following relationswill becorrectforthis atom. (K.E=Kinetic energy)

(A) P.E. = 2 K.E. (B) mv2 = 4r

K9

(C) v = 2mr2

nh

(D)All of these

Q.41 The ratio ofnumber ofbondpresent in H2SO4andH2S2O7 are respectively.(A) 2 : 3 (B) 1 : 3(C) 1 : 2 (D) None of these

Q.42 Which statement is incorrect.

(A)N

H

is lessbasic thanN

H

(B)

O||

OHCCH3 is moreacidic thanHBr due

to resonancestabilised conjugate base.

(C)

O

dimerises at room temperature

because it is aromatic

(D) Resonance energy ofN

H

is less

thanS

Q.39 fuEu ;kSfxd esa ls OD rFkk D2O (vkf/kD;) dsM~;wVsfj;e }kjk foLFkkfir H dh la[;k gks ldrh gS&

O

)(OD/OD 2 vkf/kD;

(A) 9 (B) 10(C) 11 (D) 12

Q.40 cksgj fl)kUr dh ikyuk djus okys ,d ifjdfYir

ijek.kq dh fLFkfrt tkZ] P.E. = 3r

K3ds vuqlkj

ifjofrZr gksrh gqbZ ik;h xbZAtgk "K" ,d /kukRed fu;rkad rFkk"r" cksgj d{k dhf=T;k gSAbl ijek.kq ds fy;s fuEu esa ls dkSulk lEcU/k lghgksxkA (K.E= xfrt tkZ)

(A) P.E. = 2 K.E. (B) mv2 = 4r

K9

(C) v = 2mr2

nh

(D) ;s lHkh

Q.41 H2SO4 rFkkH2S2O7 esa mifLFkfr ca/kksa dh la[;kdk vuqikr ek% gSA(A) 2 : 3 (B) 1 : 3

(C) 1 : 2 (D) buesa ls dksbZ ughaQ.42 dkSulk dFku xyr gS&

(A)N

H

dh rqyuk esaN

H

de {kkjh; gS

(B) HBrdh rqyuk esa

O||

OHCCH3 esa vuquknh

LFkk;h la;qXeh {kkj ds dkj.k vf/kd vEyh; gS(C)

O

dejs ds rki ij f}ydhd`r gksrk gS D;ksafd

;g ,sjksesfVd gS

(D)N

H

dh vuquknh tkZS

ls de gS


10/18


Q.43 A 4.6 gmofanorganic compoundwas subjectedto complete combustion and only CO2 & H2Ogases were obtained. If mass of CO2 and H2Oobtained is 8.8 gmand 5.4 gmrespectively thenidentifyincorrect statement.(A)9.6gmofO2 will be required

(B) Empirical formula of thecompoundisC2H6(C)Molecular formulacannotbedeterminedfromthegivendata(D)Organiccompoundcontainscarbon,hydrogenandoxygen.

Q.44 Which ofthefollowing is tetrahedral inshape?(A) NH4

+ (B) CH4(C) PCl4

+ (D)All of these

Q.45 Stable conformation of succinic acid in basicmediumis

(A)

COOCOO

(B)

COO

COO

(C)

COO

COO

(D) Noneof these

Q.46 The covalencyofSi incarborandum (SiC) is(A) 1 (B) 2(C) 3 (D) 4

Q.47 10moles ofBrO4 is mixed with8 moles of Brin presence of sufficient HCl to liberate Br2 (g)andwater. If thereactionundergoes100% extentthen calculate moles ofBr2 formed.

