Vmc Booster Test 2
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Transcript of Vmc Booster Test 2
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Question1.TheeneynethatproducesachiralcompoundupontreatmentwithH2inthepresenceofLindlar'scatalystis:
[A]
[B]
[C]
[D]
YourAnswer: CorrectAnswer: B
Explanation:
Thisisacaseofchiralityintermsofdifferentsubstituentsonthebasisofgeometricalconfigurations(willbecoveredinmoredetailinadvancedstereochemistrysessions).
Question2.
At ,thesolubilityproduct(Ksp)ofCaF2inwateris .Thesolubility(inmolperkgofwater)ofthesaltatthesame
temperatureis:
[A]
[B]
[C]
[D]
YourAnswer: CorrectAnswer: D
Explanation:Solutionofsparinglysolublesaltisdilutesolution.Fordilutesolution
Question3.
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Asolutionof0.1MNa2CO3istitratedagainstHClusing(1)phenolphthaleinasanindicatorand(2)methylorangeasanindicator.The
valueof isequalto:[(WherepH(1)ispHatendpointwithphenolphthaleinandpH(2)ispHatendpointwithmethyl
orange)(gasesareevolvedoffifany)][Given ]
[A] 7
[B]
[C]
[D]
YourAnswer: CorrectAnswer: C
Explanation:
Question4.Whatquantityisrepresentedbytheslopeofthelineinthegraphofthetemperaturedependenceofthenaturallogofanequilibriumconstant?
[A][B][C][D]
YourAnswer: CorrectAnswer: D
Explanation:
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Question5.
Theplotof versus (whereXAandYAarethemolefractionsofAinliquidandvapourphases,respectively)islinearwith
slopeandinterceptrespectivelyaregivenas:
[A]
[B]
[C]
[D] Noneofthese
YourAnswer: CorrectAnswer: B
Explanation:
Question6.19gofmoltenSnCl2iselectrolyzedforsometime,usinginertelectrodes.0.119gofSnisdepositedatthecathode.Ifnosubstanceislostduringtheelectrolysisthenfindwhichofthefollowingstatement(s)is(are)correct?[AtomicmassofSn=119,Cl=35.5]
[A] EquivalentofSnCl2decomposedareequalto0.002[B] Equivalentofchlorineproducedareequalto0.002[C] EquivalentofSnCl4formedareequalto0.002[D] MassofSnCl2remainedafterelectrolysisis18.62g
YourAnswer: CorrectAnswer: A,B,C,D
Explanation:
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Question7.Acellutilizesthefollowingcellreaction:
WhichofthefollowingwillchangetheEMFofthecell?[A] WhenCo(II)nitrateisdissolvedinthecathodecompartment[B] WhenCo(III)nitrateisdissolvedinthecathodecompartment[C] WhenareaofZn(s)electrodeisdoubled[D] Whenadditionalwaterisaddedtotheanodecompartment
YourAnswer: CorrectAnswer: A,B,D
Explanation:
If[Co2+]isincreased,Ecellwilldecrease
If[Co3+]isincreased,Ecellwillincrease
IfareaofZn(s)isdoubled,Ecellwillnotchange
Ifadditionalwaterisaddedinanodiccompartment,[Zn2+]willdecreaseandhenceEcellwilldecrease.
Question8.ConsiderthefollowingBronstedacidbasereactionofsomeorganiccompoundsR1andR2.
Identifycorrectstatement(s):
[A] R2,P1andP2arearomaticcompounds[B] HybridizationstateofNatominbothP1andP2issame[C] R1isantiaromatic
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[D] BothR2andP1containsacloseloopofdelocalizable
YourAnswer: CorrectAnswer: A,B,D
Explanation:R1isnotantiaromaticitisnonaromatic.
Question9.Usethestandardreductionpotentialstodeterminewhatisobservedatthecathodeduringtheelectrolysisofa1.0MsolutionofKBrthatcontainsphenolphthaleinusinginertelectrodes.Whatobservationsis(are)made?
