Post on 30-Mar-2020
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SAMPLEQUESTIONPAPER(ByCBSE)
Class-X(2017–18)Mathematics
GeneralInstructions:
1. Allquestionsarecompulsory.
2. Thequestionpaperconsistsof30questionsdividedintofoursectionsA,B,CandD.
3. SectionAcontains6questionsof1markeach.SectionBcontains6questionsof2marks
each.SectionCcontains10questionsof3markseach.SectionDcontains8questionsof4
markseach.
4. Thereisnooverallchoice.However,aninternalchoicehasbeenprovidedinfour
questionsof3markseachandthreequestionsof4markseach.Youhavetoattemptonly
oneofthealternativesinallsuchquestions.
5. Useofcalculatorsisnotpermitted.
SectionA
Questionnumbers1to6carry1markeach
1.Writewhethertherationalnumber willhaveaterminatingdecimalexpansionor
anor-terminatingrepeatingdecimalexpansion.
Ans.Nonterminatingrepeatingdecimalexpansion.
2.Findthevalue(s)ofk,ifthequadraticequation hasequalroots.
Ans.
3.FindtheeleventhtermfromthelasttermoftheAP:
27,23,19,...,–65.
Ans.
4.Findthecoordinatesofthepointony-axiswhichisnearesttothepoint(–2,5).
Ans.
5.Ingivenfigure, and Findtheratiooftheareaof
totheareaof
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Ans.
6.If findthevalueof
Ans.25
SectionB
Questionnumbers7to12carry2markseach.
7.Iftwopositiveintegerspandqarewrittenas areprime
numbers,thenverify:
Ans.
8.ThesumoffirstntermsofanAPisgivenby Findthesixteenthterm
oftheAP.
Ans.Sn=2n2+3n
S1=5=a1
S2=a1+a2=14 a2=9
d=a2–a1=4
a16=a1+15d=5+15(4)=65
9. Find the value(s) of k for which the pair of linear equations
haveinfinitelymanysolutions.
Ans.Forpairofequationskx+1y=k2and1x+ky=1
Wehave:
Forinfinitelymanysolutions,
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From(i)and(ii),k=1
10.If isthemid-pointofthelinesegmentjoiningthepoints(2,0)and
thenshowthattheline passesthroughthepoint
Ans.Since isthemid-pointofthelinesegmentjoiningthepoints
therefore,
Theline passesthroughthepoint
11.Aboxcontainscardsnumbered11to123.Acardisdrawnatrandomfromthebox.
Findtheprobabilitythatthenumberonthedrawncardis
(i)asquarenumber
(ii)amultipleof7
Ans.(i)P(squarenumber)
(ii)P(multipleof7)
12.Aboxcontains12ballsofwhichsomeareredincolour.If6moreredballsareput
intheboxandaballisdrawnatrandom,theprobabilityofdrawingaredballdoubles
thanwhatitwasbefore.Findthenumberofredballsinthebag.
Ans.Letnumberofredballsbe=x
If6moreredballsareadded:
Thenumberofredballs=x+6
Since,
Thereare3redballsinthebag.
SectionC
Questionnumbers13to22carry3markseach.
13.Showthatexactlyoneofthenumbers isdivisibleby3.
Ans.Letn=3k,3k+1or3k+2.
(i)Whenn=3k:
nisdivisibleby3.
n+2=3k+2 n+2isnotdivisibleby3.
n+4=3k+4=3(k+1)+1 n+4isnotdivisibleby3.
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(ii)Whenn=3k+1:
nisnotdivisibleby3.
n+2=(3k+1)+2=3k+3=3(k+1) n+2isdivisibleby3.
n+4=(3k+1)+4=3k+5=3(k+1)+2 n+4isnotdivisibleby3.
(iii)Whenn=3k+2:
nisnotdivisibleby3.
n+2=(3k+2)+2=3k+4=3(k+1)+1 n+2isnotdivisibleby3.
n+4=(3k+2)+4=3k+6=3(k+2) n+4isdivisibleby3.
