1QUESTTUTORIALSHead Office : E-16/289, Sector-8, Rohini, New Delhi, Ph. 653954391. AquestionpaperisdividedintotwopartsAandBandeachpartcontains5questions.Thenumberofwaysinwhi chacandi dat ecananswer6quest i onssel ect i ngat l east t woquestionsfromeachpartis:(A)80 (B)100(C)200 (D)Noneofthese2. If15C3r = 15Cr + 3 , then the value of r is(A)3 (B)4(C)2 (D)13.47C4 + r =15 52 - rC3 =(A) 47C6(B) 52C5(C) 52C4(D)Noneofthese4. If 2nC3: nC2=44:3,thenforwhichofthefollowingvaluesofr,thevalueof nCrwillbe15:(A)r = 3 (B)r = 4(C)r = 6 (D)r = 55. Therearefourbal l sofdi fferentcoloursandboxesofcolourssameasthoseoftheballs.Thenumberofwaysinwhichtheballs,oneineachbox,couldbeplacedsuchthataballdoesnotgotoboxofitsowncolouris :(A)8 (B)7(C)9 (D)Noneofthese6. Thenumberofnumbersthatcanbeformedwiththehelpofthedigits1,2,3,4,3,2,1sothatodddigitsalwaysoccupyoddplaces,is:(A)24 (B)18(C)12 (D)307. Ten different letters of an alphabet aregiven.Wordswithfivelettersareformed from these given letters . Thent henumberofwordswhi chhaveatleastoneletterrepeatedis:(A)69760 (B)30240(C)99748 (D)Noneofthese8. Eightchairsarenumbered1to8.Twowomenandthreemenwishtooccupyonechaireach. Firstthewomenchooset hechai rsfromamongstthechairsmarked1to4andt henmensel ect t hechai rsfromamongsttheremaining.Thenumberofpossiblearrangementsis:(A) 6C3 4C2(B)4C2 4P3(C)4P2 4P3(D)Noneofthese9. Thenumberofwaysinwhichthelettersoftheword ARRANGEcanbearranged such that both R do not cometogetheris:(A)360 (B)900(C)1260 (D)162010. Inhowmanywaysagarlandcanbemadefromexactly10flowers?(A)10 ! (B)9 !(C)2 (9 !) (D) 92!11. Astudentisallowedtoselectatmostn booksfromacollectionof(2n+1)books.Ifthetotalnumberofwaysinwhichhecanselectonebookis63,thenthevalueof n is:(A)2 (B)3(C)4 (D)Noneofthese12. Aboxcontainstwowhiteballs,threeblack balls and four red balls . In howmanywayscanthreeballsbedrawnfromthebox,ifatleastoneblackballPermutation & Combinations2QUESTTUTORIALSHead Office : E-16/289, Sector-8, Rohini, New Delhi, Ph. 65395439istobeincludedinthedraw?(A)64 (B)45(C)46 (D)Noneofthese13. m men and n women are to be seatedinarowsothatnotwowomensittogether.Ifm>n,thenthenumberofwaysinwhichtheycanbeseatedis :(A) m mm n! ( ) !( ) !+ +11(B)m mm n! ( ) !( ) ! +11(C)( ) ! ( ) !( ) !m mm n +1 11(D)Noneofthese14. Thesides AB,BC,CAofatriangleABChaverespectively3,4and5pointslyingonthem.Thenumbersoftrianglesthatcanbeconstructedusingthesepointsasverticesis:(A)205 (B)220(C)210 (D)Noneofthese15. 20personsareinvitedforaparty.Inhow many different ways can they andthehostbeseatedatacirculartable,ifthetwoparticularpersonsaretobeseatedoneithersideofthehost.(A)20 ! (B)2.18 !(C)18 ! (D)Noneofthese16. A five digit number divisible by 3 hastobeformedusingthenumericals0,1,2,3,4and5withoutrepetition.Thetotalnumberofwaysinwhichthiscanbedoneis:(A)216 (B)240(C)600 (D)312517. Howmanywordscanbeformedwiththe letters of the word MATHEMATICSbyrearrangingthem.(A) 112 2!! !(B)112!!(C)112 2 2!! ! !(D)11 !18. Thereare5roadsleadingtoatownfromavi l l age. Thenumberofdifferentwaysinwhichavillagercangotothetownandreturnback,is:(A)25 (B)20(C)10 (D)519. Thenumberofstraightlinesjoining8pointsonacircleis:(A)8 (B)16(C)24 (D)2820. Thevalueof 15C3+ 15C13is:(A) 16C3(B) 30C16(C) 15C10(D) 15C1521. Thenumberoftrianglesthatcanbeformedbychoosingtheverticesfromasetof12points,sevenofwhichlieonthesamestraightline,is:(A)185 (B)175(C)115 (D)10522. Choosethecorrectnumberofwaysinwhich15differentbookscanbedi vi dedi nt ofi veheapsofequalnumberofbooks.(A) 155 35!! ( !)(B)1535!( !)