[A] Solidmetalforms[B] Bubblesformandapinkcolourappears[C] DarkredBr2(aq)forms[D] Bubblesformandthesolutionremainscolourless
YourAnswer: CorrectAnswer: B
Explanation:Reductionofwatertakesplaceatthecathode.
Bubblesformduetoevolutionof andapinkcolourappearsduetoformationof .
(Phenolphthaleinshowspinkcolourationinalkalinemedium).
Question10.Whichofthefollowingplot(s)iscorrectforfirstorderreaction?(r=rateattime't'andr0istheinitialrate,k=rateconstant,t=temperature).
[A]
[B]
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[C]
[D]
YourAnswer: CorrectAnswer: A,B,C,D
Explanation:
Question11.Mercuriciodideisaddedtoanaqueoussolutionofpotassiumiodide.Identifythecorrectstatement(s).[A] Acomplexspeciesisformed[B] Numberofsoluteparticlesincrease[C] Freezingpointisraised[D] Boilingpointislowered
YourAnswer: CorrectAnswer: A,C,D
Explanation:
Whencomplexionsareformedtheirsolutionsshowabnormallylowcolligativeeffectsthanexpectedbecausetheycontainfewerparticlesofsolutethanwouldotherwisebepresent.Whenalittle isaddedtopotassiumiodidesolutionthenumberofsoluteparticlesdecreases,andthereislowvalueofcolligativepropertiesi.e.freezingpointisraisedandboilingpointislowered.
Question12.Considerthefollowingsequenceofreactionsandidentifycorrectstatement(s)
[A] In ,NOgroupshowsI,+RandRelectroniceffects
[B] In , groupshowsIandRelectroniceffects
[C] In , groupshowsIand+Relectroniceffects
[D] In , groupshowsIandRelectroniceffects
YourAnswer: CorrectAnswer: B,C
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Explanation:NOisadeactivatinggroup.
Question13.Inthethreestependothermicreaction
thanwhichofthefollowingstatementsarecorrect?[A] StepIisfavouredbyhightemperatureandlowpressure[B] StepIIisfavouredbylowtemperatureandhighpressure[C] StepIIisfavouredbyhighpressureandhightemperature[D] StepIIIisfavouredbyhighpressureandhightemperature
YourAnswer: CorrectAnswer: A,C,D
Explanation:NA
Question14.Equalvolumesoffollowingsolutionsaremixed,inwhichcasethepHofresultingsolutionwillbeaveragevalueofpHoftwosolutions?
[A] pH=3(HNO3)andpH=5(HNO3)[B] pH=2(HNO3)andpH=12(KOH)[C] pH=4.5(CH3COOH)andpH=9.5(NH3)(aq)[Ka(CH3COOH)=Kb(NH4OH)][D] pH=3(HCN)andpH=11(NaOH)[KaofHCN=1010]
YourAnswer: CorrectAnswer: B,C
Explanation:
Question15.Whichofthefollowingstatementsis(are)correctabouthalflifeperiod?[A] Itisproportionaltoinitialconcentrationforzerothorder[B] Averagelife=1.44halflifeforfirstorderreaction[C] Timeof75%reactionisthriceofhalflifeperiodinsecondorderreaction
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[D] 99.9%reactiontakesplacein100minutesforthecasewhenrateconstantis0.0693min1
YourAnswer: CorrectAnswer: A,B,C,D
Explanation:
Question16.At298K,theEMFofthecell:
is0.7530V.Thestandardpotentialofthecalomelelectrodeis0.2802V.ThepHofthesolutionis_____________.
YourAnswer: CorrectAnswer: 8
Explanation:
Question17.Howmany bondelectronpairsarelocalizedintheplanarcyclicorganiccompound(P).
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YourAnswer: CorrectAnswer: 2
Explanation:
2pairofelectrons(1eachforthespcarbonbonds)willremainlocalized.
Question18.Amixture(X)ofisomericorganiccompoundhavingmolecularformulaC4H8,onreactionwithBr2dissolvedinCCl4producesamixturecontainingfiveisomericproductshavingmolecularformulaC4H8Br2.Thenumberofisomericorganiccompoundsinthemixture(X)is____________.
