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Compiled by: Rahul Arora LL T Education Services
MATHEMATICS
General Instructions:
1. All question are compulsory.
2. The question paper consists of 30 questions divided into four section A, B, C, and D.
Section-A comprises of 6 questions of 1 mark each; Section-B compris. s of 6
questions of 2 marks each; Section-C comprises of 10 question of
Section-D comprises of 8 questions of 4 marks each.
3. There is no overall choice in this question paper.
4. Use of calculators not permitted.
1.
2.
3.
4.
�
.A
5. The diagonal of cube is JI2 cm. What is length of its edge.
l,
6. A & B are the only two outcomes of an event. Probability of P(A)= 0. 72, then what will be
the probability P(B).
SECTION-B
7. Give possible expression for the length and the breadth of the rectangle, whose area is
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6x2+x-12.
8. IfAB|DE, & ,find & .
9. Inthegivenfigure, and .ShowthatAD<BC.
10. IftwoadjacentanglesofaparallelogramPQRSare(10y–9)o&(8y+45°),Findallthefour
anglesofparallelogram.
11. Thelongestsideofarightangledtriangleis125mandoneoftheremainingtwosidedis
100m.FinditsareausingHeron sformula.
12. Thenumbers2,3,4,4,3x-1,3x+1,7,7,8arewritteninascendingorder.Ifthemedianis5,
findx.
SECTION-C
13. Findthevaluesofaandb,if
14. Factorise:(2x-y-z)3+(2y-z-x)3+(2z-x-y)3
15. Findthreedifferentsolutionsof3m-8n=27.
16. PlottwopointsP(0,-4)&Q(0.4)onthegraphpaper.NowplotR&Ssuchthat &
areisoscellestriangles.
17. ABCDisarhombuswithonediagonalequalto18cm.&lengthofeachsideequalto15
cm. Findthelengthoftheotherdiagonalandareaofrhombus.
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18. Inthefigure,APandBParethebisectorsoftwoadjacentanglesAandBofquadrilateral
ABCD.Provethat .
19. Constructatrianglewhoseperimeteris15cmanditstwobaseanglesare90°and30°.
20. AConicaltentis16mhighandthediameterofitsbaseis24m.FindthecostofCanvas
requiredtomakethetent,ifcostof1m2CanvasisRs210.
21. AHemisphericaltankfullofwateristobeemptiedbyapipeattherateof3litersper
minutes.Howlongwillitstaketoemptythetank,ifthediameterofthetankis
22. Themarksof80students(outof80)inEnglishspeakingskillswasrecordedasfollows:
Marks 0-20 21-39 40-60 61-80
No.ofstudents 18 19 23 20
Ifthepassingmarksare50%thenfindtheprobabilitythatthestudentchosenatrandom:
i. Gotthepassingmark.
ii. Failedtogetthepassingmarks.
iii. Gotbelow21marks.
SECTION-D
23. Represent onthenumberline.
24. x+2isafactorofpolynomialax3+bx2+x-2andtheremainder4isobtainedby
dividingthispolynomialbyx-2.Findthevalueofaandb.
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25. Solveforx:
26. Iftwoparallellinesareintersectedbyatransversalprovethatthebisectorsofthe
interioranglesonthesamesideoftransversalintersecteachotheratrightangles.
27. InasquarePQRS,diagonalsPRandQSintersectatO.Showthat
.
28. InthegivenfigureOisthecentreofthecircleofradius5cm, ,AB||CD,AB=
6cmandCD=8cm,DeterminePQ.
29. Arighttrianglehavingsides6cm,8cmand10misrevolvedaboutthesideoflength6cm.
Findthevolumeofsolidsoformed.
30. Ifthe26EnglishalphabetsaretakensuchthatA=1,B=2,C=3,....Z=26thenfind
i. Themean&medianofthenumberscorrespondingtothevowels.
ii. Whichalphabetcorrespondstothemedian.
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ANSWERS
1. 2017.0101001.......,2017.020020002.......(otheranswersarealsopossible)
2. -1
3. y-axis
4. 47
5. 2cm
6. 0.28
7. (2x+3,(3x-4)
8.
9. NA
10. 71o,119o,71o,119o
11. 3750m2
12. 2
13.
14. 3(2x-y-z)(2y-z-x)(2z-x-y)
15. Any3correctionsolutions
16. NA
17. AC=24cm,Area=216cm2
18.
19.
20. 158400
21. 7.8hours(approx)
22. i. ii. iii.
23.
24. a=0,b=2
25. x=4
26.
27.
28. 1cm
29.
30. i. Mean=9.8,Median=9
ii. I
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