Henceexactlyoneofthenumbersn,n+2orn+4isdivisibleby3.
14.Findallthezeroesofthepolynomial iftwoofitszeroes
are
Ans.Since arethetwozeroestherefore,
isafactorofgivenpolynomial.
Wedividethegivenpolynomialby
Forotherzeroes,
Zeroesofthegivenpolynomialare
15.Seventimesatwodigitnumberisequaltofourtimesthenumberobtainedby
reversingtheorderofitsdigits.Ifthedifferenceofthedigitsis3,determinethe
number.
Ans.Lettheten’sandtheunitsdigitbeyandxrespectively.
So,thenumberis10y+x.
Thenumberwhendigitsarereversedis10x+y.
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Now,7(10y+x)=4(10x+y) 2y=x…(i)
Alsox–y=3…(ii)
Solving(1)and(2),wegety=3andx=6.
Hencethenumberis36
16.Inwhatratiodoesthex-axisdividethelinesegmentjoiningthepoints
Findtheco-ordinatesofthepointofdivision.
OR
Thepoints formaparallelogram.Findthe
lengthofthealtitudeoftheparallelogramonthebaseAB.
Ans.Letx-axisdividesthelinesegmentjoining atthepointPinthe
ratio1:k.
Now,coordinatesofpointofdivision
SincePliesonx-axis,therefore
Hencetheratiois
Now,thecoordinatesofPare
OR
LettheheightofparallelogramtakingABasbasebeh.
NowAB
17.Ingivenfigure thenprovethat
OR
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InanequilateraltriangleABC,DisapointonthesideBCsuchthat Prove
that
Ans.
Since,
Also
And
OR
Construction:Draw
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18.Ingivenfigure aretwoparalleltangentstoacirclewithcentreO
andanothertangentABwithpointofcontactCintersecting atAand atB.
Provethat
Ans.JoinOC
In
OP=OC(radiiofsamecircle)
PA=CA(lengthoftwotangents)
AO=AO(Common)
(BySSScongruencycriterion)
Hence,
Similarly
Now,
19.Evaluate:
OR
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If thenevaluate:
Ans.
OR
20.IngivenfigureABPCisaquadrantofacircleofradius14cmandasemicircleis
drawnwithBCasdiameter.Findtheareaoftheshadedregion.
Ans.Weknow,AC=r
Requiredarea= +ar(semicircleonBCasdiameter)–ar(quadrantABPC
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21.Waterinacanal,6mwideand1.5mdeep,isflowingwithaspeedof10km/h.How
muchareawillitirrigatein30minutes,if8cmofstandingwaterisneeded?
OR
Aconeofmaximumsizeiscarvedoutfromacubeofedge14cm.Findthesurfacearea
oftheremainingsolidaftertheconeiscarvedout.
Ans.Lettheareathatcanbeirrigatedin30minutebeA
Waterflowingincanalin30minutes
Volumeofwaterflowingoutin30minutes
Volumeofwaterrequiredtoirrigatethefield
Equating(i)and(ii),weget
Or
Surfaceareaofremainingsolid whererandlaretheradiusandslant
heightofthecone.
22.Findthemodeofthefollowingdistributionofmarksobtainedbythestudentsinan
examination:
Marksobtained 0-20 20-40 40-60 60-80 80-100
Numberofstudents 15 18 21 29 17
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Giventhemeanoftheabovedistributionis53,usingempiricalrelationshipestimate
thevalueofitsmedian.
Ans.
So,themodemarksis68.
Empiricalrelationshipbetweenthethreemeasuresofcentraltendenciesis:
SectionD
Questionnumbers23to30carry4markseach.
23.Atraintravellingatauniformspeedfor360kmwouldhavetaken48minuteslessto
travelthesamedistanceifitsspeedwere5km/hourmore.Findtheoriginalspeedof
thetrain.
OR
Checkwhethertheequation hasrealrootsandifithas,findthemby
themethodofcompletingthesquare.Alsoverifythatrootsobtainedsatisfythegiven
equation.
Ans.Letoriginalspeedofthetrainbexkm/h.
Timetakenatoriginalspeed
Timetakenatincreasedspeed
Now,
OR
Discriminant
So,thegivenequationhastwodistinctrealroots
Multiplyingbothsidesby5.
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Verification:
Similarly,
24.AnAPconsistsof37terms.Thesumofthethreemiddlemosttermsis225andthe
sumofthelastthreetermsis429.FindtheAP.
Ans.LetthethreemiddlemosttermsoftheAPbea–d,a,a+d.
Wehave,(a–d)+a+(a+d)=225
Now,theAPis
a–18d,…,a–2d,a–d,a,a+d,a+2d,…,a+18d
Sumoflastthreeterms:
Now,firstterm
TheAPis3,7,11,…,147.
25.Showthatinarighttriangle,thesquareofthehypotenuseisequaltothesumofthe
squaresoftheothertwosides.
OR
Provethattheratiooftheareasoftwosimilartrianglesisequaltotheratioofthe
squaresoftheircorrespondingsides.
Ans.Given:ArighttriangleABCrightangledatB.
Toprove:
Construction:Draw
Proof:In
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Now, (correspondingsidesareproportional)
Similarly
Adding(1)and(2)
OR
Given:
Toprove:
Construction:Draw
In
Therefore,
But
Hence,
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26.DrawatriangleABCwithside Then,construct
atrianglewhosesidesare timesthecorrespondingsidesof
Ans.Draw inwhich andhence
Constructionofsimilartriangle asshownbelow:
27.Provethat
Ans.
28.Theanglesofdepressionofthetopandbottomofabuilding50metreshighas
observedfromthetopofatowerare respectively.Findtheheightofthe
towerandalsothehorizontaldistancebetweenthebuildingandthetower.
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Ans.
Now,
Now,
Heightoftower=TR=75m
Distancebetweenbuildingandtower
29.TwodairyownersAandBsellflavouredmilkfilledtocapacityinmugsofnegligible
thickness,whicharecylindricalinshapewitharaisedhemisphericalbottom.Themugs
are14cmhighandhavediameterof7cmasshowningivenfigure.BothAandBsell
flavouredmilkattherateof perlitre.ThedairyownerAusestheformula
tofindthevolumeofmilkinthemugandcharges forit.ThedairyownerB
isoftheviewthatthepriceofactualquantityofmilkshouldbecharged.What
accordingtohimshouldbethepriceofonemugofmilk?Whichvalueisexhibitedby
thedairyownerB?
Ans.Capacityofmug(actualquantityofmilk)
AmountdairyownerBshouldchargeforonemugofmilk
ValueexhibitedbydairyownerB:honesty(oranysimilarvalue)
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30.Thefollowingdistributionshowsthedailypocketallowanceofchildrenofalocality.
Themeanpocketallowanceis Findthemissingfrequencyk.
Dailypocketallowance(inRs.) 11-13 13-15 15-17 17-19 19-21 21-23 23-25
Numberofchildren 3 6 9 13 k 5 4
OR
Thefollowingfrequencydistributionshowsthedistance(inmetres)thrownby68
studentsinaJavelinthrowcompetition.
Distance(inm) 0-10 10-20 20-30 30-40 40-50 50-60 60-70
Numberofstudents 4 5 13 20 14 8 4
DrawalessthantypeOgiveforthegivendataandfindthemediandistancethrown
usingthiscurve.
Ans.
Dailypocketallowance
(inRs.)
Numberofchildren Mid-point
11-13 3 12 -3 -9
13–15 6 14 -2 -12
15-17 9 16 -1 -9
17–19 13 18 0 0
19–21 K 20 1 k
21–23 5 22 2 10
23-25 4 24 3 12
OR
Lessthan NumberofStudents
10 4
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20 9
30 22
40 42
50 56
60 64
70 68
MediandistanceisvalueofxthatcorrespondstoCumulativefrequency
Therefore,Mediandistance=36m