YourAnswer: CorrectAnswer: 3
Explanation:
Question19.Howmanystereocentresdoesthefollowingmoleculecontain?
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YourAnswer: CorrectAnswer: 9
Explanation:
Question20.Howmanymillimolesofgaseoussubstanceswouldbeformedduringelectrolysisofaqueous usinginertelectrodebypassingacurrentof10milliampwithcurrentefficiency50%for965min?(Assumenoreactionbetweenproductofelectrolysis,ifany).
YourAnswer: CorrectAnswer: 6
Explanation:
Question21.AtimevaryingforceF=2tisappliedonspoolasshowninfigureanditrollswithoutslidingasfrictionissufficient.Theangularmomentumofspoolattimetaboutbottomofspoolis:
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[A]
[B]
[C]
[D] Insufficientdata
YourAnswer: CorrectAnswer: C
Explanation:
Question22.Thecurrentthrough resistanceiszero.
ThevalueofEis:
[A] 24V[B] 36V[C] 42V[D] 45V
YourAnswer: CorrectAnswer: C
Explanation:
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and areinparallel,socurrentin isalsozero,theycanberemoved.Andthecurrentsareasshown:
Question23.Att=0,astone(ofmassm)isreleasedfromthetopofabuildingofheighth.Attimet,kineticenergyoftheparticleis3timesthepotentialenergyoftheparticlew.r.t.theground.Averagepowerdeliveredtotheparticlebetweent=0andt=tequals:
[A]
[B]
[C]
[D]
YourAnswer: CorrectAnswer: A
Explanation:
Attimet,ithasfallthrough3/4thheightoftotalheighth
Averagepowerdelivered=
Averagepower=
Question24.Aringofradius hascharge uniformlydistributedonitscircumference.Theaxisoftheringpasses
throughthecentreofasolidsphereofradius whichhascharge uniformlydistributedwithinitsvolume.Thedistance
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betweenthetwocentreoftheringandthesphereis .ThereisaverythintunnelMNalongtheaxisoftheringthroughthecentreofthesolidsphere.
Whatisthevalueof sothatthereisanullpointatM.
[A]
[B]
[C]
[D]
YourAnswer: CorrectAnswer: B
Explanation:
Question25.Aringofradius hascharge uniformlydistributedonitscircumference.Theaxisoftheringpasses
throughthecentreofasolidsphereofradius whichhascharge uniformlydistributedwithinitsvolume.Thedistance
betweenthetwocentreoftheringandthesphereis .ThereisaverythintunnelMNalongtheaxisoftheringthroughthecentreofthesolidsphere.
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Withwhatminimumvelocity shouldaparticleofmass20gmandcharge shouldbeprojectedfromthecentreoftheringalongitsaxissothatitmaybeabletoenterthetunnel.[A] 6m/s[B] 60m/s[C] 300m/s[D] 500m/s
YourAnswer: CorrectAnswer: B
Explanation:
Question26.TwochargesQ1andQ2placedat(0,0,0)and(a,0,0)aresuchthatxcomponentoffieldiszeroat(a/2,a,0).ycomponentoffieldwillbezeroat:
[A]
[B]
[C]
[D]
YourAnswer: CorrectAnswer: A,B,C
Explanation:
Thexcomponentcannotbezeroiftheboththechangesareofoppositesign.]
