SAMPLE QUESTION PAPER 01 - JSUNIL TUTORIAL ... downloaded from myCBSEguide.com. 1 / 17 SAMPLE...
Transcript of SAMPLE QUESTION PAPER 01 - JSUNIL TUTORIAL ... downloaded from myCBSEguide.com. 1 / 17 SAMPLE...
MaterialdownloadedfrommyCBSEguide.com. 1/17
SAMPLEQUESTIONPAPER01
Class-X(2017–18)
Mathematics
Timeallowed:3HoursMax.Marks:80
GeneralInstructions:
(i)Allquestionsarecompulsory.
(ii)Thequestionpaperconsistsof30questionsdividedintofoursectionsA,B,CandD.
(iii)SectionAcontains6questionsof1markeach.SectionBcontains6questionsof2marks
each.SectionCcontains10questionsof3markseach.SectionDcontains8questionsof4
markseach.
(iv)Thereisnooverallchoice.However,aninternalchoicehasbeenprovidedinfour
questionsof3markseachandthreequestionsof4markseach.Youhavetoattemptonlyone
ofthealternativesinallsuchquestions.
(v)Useofcalculatorsisnotpermitted.
Section-A
1.Cantwonumbershave18astheirHCFand380astheirLCM?Givereason.
2.Findtherootoftheequation .
3.Determinewhether50cm,80cm,100cmcanbethesidesofarighttriangleornot.
4.Thelengthoftheshadowofamanisequaltotheheightofman.Theangleofelevationis
________.
5.Iftheperimeterandareaofacirclearenumericallyequal,thenfindtheradiusofthe
circle.
6.Ifthreecoinsaretossedsimultaneously,thenfindtheprobabilityofgettingatleasttwo
heads.
Section-B
7.Is7×6×5×4×3×2×1+5acompositenumber?Justifyyouranswer.
MaterialdownloadedfrommyCBSEguide.com. 2/17
8.The11thtermofanA.P.exceedsits4thtermby14.Findthecommondifference.
9.Findtherelationbetween‘x’and‘y’,ifthepoints ,(1,2)and(7,0)arecollinear.
10.Twotangentsmakinganangleof120°witheachotheraredrawntoacircleofradius6
cm,findthelengthofeachtangent.
11.Provethat
12.Aconeofheight20cmandradiusofbase5cmismadeupofmodellingclay.Achild
reshapesitintheformofasphere.Findthediameterofthesphere.
Section-C
13.UseEuclid’sdivisionlemmatoshowthatcubeofanypositiveintegeriseitheroftheform
9q,9q+1or9q+8forsomeinteger‘q’.
14.Obtainallotherzeroesofx4+5x3-2x2-40x-48iftwoofitszeroesare
15.Solvefor‘x’: ,x≠0.
16.Howmanytermsoftheseries54,51,48,…….betakensothattheirsumis513?Explainthe
doubleanswer.
Or
InanAPpth,qthandrthtermsarerespectivelya,bandc.Provethat
p(b-c)+q(c-a)+r(a-b)=0
17.ThepointA(3,y)isequidistantfromthepointsP(6,5)andQ(0,-3).Findthevalueofy.
Or
IfA(4,6),B(3,-2)andC(5,2)aretheverticesofΔABC,thenverifythefactthatamedianofa
triangleABCdividesitintotwotrianglesofequalareas.
18.If provethat
19.Anobserver1.5mtallis28.5mawayfromachimney.Theangleofelevationofthetopof
MaterialdownloadedfrommyCBSEguide.com. 3/17
thechimneyfromhereyesis45°.Whatistheheightofthechimney?
Or
Fromthetopofa7mhighbuilding,theangleofelevationofthetopofacabletoweris
60oandtheangleofdepressionofthefootofthetoweris30o.Findtheheightofthetower.
20.Aboyiscyclingsuchthatthewheelsofthecyclearemaking140revolutionsperminute.
Ifthediameterofthewheelis60cm,calculatethespeedinKmperhourinwhichtheboyis
cycling.
21.Thefollowingtableshowsthegaininweightby50childreninayear.Calculatemodal
gaininweight.
Gaininweight(inkg) 1-3 3-5 5-7 7-9 9-11 11-13
No.ofchildren 4 6 10 18 7 5
Or
ComputetheMedianforthegivendata
Class–interval 100-110 110-120 120-130 130-140 140-150 150-160
Frequency 6 35 48 72 100 4
22.Whatistheprobabilitythataleapyear,selectedatrandomwillcontain53Thursdays?
Section-D
23.Solvegraphicallythefollowingequations2x+3y=9;x–2y=1.Shadetheregionbounded
bythetwolinesandthexaxis.
Or
Checkgraphicallywhetherthepairofequationsx+y=8andx–2y=2isconsistent.Ifso,
solvethemgraphically.Alsofindthecoordinatesofthepointswherethetwolinesmeetthe
y-axis.