(C) 15C5(D) 15P523. Everybodyinaroomshakeshand3QUESTTUTORIALSHead Office : E-16/289, Sector-8, Rohini, New Delhi, Ph. 65395439wi t heverybodyel se. Thet ot alnumberofhandshakesis66.Thetotalnumberofpersonsintheroomis :(A)11 (B)12(C)13 (D)1424. LetAbeasetcontaining10distinctelements.Thenthetotalnumberofdistinctfunctionsfrom Ato A,is:(A)10! (B)1010(C)210(D)210-125. Fiveballsofdifferentcoloursaretobeplacedinthreeboxesofdifferentsizes.Eachboxcanholdallfiveballs. In how many ways can we placet hebal l ssot hat noboxremai nsempty?(A)50 (B)100(C)150 (D)20026. How many numbers can be made withthe digits 3, 4, 5, 6, 7, 8 lying between3000and4000whicharedivisibleby5whilerepetitionofanydigitisnotallowedinanynumber.(A)60 (B)12(C)120 (D)2427. Six+andfour-signsaretobeplaced in a straight line so that no two-signscometogether,thenthetotalnumberofwaysare:(A)15 (B)18(C)35 (D)4228. Theproductofany r consecutivenatural numbers is always divisible by(A)r ! (B)r2(C)rn(D)Noneofthese29. Inacert ai nt est a1st udent sgavewronganswerstoatleast i questionswherei=1,2,3....k.Nostudentgavemorethankwronganswers.Thetotalnumbersofwronganswersgivenis:(A)a1 + 2 a2 + 3 a3 + ...... + k ak(B)a1+a2 + a3+......+ak(C)Zero(D)Noneofthese30. Sixshavetobeplacedinthesquare of the figure such that each rowcontainsatleastone .Inhowmanydifferentwayscanthisbedone?(A)28 (B)27(C)26 (D)Noneofthese31. The solution set of10Cx 1 > 2 . 10Cx is(A){1,2,3} (B){4,5,6}(C){8,9,10} (D){9,10,11}32. Inanelectionthereare5candidatesandthreevacancies. Avotercanvotemaximumtothreecandidates,theninhowmanywayshevote.(A)125 (B)60(C)10 (D)2533. Thereare16pointsinaplaneoutofwhich6arecollinear,thenhowmanylinescanbedrawnbyjoiningthesepoints.(A)106 (B)105(C)60 (D)5534. Outof6boysand4girls,agroupof7 is to be formed . In how many wayscan this be done if the group is to haveamajorityofboys.(A)120 (B)904QUESTTUTORIALSHead Office : E-16/289, Sector-8, Rohini, New Delhi, Ph. 65395439(C)100 (D)8035. The letters of the word MODESTY arewritterninallpossibleordersandthesewordsarewrittenoutasinadictionary,thentherankofthewordMODESTYis:(A)5040 (B)720(C)1681 (D)252036. The sum of the digits in the unit placeofallnumbersformedwiththehelpof3,4,5,6takenallatatimeis:(A)18 (B)432(C)108 (D)14437. In a football championship there wereplayed153matches. Everyteamplayedonematchwitheachother.Thenumberofteamsparticipatinginthechampoinshipis:(A)17 (B)18(C)9 (D)Noneofthese38. ThestraightlinesI1,I2,I3areparallelandlieinthesameplane.Atotalnumberof m points aretakenonI1,n pointsonI2, k pointsonI3.Themaxi mumnumberoft ri angl esformedwithverrticesatthestpointsare:(A) m+n+kC3(B) m+n+kC3- mC3- nC3- kC3(C) mC3+ nC3+ kC3(D)Noneofthese39. The number of parallelograms that canbeformedfromasetoffourparallellinesintersectinganothersetofthreeparallellinesis:(A)6 (B)18(C)12 (D)940. If nP4=30 nC5,thenn=(A)6 (B)7(C)8 (D)941. There are (n + 1) white & (n + 1) blackballseachsetnumbered1ton+1.The number of ways in which the ballscanbearrangedinarowsothattheadjacentballsareofdifferentcoloursis :(A)(2n + 2) ! (B)(2n + 2) ! 2(C)(n + 1) ! 2 (D)2 {(n + 1) !}242. 12personsaretobearrangedtoaroundtable.Iftwoparticularpersonsamong them are not to be side by side,thetotalnumberofarrangementsis:(A)9(10) ! (B)2(10 !)(C)45(8 !) (D)10 !43. If x, y and r are positive integers, thenxCr + xCr - 1 yC1 + xCr - 2 yC2 + ..... + yCr =(A) x yr! !!(B)( ) !!x yr+(C) x+yCr(D) xyCrANSWERS1.C 2. A 3.C 4.B 5.C 6.B7.A 8.D 9.B 10.D 11.B 12.A13.A 14.A 15.B 16.A 17.C 18.A19.D 20.A 21.A 22.A 23.B 24.B25.C 26.B 27.C 28.A 29.B 30.C31.D 32.D 33.A 34.C 35.C 36.C37.B 38.B 39.B 40.C 41.D 42.A43.C