Fromthefigure,itfollows asxcomponentofE1andE2equal.
atallpointsinthexzplane,theycomponentoffieldwillbezero
Question27.AnunchargedcapacitorhavingcapacitanceCisconnectedacrossabatteryofemfV.Nowthecapacitorisdisconnectedandthenreconnectedacrossthesamebatterybutwithreversedpolarity.Then:
[A] afterreconnection,thermalenergyproducedinthecircuitwillbeequalto2CV2
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[B] afterreconnection,thermalenergyproducedinthecircuitwillbeequaltotwothirdofthetotalenergysuppliedbythebattery[C] afterreconnection,noenergyissuppliedbythebattery[D] afterreconnection,energyproducedbythebatteryisconvertedintoheat
YourAnswer: CorrectAnswer: A,B,D
Explanation:
Question28.Whentheterminalsofacellofemf1.5Vareconnectedtoanammeterofresistance ,theammeterreads0.30amp.Whichofthefollowingstatementsarecorrect?[A] Thecellisnonideal[B] Ifa resistorisalsoconnectedacrossterminalsofthecell,theammeterwillread0.50amp
[C] Ifa resistorisalsoconnectedacrosstheterminalofthecell,onethirdoftheelectricalpowergeneratedwilldissipateasheatwithinthecell
[D] Ifavoltmeterofresistance isusedtomeasurepotentialdifferencebetweenterminalsofthecell,itwillread1.2V
YourAnswer: CorrectAnswer: A,C,D
Explanation:
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Question29.
Theelectricpotentialinaregionalongthexaxisvarieswithxaccordingtotherelation .Then:
[A] potentialdifferencebetweenthepointsx=1andx=2is15V[B] forceexperiencedbyaonecoulombchargeat willbe10N[C] theforceexperiencedbytheabovechargewillbetowards+xaxis[D] auniformelectricfieldexistsinthisregionalongthe+xaxis
YourAnswer: CorrectAnswer: A,B,C
Explanation:
Question30.EandVonetheelectricfieldandelectricpotentialatOifthelinearchargedensityofthesystemis :
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[A]
[B]
[C]
[D]
YourAnswer: CorrectAnswer: A,C
Explanation:
Question31.Fiveidenticalconductingplatesarefixedparalleltoandequidistantfromother.Givend=distancebetweenanytwosuccessiveplatesandA=areaofeitherfaceofeachplate.
[A] Totalchargeonplate3is4timesthetotalchargeonplate1[B] Totalchargeonplate2isnegative
[C] Chargeontheuppersurfaceofplate5is
[D] Chargeonthelowersurfaceofplate1iszero
YourAnswer: CorrectAnswer: A,B,D
Explanation:
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Chargedrawnfromthebattery=
Totalchargeonplate1=Chargeath
Totalchargeonplate2=Chargesatfandg(sum)
Totalchargeonplate3=chargesatdande= =4
timesthetotalchargeonplate1
Question32.Threeidenticalspheresareinastraightlineonatableandonemovestowardstheothertwowhichareatrestandnotincontact,if
,then:
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[A] therearetwoimpactsbetweenthem[B] therearethreeimpactsbetweenthem[C] theratiooftheirfinalvelocitiesis13:15:63[D] theratiooftheirfinalvelocitiesis13:15:36
YourAnswer: CorrectAnswer: B,D
Explanation:
AandBwillcollideagain
ThirdcollisionbetweenAandB: and
BandCwillnotcollideagain
Ratiooffinalvelocities= =13:15:36
Question33.Asphereofmass2.8kgisrollingwithoutslippingonaninclinedplaneofangle fromhorizontal.Choosethecorrectstatement(s).
[A] theminimumcoefficientoffrictionrequiredis
[B] thetranslationalkineticenergyisalwaysgreaterthanrotationalkineticenergy[C] thefrictionforceonthesphereis4.8N
[D] theaccelerationofthesphereis
YourAnswer: CorrectAnswer: B,C,D
Explanation:
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Question34.Intheadjacentfigure,auniformrodoflength andmassmiskeptatrestinhorizontalpositiononanelevatededge.Thevalueofx(considerthefigure)issuchthattherodwillhavemaximumangularacceleration ,assoonasitissetfree.
[A] xisequalto
[B] isequalto
[C] isequalto
[D] xisequalto
YourAnswer: CorrectAnswer: A,C
Explanation:
Question35.Acapacitorof ischargedtoapotentialof100V.Now,thischargedcapacitorisconnectedtobatteryof100Vwithpositiveterminalofbatteryconnectedtonegativeplateofthecapacitor.