MaterialdownloadedfrommyCBSEguide.com. 4/17
24.AthiefawayfromaPoliceStationwithauniformspeed100m/minutes.Afteroneminute
aPolicemanrunsbehindthethieftocatchhim.Hegoesataspeedof100m/minuteinfirst
minuteandincreasesthespeed10m/minuteoneachsucceedingminute.Afterhowmany
minutesthePolicemancatchesthethief.
Nowanswerthesequestions:
(i)Whichmathematicalconceptisbeingusedtosolvetheaboveproblem?
(ii)Whichtraitofpersonalityofthepolicemanisshowed?
25.Intheadjoiningfigure,PQR,isarighttriangle,rightangledatQ.XandYarethepoints
onPQandQRsuchthatPX:XQ=1:2andQY:YR=2:1.Provethat9(PY2+XR2)=13PR2
Or
AquadrilateralABCDisdrawntocircumscribeacircle(fig-2).Provethat,AB+CD=AD+BC.
26.Provethatthelengthsoftwotangentsdrawnfromanexternalpointtoacircleareequal.
27.Constructanisoscelestrianglewhosebaseis7cmandaltitude5cmandthenconstruct
anothertrianglewhosesidesare timesthecorrespondingsidesoftheisoscelestriangle.
28.Supposeapersonisstandingonatowerofheight mandobservingacar
comingtowardsthetower.Heobservedthatangleofdepressionchangesfrom30°to45°,in
3seconds.Findthespeedofthecar.
29.Acontaineropensatthetopandmadeupofmetalsheetisintheformofafrustumofa
MaterialdownloadedfrommyCBSEguide.com. 5/17
coneofheight16cmwithdiametersofitslowerandupperendsas16cmand40cm
respectively.Findthecostofmetalsheetusedtomakethecontainer,ifitcostsRs.10per
100cm2.(Use =3.14)
30.Themeanofthefollowingfrequencydistributionis47.Findthevalueof‘p’.
Classes 0-20 20-40 40-60 60-80 80-100
Frequency 8 15 20 p 5
Or
Computethemodeforthefollowingfrequencydistribution.
Sizeofitems: 0-4 4-8 8-12 12-16 16-20 20-40 24-28 28-32 32-36 36-40
Frequency: 5 7 9 17 12 10 6 3 1 0
MaterialdownloadedfrommyCBSEguide.com. 6/17
CBSESAMPLEPAPER01
CLASSXMATHEMATICS
MarkingScheme
1.No.BecauseHCFisalwaysafactorofLCMbuthere18isnotafactorof380.
2.16x2-27x-10=0
(16x+5)(x-2)=0
x= ,x=2
3.
Clearly,thesumofthesquaresofthelengthsoftwosidesisnotequaltothesquareofthe
lengthofthethirdside.Hence,givensidesdonotmakearighttrianglebecauseitdoesnot
satisfythepropertyofPythagorastheorem.
4.45°
5.PerimetreoftheCircle=AreaoftheCircle
6.Numberofpossibleoutcomes=8(HHH,HHT,HTH,HTT,THH,THT,TTH,TTT)
Numberoffavorableoutcomes(2head)=4
Soprobability=
7.Yes,5040+5=5045Ithasmorethantwofactors
8.LetthefirsttermofAPisaanddiscommondifferencethenAccordingtoQuestion
a11–a4=14;
=>a+10d–(a+3d)=14
=>a+10d-a-3d=14
=>7d=14
=>d=2
9. [ ]
MaterialdownloadedfrommyCBSEguide.com. 7/17
x=7–3y
10.
PT=PS(lengthoftangents)
60°
ΔOTPtan60°=
PT= cm
11.LHS=
=RHS
12.Volumeofcone=Volumeofsphere
r=5cm
MaterialdownloadedfrommyCBSEguide.com. 8/17
13.a=bq+r;b=3;r=0,1,2
a3=(3m)3
=9(3m3)
=9q
a3=(3m+1)3
=27m3+27m2+9m+1
=9q+1
a3=(3m+2)3
=27m3+54m2+18m+8
=9q+8
14.Twozeroesare
Therefore
15.
MaterialdownloadedfrommyCBSEguide.com. 9/17
=>2x2+2ax+bx+ab=0
=>2x(x+a)+b(x+a)=0
=>(x+a)(2x+b)=0
=>x=-a,
16.a=54,d=-3,sn=513
Sn=
513=
=>
n=18,19
Sincedisnegative.wegetdoubleanswerbecausesumof18termsand19termsiszero,as
fewtermsarepositiveandfewarenegative.
Or
A+(p-1)D=a..(i)
A+(q-1)D=b….(ii)
A+(r-1)D=c…….(iii)
(ii)-(iii)
b-c=(q-1)D–(r-1)D
Similarly,
MaterialdownloadedfrommyCBSEguide.com. 10/17
Adding(iv),(v)and(vi)
17.PA=QA17.ThepointA(3,y)isequidistantfromthepointsP(6,5)andQ(0,-3).Findthevalueofy.
18.
19.
MaterialdownloadedfrommyCBSEguide.com. 11/17
GiventheheightoftheobserverbeDE=1.5m
ThatisAB=1.5m
LetBC=hisheightofthechimney
HenceAC=(h–1.5)m
Givendistancebetweentheobserverandthechimneyis
AD=BE=28.5m
InrighttriangleDCA,θ=45°
tan45°=
∴h=28.5+1.5=30mThustheheightofthechimneyis30m.
20.Circumferenceofwheel=πd=60πcm
Distancecoveredin1revolution= km
Distancecoveredin140revolution= km
(Distancecoveredin1min)
Distancecoveredin1hr=
Speedofcycle=15.84km/hr
21.Modalclass=7-9
Mode-
MaterialdownloadedfrommyCBSEguide.com. 12/17
=
22.Thereare366daysinaleapyearthatcontain52weeksand2moredays.So,52
Thursdaysand2days.
These2dayscanbe:
(Mon,Tue},{Tue,Wed},{Wed,Thu},{Thu,Fri},{Fri,Sat},{Sat,Sun}and{Sun,Mon}(7cases).
Inordertohave53Thursdaysweshouldhaveeither{Thu,Fri}or{Wed,Thu}case.
No.ofsamplespaces=7.
No.ofeventthatgives53ThursdaysinaleapYear=2.
RequiredProbability=
23.
TableforEqn.1anditsline
TableforEqn.2anditsline
Solutionx=3andy=1
Shadedareaisrequiredsolution.
Or
x 0 4 8
MaterialdownloadedfrommyCBSEguide.com. 13/17
y=8–x 8 4 0
Threesolutionsforequation(i)aregiveninthetable:
Threesolutionsforequation(ii)aregiveninthetable:
x 0 2 8
–1 0 3
DrawingLineAC
DrawingLinePR
PlottingpointsA(0,8),B(4,4)andC(8,0)ongraphpaperthestraightlineACisobtainedas
graphoftheequation
(i)PlottingpointsP(0,–1),Q(2,0)andR(8,3)ongraphpaperthestraightlinePRisobtained
asgraphoftheequation
(ii).Fromthegraph,itisclearthatapointM(6,2)commontoboththelinesACandPR.
Sothepairofequationsisconsistentandthesolutionsoftheequationsarex=6andy=2.
FromthegraphitisseenthatthecoordinatesofthepointswherethelinesACandPRmeets
they-axisare(0,8)and(0,–1)respectively.
24.TimetakenbyThiefbeforebeingcaught=n+1
MaterialdownloadedfrommyCBSEguide.com. 14/17
DistancetravelledbyThief=100(n+1)
100(n+1)=
n=5minutes
i)ArithmeticProgression
ii)Responsibilityoftheirwork(duty)andhonesty
25.
Or
Since,thelengthsoftangentsdrawnfromanexternalpointtoacircleareequal.
AP=AS…(i)BP=BQ…(ii)
MaterialdownloadedfrommyCBSEguide.com. 15/17
CQ=CR…(iii)DR=DS…(iv)
Now,AB+CD
=AP+PB+CR+RD
=AS+BQ+CQ+DS
=(AS+DS)+(BQ+CQ)
=AD+BC
Henceproved.
26.Construction:DrawacirclewithcentreO.FromapointPoutsidethecircle,drawtwo
tangentsPandR.
ToProve:PQ=PR
Proof:InΔPOQandΔPOR
OQ=OR(radii)
PO=PO(commonside)
∠PQO=∠PRO(Rightangle)
ΔPOQ ΔPOR(ByRHSCongruencyrule)
Henceproved
MaterialdownloadedfrommyCBSEguide.com. 16/17
27.
28.
ΔPQBtan45°= ,x=15( ------------(1)
ΔPQAtan30°= x+y=15 ( ---------(2)
From(1)and(2)y=30m
SincethecarmovingfromAtoBin3seconds
Speed= =10m/sec
29.R=20cm,r=8cm,h=16cm
l= =20cm
MaterialdownloadedfrommyCBSEguide.com. 17/17
Totalsurfacearea=CSAoffrustum+areaofbase
=πl(R+r)+
=1959.36
Rateofmetalsheetused=Rs.10per100cm2
Costofmetalsheetused=1959.36× =Rs.195.94(Approximately)
30.
CI fi xi fixi
0-20 8 10 80
20-40 15 30 450
40-60 20 50 1000
60-80 p 70 70p
80-100 5 90 450
48+p 1980+70p