(A) 9moles (B)7

16moles

(C) 40 moles (D)7

32moles

Q.43 4.6 gm dkcZfud ;kSfxd dk iw.kZ ngu fd;k x;k rFkkdsoy CO2 oH2O xSls kIr gqbZA ;fn CO2 rFkkH2O dk nzO;eku e'k% 8.8 gmrFkk5.4 gm kIr gks]

rks vlR; dFku dks igpkfu;sA(A) 9.6 gm O2 dh vko';drk gksxh(B) ;kSfxd ewykuqikrh lw= C2H6 gksrk gS

(C) fn;s x;s vkdM+ks ls vkf.od lw= Kkr ugha djldrs gS(D) dkcZfud ;kSfxd esa dkcZu] gkbMkstu rFkk vkWDlhtugksrs gS

Q.44 fuEu esa ls dkSulk prq"Qydh; vkd`fr dk gksxk\(A) NH4

+ (B) CH4(C) PCl4

+ (D) mijksDr lHkh

Q.45 {kkjh; ek/;e esa lfDlfud vEy dk LFkk;h la:i.k gS&

(A)

COO

COO

(B)

COO

COO

(C)

COO

COO

(D) buesa ls dksbZ ugha

Q.46 dkWcksZjs.Me (SiC) esa Si dh lgla;kstdrk gS\

(A) 1 (B) 2(C) 3 (D) 4

Q.47 10 eksyBrO4dks i;kZIrHCl dh mifLFkr esa 8 eksyBresa feykus ijBr2 (g)rFkk ty eqDr gksrs gSA ;fnvfHkf;k dks 100 % djk;h tk;s rks fufeZr Br2 dseksyksa dh x.kuk dhft,A

(A) 9 eksy (B)7

16eksy

(C) 40 eksy (D)7

32eksy


11/18


Q.48 Which order is incorrect for stability ofintermediates.

(A)

3

23

3

CH|

HCCCH|

CH

< 23 HCCH

(B)

(D) (Heatof hydrogenation)

(C)

COOH

CMe3

>

COOH

CMe3

(Acidicstrength)

(D)N

H

>N

(Basic strength)

Q.52 Threedifferent powersourcehavingpowersource0.64 watt, 1.28 watt and 0.32 watt are chosenforphotoelectriceffect. If thewavelengthof lightused by them is 310 nm, 155 nm and 620 nmrespectively, thencalculatetotalphotocurrent.[Given : Work function of the metal is

3.5 1019 Joule]

(A) 0.64 amp (B) 0.48 amp

(C) 1.28 amp (D) 0.32 amp

Q.53 Whichofthefollowing isplanar?(A) ClF3 (B) I3(C) BeCl2 (D)All of these

Q.54 Number of structuresof monochloro derivativeformedbyreplacement of H byCl for compound

CH3CH3

CH3H3C H

H

are

(A) 2 (B) 4(C) 6 (D) 8

Q.51 dkSulk e xyr gS&

(A) > (ngu dh m"ek)

(B) > (gkbMkstuhdj.k dh m"ek)

(C)

COOH

CMe3

>

COOH

CMe3

(vEyh; lkeF;Z)

(D)N

H

>N

({kkjh; lkeF;Z)

Q.52 0.64okV] 1.28okV rFkk0.32okV ds 'kfDr lzksr okysrhu fHkUu 'kfDr lzksrks dks dk'k fo|qr Hkko ds fy;spquk tkrk gSA ;fn buds }kjk mi;ksx dh xbZ dk'kdh rjaxnS/;Z e'k% 310nm,155nmrFkk620nm gS]

rks dqy dk'k /kkjk dh x.kuk dhft,A[fn;k x;k gS %/kkrq dk dk;ZQyu 3.5 1019 twygS ]

(A) 0.64 amp (B) 0.48amp(C) 1.28 amp (D) 0.32 amp

Q.53 fuEu esa ls dkSulk leryh; gS\(A) ClF3 (B) I3(C)BeCl2 (D) mijksDr lHkh

Q.54 ;kSfxd

CH3CH3

CH3

H3C H

H

ls Cl }kjk H ds

foLFkkiu }kjk cus eksuksDyksjks O;qRiUu ds lajpuk dhla[;k gS&(A) 2 (B) 4(C) 6 (D) 8


13/18


[MATHEMATICS]

Q.55 Let f (x) = 3 2x x2.Ifthevalueof f(x)isnonnegative then x lies in theinterval(A) [ 3, 1] (B) ( 3, 1)(C) (, 3] (D) [1, )

Q.56 Anequilateral trianglehas sides 1cmlong.An antwalksaroundthetriangle,maintaininga distanceof 1 cm from the triangle at all time. Distancetravelled bytheant inone round is

(A) 333 (B) 363

(C) 3 + 2 (D) 3 +2

3

Q.57 The points P(0, 2) ; Q( 2, 3), R(3, 5) and

S(5, 0) in order(A) formthevertices ofa parallelogram which isnot a rectangle.(B) formthe verticesofa rectangle which isnot asquare.(C) form the verticesof a square.(D)arecollinear.

Q.58 In ABCifa=8,b=9,c=10,thenthevalueof

Bsin

Ctan

is equal to[Note :All symbols used haveusual meaningintriangleABC.]

(A)9

32(B)

7

24

(C)4

21(D)

5

18

Q.59 If 3a + c = 2b then the variable line

ax+by+c=0passesthroughafixedpointwhosecoordinatesare(A) (3, 2) (B) ( 3, 2)(C) (3, 2) (D) ( 3, 2)

Q.60 The locus of the middle points of the system ofchordsof thecircle x+y =16 which are paralleltotheline 2y=4x+5 is(A) x = 2y (B) x + 2y = 0(C) y + 2x = 0 (D) y = 2x

Q.55 ekuk f (x) = 3 2x x2 gSA ;fn f (x) dk ekuv_.kkRed gS] rks x fdl vUrjky esa fLFkr gS(A) [ 3, 1] (B) ( 3, 1)(C) (, 3] (D) [1, )

Q.56 ,d leckgq f=Hkqt dh Hkqtk;sa 1 cm yEch gSA ,d phaVhf=Hkqt ls iwjs le; 1 cm dh nwjh cuk;s j[kdj f=Hkqtds pDdj yxkrh gS] rks phaVh }kjk ,d pDdj esa r; dhxbZ nwjh gS

(A) 333 (B) 363

(C) 3 + 2 (D) 3 +2

3

Q.57 fcUn q P(0, 2) ; Q( 2, 3), R(3, 5) rFkk

S(5, 0) e esa(A) ,d lekUrj prqHkqZt] tks vk;r ugha gS] ds 'kh"kZ gS(B) ,d vk;r] tks fd oxZ ugha] ds 'kh"kZ gS(C) ,d oxZ ds 'kh"kZ gS(D) lejs[kh; gS

Q.58 f=Hkqt ABC esa] ;fn a = 8, b = 9, c = 10 gS] rks

Bsin

Ctandk eku gS

[fVIi .kh: iz;qDr fd;s x;s lHkh izrhdksa dk ,d f=HkqtABC esa lkekU; vFkZ gS]

(A)9

32(B)

7

24

(C)4

21(D)

5

18

Q.59 ;fn 3a + c = 2b gS] rks pj js[kk ax + by + c = 0

,d fLFkj fcUnq ls xqtjrh gS ftlds funsZ'kkad gS(A) (3, 2) (B) ( 3, 2)(C) (3, 2) (D) ( 3, 2)

Q.60 o`k x + y = 16 dh mu thokvksa ds fudk; ds e/;fcUnqvksa dk fcUnqiFk] tks fd js[kk 2y = 4x + 5 ds

lekUrj gS] gksxk(A) x = 2y (B) x + 2y = 0(C) y + 2x = 0 (D) y = 2x


14/18


Q.61 The roots r1 and r2 of the quadratic equation5x2 px + 1 = 0 are such r1 r2 = 1 then thevalue of p is

(A) 3 (B) 33(C) 53 (D) 35

Q.62 In ABC , angleAis twice angle B, then[Note :All symbols used haveusual meaningintriangleABC.](A) a2 = b ( b + c) (B) b2 = a ( a + c)

(C) cosA =a2

b(D) cosB =

a

b2

Q.63 Let and be the roots of the equationx2 (7 i)x + (18 i) = 0 such that

Re()> Re(). The value of (2 + 3) is(A) 15 (B) 17(C) 13 (D) 19

Q.64

x2

3tan

2xcos

x2

7sinx

2

3cos

2xtan 3

when simplified reducesto

(A) sinx cosx (B) sin2

x(C) sinx cosx (D) sin2x

Q.65 If one roots of the equation ay2 + by + c = 0 is

the square of the other thenabc

accab 223 has

thevalue equal to(A) 4 (B) 3(C) 2 (D) 1

Q.66 The locus of the centers of the circles which cutthe circles x2 + y2 + 4x 6y + 9 = 0 andx2 + y2 5x+4y 2 = 0 orthogonally is(A) 9x+10y 7 = 0(B) x y + 2 = 0(C) 9x 10y + 11 = 0(D) 9x + 10y + 7 = 0

Q.67 Apalindromelyingbetween1000and10000mustbedivisible by

(A) 3 (B) 7(C) 11 (D) 13

Q.61 f}?kkr lehdj.k5x2 px + 1 = 0 ds ewy r1 rFkkr2bl izdkj gS fd r1 r2 = 1 gS] rks p dk eku gS

(A) 3 (B) 33(C) 53 (D) 35

Q.62 f=Hkqt ABC esa, dks.k A dks.k B dk nqxquk gS] rks[fVIi .kh: iz;qDr fd;s x;s lHkh izrhdksa dk ,d f=HkqtABC esa lkekU; vFkZ gS](A) a2 = b ( b + c) (B) b2 = a ( a + c)

(C) cosA =a2

b(D) cosB =

a

b2

Q.63 ekuk ,oa lehdj.kx2 (7 i)x + (18 i) = 0ds ewy bl izdkj gS fd Re() > Re() gS] rks

(2 + 3) dk eku gS(A) 15 (B) 17(C) 13 (D) 19

Q.64

x2

3tan

2xcos

x2

7sinx

2

3cos

2xtan 3

dks ljy djus ij gS(A) sinx cosx (B) sin2 x(C) sinx cosx (D) sin2x

Q.65 ;fn lehdj.k ay2 + b y + c = 0 dk ,d ewy vU; dk

oxZ gS] rksabc

accab 223 dk eku gS

(A) 4 (B) 3(C) 2 (D) 1

Q.66 o ` k k s a x2 + y2 + 4x 6 y + 9 = 0 ,o ax2 +y2 5x+4y 2 = 0 dks yEcdks.kh; dkVus okys

o`kksa ds dsUnzksa dk fcUnqiFk gS(A) 9x+10y 7 = 0(B) x y + 2 = 0(C) 9x 10y + 11 = 0(D) 9x + 10y+ 7 = 0

Q.67 1000 ,oa 10000 ds e/; fLFkr foykse in(palindrome)fuEu esa ls fdlls vo'; gh HkkT; gS

(A) 3 (B) 7(C) 11 (D) 13


15/18


Q.68 Numberofprincipal solution(s)ofthe equation,

xsin6xsin 21642

, is

(A) 1 (B) 2(C) 3 (D) 4

Q.69 The 5th, 8th and 11th term of a G.P. are p, qand s respectivelythen(A) s2 = pq (B) p2 = qs(C) q2 = ps (D) none

Q.70 The l ines L1 : x 2y + 6 = 0 andL2 : x 2y 9 = 0 are tangents to the samecircle . If the point ofcontactofL1 with thecircleis ( 2, 2), then(A) the centre of the circle is ( 7/2, 5)(B) the centreof the circle is ( 1/2, 1)

(C) area of the circle is 45/8 sq. units(D) the point ofcontactofL2 with the circle hasthe coordinates ( 5,8)

Q.71 Suppose x and y are real numbers such that 1 < x < y < 1. Let G be the sum of thegeometricserieswhosefirst term is x andwhosecommonratio is y, and let G' be the sum of thegeometric series whose first term is y andcommonratio is x. If G = G', then the value of

(x+y) is

(A) 1 (B)2

3

(C)3

2(D)

4

5

Q.72 If denotes the area of the triangle then whichone of the following resultsdoesnot holdgoodina triangle?

[Note:Allsymbolshave their usualmeaning inatriangle.]

(A) R =4

abc

(B) = rs

(C) r = 4R2

Csin

2

Bsin

2

Asin

(D)2

Atan =

)as(s

Q.68 lehdj.k xsin6xsin 21642

ds eq[; gy@gyksa dh

la[;k(A) 1 (B) 2(C) 3 (D) 4

Q.69 ,d xq.kkskj Js.kh dk 5ok, 8ok ,oa 11ok in e'k%p, q ,oa s gS] rks(A) s2 = pq (B) p2 = qs(C) q2 = ps (D) dksbZ ugha

Q.70 j s[ k k; s a L1 : x 2y + 6 = 0 ,o aL2 : x 2y 9 = 0 ,d gh o`k dh Li'kZ js[kk;sa gSA;fn o`k ds lkFk L1 dk Li'kZ fcUnq ( 2, 2) gS] rks(A) o`k dk dsUnz ( 7/2, 5) gSA(B) o`k dk dsUnz ( 1/2, 1) gSA

(C) o`k dk {ks=Qy 45/8 oxZ bdkbZ gSA(D) ok ds lkFkL2 ds Li'kZ fcUnq ds funsZ'kkad( 5, 8) gS

Q.71 ekuk x rFkk y okLrfod la[;k;sa bl dkj gSfd 1 < x < y < 1 gSA ekuk G ml xq.kkskj Js.kh dk;ksxQy gS ftldk Fke in x rFkk lkoZ vuqikr ygS vk Sj ekuk G' ml xq.kkskj Js.kh dk ;ksxQy gSftldk Fke in y rFkk lkoZ vuqikr x gSA ;fn

G = G' gks] rks (x + y) dk eku gS

(A) 1 (B)2

3

(C)3

2(D)

4

5

Q.72 ;fn f=Hkqt ds {k s=Qy dks fu:fir djrk gS] rksfuEu esa ls dkSulk ifj.kke f=Hkqt esa lR; ugha gS

[fVIi .kh: iz;qDr fd;s x;s lHkh izrhdksa dk ,d f=Hkqt esalkekU; vFkZ gS]

(A) R =4

abc

(B) = rs

(C) r = 4R2

Csin

2

Bsin

2

Asin

(D)2

Atan =

)as(s


16/18


Q.73 Number of words each of 3 vowels and2 consonants that can be formed from the letterof the word "INVOLUTE", is (k) 6!.The valueof k, is(A) 4 (B) 3(C) 2 (D) 1

Q.74 Let x and y be positivereal numbers such that

x2 + y2 = 1 and (3x 4x3) (3y 4y3) =2

1,

then the value of (x + y) is

(A)2

3(B)

2

3

(C)2

3(D)

2

3

Q.75 The term independent of z in the binomial

expansion of

11

z

1z

, is

(A) 964 (B) 962(C) 924 (D) none

Q.76 A triangle has sides of length 13, 30 and 37.The radiusofthe inscribed circle is

(A) 7 + 2 (B) 29

(C) 7 2 (D) 2

7

Q.77 If Cr denotes the combinatorial coefficients100Cr in the expansion of (1 + x)

100 then thevalueof

99

100

2

3

1

2

0

1

C

C100.......

C

C3

C

C2

C

C ,

is equal to(A) 4950 (B) 5050(C) 5051 (D) 5151

Q.78 If tan x + tan y = 25 and cot x + cot y = 30,then the value of tan(x + y) is(A) 150 (B) 200(C) 250 (D) 100

Q.73 'kCn"INVOLUTE" ds v{kjksa ls cuk;s x;s izR;sd3Lojksa ,oa 2 O;atuksa okys 'kCnksa dh la[;k (k) 6! gS]rks kdk eku gS(A) 4 (B) 3(C) 2 (D) 1

Q.74 ekuk x ,oa y /kukRed okLrfod la[;k;sa bl dkj

gS fdx2 + y2 = 1 ,oa (3x 4x3)(3y4y3) =2

1

gS] rks (x + y) dk eku gS

(A)2

3(B)

2

3

(C)2

3(D)

2

3

Q.75

11

z

1z

ds f}in izlkj esa z ls Lora= in gS

(A) 964 (B) 962(C) 924 (D) dksbZ ugha

Q.76 ,d f=Hkqt dh Hkqtkvksa dh yEckbZ 13, 30 ,oa 37 gS]rks vUroZ`k dh f=T;k gS

(A) 7 + 2 (B) 2

9

(C) 7 2 (D) 2

7

Q.77 ;fn (1 + x)100 ds izlkj esa lap;kRed xq.kk ad100Cr dks Cr ls fu:fir djrs gS] rks

99

100

2

3

1

2

0

1

C

C100.......

C

C3

C

C2

C

C dk eku

gS(A) 4950 (B) 5050(C) 5051 (D) 5151

Q.78 ;fn tan x + tan y = 25 ,oa cot x + cot y = 30 gS]rks tan(x + y) dk eku gS(A) 150 (B) 200(C) 250 (D) 100


17/18


Q.79 Coefficient of x8y6 intheexpansionof (x2 y)10,is(A) 240 (B) 110(C) 210 (D) 290

Q.80 Maximum valueoftheexpression

cos sin

6 R,is

(A)2

1(B)

4

3

(C)4

1(D) 1

Q.81 The equationofthe circlesymmetric to the circlex2 + y2 2x 4y + 4 = 0 about the line x y = 3is(A) x2 + y2 10x + 4y + 28 = 0(B) x2 + y2 + 6x + 8 = 0(C) x2 + y2 14x 2y + 49 = 0(D) x2 + y2 + 8x + 2y + 16 = 0

Q.79 (x2 y)10 ds izlkj esa x8y6 dk xq.kkad gS(A) 240 (B) 110(C) 210 (D) 290

Q.80 O;atd cos sin

6

Rdk vf/kdre

eku gS

(A)2

1(B)

4

3

(C)4

1(D)1

Q.81 js[kk x y = 3 ds lkis{k o`k

x2

+ y2

2x 4y + 4 = 0ds lefer ok dk lehdj.k gS(A) x2 + y2 10x + 4y + 28 = 0(B) x2 + y2 + 6x + 8 = 0(C) x2 + y2 14x 2y + 49 = 0(D) x2 + y2 + 8x + 2y + 16 = 0


18/18


ANSWER KEY (NUCLEUS-25-03-2012)

Q.1 B Q.2 C Q.3 B Q.4 D Q.5 B Q.6 B Q.7 DQ.8 D Q.9 A Q.10 D Q.11 A Q.12 B Q.13 C Q.14 DQ.15 C Q.16 D Q.17 A Q.18 A Q.19 B Q.20 C Q.21 CQ.22 C Q.23 B Q.24 A Q.25 D Q.26 D Q.27 B Q.28 AQ.29 B Q.30 B Q.31 C Q.32 A Q.33 C Q.34 A Q.35 C

Q.36 A Q.37 C Q.38 B Q.39 D Q.40 B Q.41 C Q.42 BQ.43 B Q.44 D Q.45 C Q.46 D Q.47 D Q.48 B Q.49 BQ.50 A Q.51 D Q.52 D Q.53 D Q.54 A Q.55 A Q.56 CQ.57 C Q.58 A Q.59 C Q.60 B Q.61 C Q.62 A Q.63 BQ.64 D Q.65 B Q.66 C Q.67 C Q.68 C Q.69 C Q.70 BQ.71 A Q.72 D Q.73 A Q.74 B Q.75 D Q.76 B Q.77 BQ.78 A Q.79 C Q.80 C Q.81 A

nucleus sample test paper 2013

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