Forthegivensituation,markthecorrectstatement(s).
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[A] Thechargeflownthrough100Vbatteryis
[B] Thechargeflownthrough100Vbatteryis[C] Heatdissipatedinthecircuitis0.1J[D] Workdoneonthebatteryis0.1J
YourAnswer: CorrectAnswer: B,C
Explanation:
Changesuppliedbybattery= Heat=
Question36.Theresistivityofrodoflengthlandofuniformcrosssectionvarieslinearlyfrom fromoneendAtotheotherendB.A
potentialdifferenceofVvoltsismaintainedacrosstherod.Theelectricfieldatadistance fromendAis .Findn.
YourAnswer: CorrectAnswer: 6
Explanation:
Question37.Asmallsphereofmassm=0.5kgcarryingapositivecharge isconnectedwithalight,flexibleandinextensiblestringof
lengthr=60cmandwhiledinaverticalcircle.Ifaverticallyupwardelectricfieldofstrength existsinthespace,
calculateminimumvelocityofsphererequiredathighestpointsothatitmayjustcompletethecircle.
YourAnswer: CorrectAnswer: 6
Explanation:
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Question38.ABisahorizontaldiameterofaballmassm=0.4kgandradiusR=0.10m.Attimet=0,asharpimpulseisappliedatBatangleof
withthehorizontal,asshowninfig.,sothatballimmediatelystartstomovewithvelocity .Findthevelocityofthe
ballwhenslidingceasesandpurerollingbegins.
YourAnswer: CorrectAnswer: 0
Explanation:
At horizontalandverticalcomponentofimpulseareequal(=Ilet)
Byhorizontalcomponentofimpulse,I=mV0
Angularimpulsebyverticalcomponent=
......(i)
Let bevelocityofcentreandangularvelocityrespectivelywhenpurerollingbeginsaftertimet
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ballwillstoppermanently
Question39.Adisc'A'ofmassMisplacedatrestonthesmoothinclinesurfaceofinclination .AballBofmassmissuspendedverticallyfromthecentreofthediscAbyalightinextensiblestringoflength asshowninthefigure.IftheaccelerationofthediscBimmediately
afterthesystemisreleasedfromrestis Thevalueofkis:
YourAnswer: CorrectAnswer: 1
Explanation:
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Question40.
Inthecircuitshowninfigure,findthevalueof inVolt.
YourAnswer: CorrectAnswer: 8
Explanation:
Question41.
If (Cbeingtheconstantofintegration).Then:
[A]
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[B] iscontinuousforall
[C]
[D]
YourAnswer: CorrectAnswer: C
Explanation:
Question42.
If ,thenthevalueof isequalto:
[A] 0[B][C] 2207[D] 1
YourAnswer: CorrectAnswer: D
Explanation:
Question43.
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Solutionoftheequation isequalto:
[A] 2[B] 3[C] 4[D] 5
YourAnswer: CorrectAnswer: A
Explanation:
Question44.
Thevaluesofaandbforwhichthefunction iscontinuousfor ,are:
[A]
[B]
[C]
[D]
YourAnswer: CorrectAnswer: B
Explanation:
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Question45.
If and bothare
differentiableatx=0,theng(x)isnondifferentiableatxisequalto:[A][B]
[C]
[D] 4
YourAnswer: CorrectAnswer: B
Explanation:
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Question46.Consideravariableline'L'whichpassesthroughthepointofintersection'p'ofthelines andmeetingthecoordinateaxesatpointsAandB:
[A] thenthelocusofmiddlepointofthesegmentABhastheequation
[B]thenthelocusofthefeetoftheperpendicularfromtheoriginonthevariableline'L'hastheequation
[C] LocusofthecentroidofthevariabletriangleOABhastheequation(where'O'istheorigin)[D] LocusofthecentroidofthevariabletriangleOABhastheequation(where'O'istheorigin)
YourAnswer: CorrectAnswer: A,B,C
Explanation:
Question47.
Letx,yberealvariablesatisfythe Leta=max andb=min
,then:
[A][B]
[C][D]
YourAnswer: CorrectAnswer: A,C,D
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Explanation:
Question48.LetA,B,C,D,lieonalinesuchthatAB=BC=CD=1.ThepointsAandCarealsojoinedbyasemicirclewithACasdiameterandPisavariablepointonthissemicirclesuchthat .LetRistheregionboundedbyareAP,thestraightlinePDandlineAD
[A] ThemaximumpossibleareaofregionRis
[B] If'L'istheperimeterofregion'R',thenLisequalto
[C] ThemaximumpossibleareaofregionRis
[D] If'L'istheperimeterofregion'R',thenLisequalto
YourAnswer: CorrectAnswer: A,B
Explanation:
Question49.
If then:
[A] numberofsolutionsis7[B] numberofsolutionsis6[C] numberofintegralsolutionsis5[D] numberofintegralsolutionsis6
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YourAnswer: CorrectAnswer: A,C
Explanation:
Question50.Iff(x)andh(x)areoddfunctionandg(x)isevenfunction,thenwhichofthefollowingisoddfunction:
[A]
[B]
[C]
[D]
YourAnswer: CorrectAnswer: B,C,D
Explanation:
Question51.
Iff: satisfiescondition ,then:
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[A] f(x)isontofunction[B] f(x)isoneonefunction[C] f(x)isanoddfunction[D] and areidentical
YourAnswer: CorrectAnswer: A,B,C,D
Explanation:
Question52.
Letf: andlet ,then:
[A] f(x)isoneonefunction[B] f(x)isoddfunction[C] g(x)iscontinuousis
[D] f(x)iscontinuousforall
YourAnswer: CorrectAnswer: B,C,D
Explanation:
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Question53.
If ,thenwhichofthefollowingis(are)false?
[A]
[B] inthedomainoff(x)
[C] f(x)isidenticalto
[D] Numberofrootsofequation islessthan2
YourAnswer: CorrectAnswer: A,D
Explanation:
Notethatx=0isnotindomainof
CaseI:Ifx>0,let
Nowlet
CaseII:x
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as &usingCaseI
So,
doesnotexist
Alsonotethat
isnotindomainof
identicalto
Question54.
Thefunctionf(x)= dtissuchthat:
[A] itisdefinedontheinterval[1,1][B] itisanincreasingfunction[C] itisanoddfunction[D] thepoint(0,0)isthepointofinflection
YourAnswer: CorrectAnswer: A,B,C,D
Explanation:
Now
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Again whichvanishedatx=0andchangessign isinflectionsincefiswelldefinedin
Question55.Forthefunctionf(x)=ln(1lnx)whichofthefollowingdonotholdgood?[A] Increasingin(0,1)anddecreasingin(1,e)[B] Decreasingin(0,1)andincreasingin(1,e)[C] x=1isthecriticalnumberforf(x)[D] fhastwoasymptotes
YourAnswer: CorrectAnswer: A,B,C
Explanation:
f(x)=ln(1lnx)
Domain(0,e)
f"(1)=0whichisapointofinflectiongraphisasshownyaxisandx=earetwoasymptotes
Question56.
Let ,thenkisequalto_________.
YourAnswer: CorrectAnswer: 8
Explanation:
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Put inaboveintegraltoget:
Question57.
Let .Ifx1andx2aretworootsoftheequation in
,(where[.]denotesgreatestintegerfunction,{.}denotesfractionalpartofx).Let representsnumberofpointsof
discontinuityoff(x), representsnumberofpointsofnondifferentiability. and then
is_________.
YourAnswer: CorrectAnswer: 6
Explanation:
(Wehavemade )
Question58.
If andif ,thennis________.
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YourAnswer: CorrectAnswer: 8
Explanation:
Question59.
If ,then3kisequalto____________.
YourAnswer: CorrectAnswer: 4
Explanation:NA
Question60.
Let thenfindthenumberofpositiveintegralvaluesofxwhichsatisfies
YourAnswer: CorrectAnswer: 2
Explanation: