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drbJerd dpdr,lduo dDe{- d.rDa$r 2OIsPREPARATORY EXAffi]IAIIOII MARCH I 2OI5

Euood / Date :

o$Qrofi d.neoded doa3,Register Number of the Cand,idate

d0q oodrldr/Maximum Marks : 80

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Dear Students,

The present Question Paper cum Answer Booklet has been designed on the basisof 2015 S'S'L'G Public Examination. Read the instructions carefully before answering.Handover the Question cum Answer Booklet to the Room Supervisor before leaving theexaminat ion hal l .

Extra Fifteen minutes have been given for Question paper Reading.Instruction for the I Main

For each of the following question / statement four answers are given. choose the mostappropriate answer and write it along with its atphabet in the "p"I"

provided below eachq uest ion. ,

choose the correct answer from column 'B' and fi l l in the blanks under column ,c,

.rdob :

Subject :

idrab/Time

rlsddMATHEMATrcS

d"od8 dreOra.oddd d&/ bnroodSignature of the Room Supervisor,s/Date

,S* elodrldr

Total MarksdDed.rdd d&

Examiner's Signature

$crorFrd9,

KSSSHMS & CPUCPA . MATHS - MAR .2015 lOTH STD. Page : 01

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DSTATE LEVE,L PREPARATORY EXAMINATION-MARCH 2OI5

MATHEMATICS / ?f tdd Marks /qeodds: : 80

tr. Choose the correct answer and write.

iooind wd-ddd1 e*o:, ;bq udoroo.

l. The third term of a G.P. is 2 then the product of first 5 terms is,

e.ocb rbdoed.,d drepo$ drnd$e dd 2eictdrl a& ddrl$ rbeoe.:a},

B) 2s

1x8=8

A) 52 c) 10 D) 15

Ans./erud d

rof *.h isequalto,a--D- D--A-

a2 62 ,rri.:T +- 'o,o,e,IV *no-i* i*Gd)d),a--D- D--A-

A) a-b B) a+b C) a2-b2 D) 1

Ans./erud d

3. The distance between the origin and the point -6, 8 is,

(-6, 8) ooar ubq droE zrodrad d&d e&d drad, :

A) 14 B) +2 C) -7 D) 10

Ans./et)d d.,4

4. (1-Sin2o) (Sec2o) is equal to,

(1-Sin20) (Sec2e)'aa** idroadrub,

A)o B)-1 c) r D)2

Ans./etDd d

Space for Rough work

KSSSnMS & CPUCPA Mathematics '2015 . . . . . 1

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5. The slope of the line joining the points (3, -2) and (4, 5) is(3, -2) d:dr (1, s) ?iocbrrs{ ieoxbd deajo$ ae.ro&A)7 B)e c)8 D) t0

Ans./*n_O

6. f(x) = x2+5 then f (-4) = ,

f(x) = x2+S ercarl f (-4) - ,

A) 2r B) 26 c) 20 D) -2A

Ans./eru{d

v. The number of terms in the series 7+r3+r9*.........97 is,7 + 13 +19 *... .... ..97 d, e $ d> e_ d) O_ d d d d$J i oa3o o3l,

A) 15 B) L6 c) 17 D) e7

Ans./wd.,d

8' n(A) - 20, n(B) = 30 and n(AUB) = 40 then n(AflB) is equal ton(A) - 20, n(B) = 30 abdl n(AUB) = 40 qrurodn(AnB)zt i;bin6bub.A) s0 B) 70 c) lo D) 40

D

Ans./erud d_,3

Space for Roagh work

KSSSHMS & CPUCPA Mathematics -2015.....2

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Dr,II. Answer the following / ddnd {rd4ilgfi etr)d-oA' 1x6=6

'9. A dte iS iolled. Find the Probability of getting the number 5'

uodr oaC{ w$gaafi 5 noa{o3rQ ddo3Dd no{dileo$€o3:Q dod)bao9oo'

L0. (7x1,1xL3+13) is a composite number. Justify the statement.

(1x11x13+13) e,odr ioo3pd no4 dr deedo$q id:Qr:r'

LL. Subtract 2 \F+ 3 \f from 5\E-- WZlE+3wo3)q5\F_vTdoodd€0300.

1.2. Find the GM between 4 and 36

4d)$360d&sdrbdoed-dd 'c ,dd ldod lbBogco .-s

)

2

)

rssffipn Mathematics -2015 . . . . .3

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13. In a circle, a chord ofCalculate the radius ofdeg_de* l6cm. €,gJc t.oc$gxri$: dd*a,rod iJaG.

16cm. is at a distance ofthe circle..ro, Ed. .qcb deo{rood 15cm.

l5cm. from,,the centDre.

qroddde d. aariaddoa

S^J I (,ei -,

)a

14. Find the slope of the line whose inclination is 600600 Ld 'adrc aod: dea3o$ evcodnb dod: bBobo.

2

III. Answer the fotlowing / dsnd €.,d"(ileil wd.,ot.

15. Rationalise the denominator and simplify.$e didl qrddrde do,x *d>- iod, ecb:r.

srt-3\E-

V3G

2:

KSSSHMS & CPUCPA Mathematics -2015 . . . . .4

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: r .

16. Prove that lEis an irrational number.'

\E e'osb elqnrlotg no4 aoe^:rdnb 50Qtu.

17. Draw Venn diagram.doc dd udogDo.

€al

D2

2

i) (AUB) ii) (AuB)l i i i) AluB iv) AflBl

KSSSHMS & CPUCPA . . . . .5Mathematics - 2015

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18. Find the sum of all the first n odd natural numbers. ,," d.'ude oq n z3i Eiodqrosd noa3rrrg d^d-dq dodrbGobo. .

rn H.P. T - I ^*r ,'- ot'?*T

.,n .r-s=12 andTl=ft f ind Tzsd-s. d dreeojro- Ts =

# *r, Tr, = #

qrdd Tzs{ dod>Eo*o.Do.

19 ' A coin is tossed repeatedly twice. Find the probability of each event givenbelow. i) The faces shown up^u.* Identicarii) Thil appears at most once.

:tT T31Q dde, d{, oddr t,too ?3dueDnd. 4.eo3Jaocb gBSo$ no{dseo$do$d)dod:baobo. i) e_oub udoSr ipelrtgAa.o d>eej ucbgub.

'- ---'-i

ii) dq (rail) d{odd a.ocj: ner dn{, ucb{ub.

D)

! " -

KSSSHMS & CPUCPA Mathematics - 2015 .....6

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tan A- tan B20.lf[ = 600 and $ = 30o then prove that tan (A-B) =

l,+tan A.tan Btan A- tan B aod> ;iaQr.

d = 600 d:ar^ $ = 30o egcsDrl tan (A-B) =L+tan A.tan B

Or/egCEro

A tree is broken over by the wind fbrms a right aryJed triangle with the

ground. If the broken part makes.;;tle of?O" with the ground and the

top of the tre* i, now 26mts. from its bas6, how tall was the tree ?

zrdlrroerl 'rE* r,oub abdc d)rod), se;d, sanE od r-od: e)oufoed $ti:csddl et0ot& dsad'

aarto *:ro* de.:d* sDRo"d i;#.;tr dO" doef;d1 T1* dDtrd *{ *d.d &aosD *dd

r,^ld.od 20 are. u3.,oddo_ qond. oanadd *)ocb ce$r* dDq *dd ad-E ar'g e{ aoulddl

e3d*esod dtoa.

2

TSSSNMS & CPUCPAMathematics - 2015 . . . . .7

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D)21. Prove that n+lP.*t = (n+1) np.

n+lP.*t - (n+1) np, aodr ;l-oer.

22. Solve by using formula. .,n/odrddl erudo3,oen,x s3a$ .

x"-2x-2=A)-

KSSSHMS & CPUCPA Mathematics - 2015 . . . . .8

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23. ABCD is a TFapezium 48 ll CD. AB = zcD andArea of A AoB = 84cmz. find the area of a coD.ABCD e",odr o,&Eo AB ll CD

AB = 2CDurrdl AbB grqbcid ctu eror 84cm2

eidd COD grqbcsd A:r e rorddl do&bBo3DO.

24.lnA WAL, I WAL = 90o I ANL = 90oand WL = 26cm., LN =6cm.r and AN = 8'Calculate the length of WA.

wAI-, 9z;berde- I WAL = 90o I ANL = 90o E

WL 26cms., LN =6cms., *q

AN = 8cm., uoorl WA dod:b6o9oo. fr

)a

KSSSHMS & CPUCPA Mathematics - 2015 . . . . .9

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D225.ln Alt ABC, AD t- BC . Prove that AB2-BD2=AC2-CD}

ABC erqb6dq, AD I BC erdorl AB2-BD2=AC2-CDZ aodr xDQtu.

KSSSHMS & CPUCPA Mathematics '2015)' lI

II

. . . . .1 0

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Dof26. What is traversable

graph.erod;ndd dE, ooddeib ?

graph ? and write two conditions for traversibility

dt tJ" c.r.. datE ddun du3 ea dd e,drd od dr Ouo d d ii#rb ud or: O.)

27 . Draw the plan of a field using the follorving measurements(Scale 20 mts. = lcm.)doe"fd:i duad 4t{ta ro$e3rlpod r&oe$S drado$q udogoo. ({ralnm:

Meters to DDrl tue.

TuE80

150

100 ->

<- 80

30 --+

70 toC

40toB

FromAA ol:od

of a field book

20 Aoe. = l io.soe.)

)

KSSSHMS & CPUCPA Mathematics - 2015I

. . . . .1 1

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28. In a circle of radius 4cm. drarv a chordtangents at the ends of the chord.4cm. Srrr{)-9o qqdq 7cm, r,"qd *r*di aq3cbJ a 9 qu u5ij"

of length Tcm.,

qrdd qeod. r,Socbd$e

Construct tD

wo

;gd , i r r rnv t re , ) J d c . J 4

)

29. Prove that the points A (10 -3), B(-30 0) and C(4,1) are the vertices of a rightangled Isosceles triangle.A (1' -3)' B(-3, 0) d*q C@rl) Docbrlg: z"ocb nabeenad: Eoud.oe d Qrq$rd drortdvanCcoub Taee. v

2

KSSSHMS & CPUCPA Mathematics - 2015 . . . . "12

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30. Draw the graph of y = + x2 and find the value of VTO

y = +x2 sloc{ o€dr, f[00 deSo$q dodrbao3oo.

D)

KSSSHMS & CPI,ICPA Mathematics - 2015 . . . . .1 3

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fV. Answer the following I d$nd {.,dqrted wd_ot.31. T\'vo Circular Cylinders of equal volumes have their heights in the ratio

Find the ratio of their radii.add: -dt #1 q?99" {r*--od ,toodcrrl$ od_dd l:2d erd:Foddo_{d, erdzis grrdsqr$Fadddi dod:6oGo3:O.

Or/erCilaA rocket is in the shape of a cylinder with a cone attached to one end and ahemisphere attached to the other end. All of them are of the same radius ofl.Smeter. The_total length of the rocket is 7 meter and height of the cone is2meter. Calculate the volume of the rocket.*?o{ooaduso3re o:C oado,serl a.od: ?Ja dod:an'Ddog d:d: d:d.o_od: uDoS:O_ufrrtnevauaddd> Osoriold.

?d& e{9d$ gr, 1.5 aoi. qrnd. Ja*urd

"t^li erueb ZCIt

;b* dodrcd aU-J 2aoe. qrdd cndr.srd +3*E;e dcd:badoo.3

I

KSSSHMS & CPUCPA Mathematics -2015 . . . . .14

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D32. F'ind the 31st term of an Arithmetic Progression whose llth term is 38 and

the 16th terrn is 73.z,oc3.r idnodd drepofr l1de dd 38 *d> 16de dd 73 et6"rl 31de dddq dod>btro9oo.

Or/qrdEiEThe 6 'h and 13th term of a Geometr ic Progress ion are 24 and *respectively. Find the sequence.r,odl rbrSoed-d dreQoSre)- 6*e ;fra 13de ddds: drdoaan ,16 eind sarrodd qt dre po$d1dod:EoGo3r0.

KSSSHMS & CPUGPA Mathematics - 2015 . . . . .1 5

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33.Prove : r r l -S in0 . . r - - ,a t - - -A - J - - ^ali-= Sec 0- tan 0 aod:;laQtu.Y 1+Sin0

Or/erCilD

prove . Sin 50-1 ,- -cosec 40o r ..nc {oo cr

f*-4=-0-"+-S*. 50" -4Cos 50" Cosec 40o =- 2 oodrraQtu'

D

KSSSHMS & CPUCPA Mathematics -2015 . . . . .1 6

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D34. The pupils of tenth standard ofa school hid arranged for a picnic at a total

gopt 9f Rs.300, which had to be shared equany u"y tnem. stnce s of themfailed to join the party, each of the others-had-to

-pay Rs.2 more. Find the

strength of the class.?-cdr sero$ dg de ddd.}o$ aF*FFrrcr r"r.o, 300do. d?.i do_ ?"od) Eardd io?sdd6badFaad6. e, 6d.d, glos.6ri.i; *ar-n d..tJii;r; ft;.1;; ;;ffi;h?*?d?od suedd*

:: 2*. aa1 eoa*eooucr.

-6amadel cCrredrot s6geld+

loeSrojlib tocb8eaogoo.

Or/e6orf a cyclist_had gone 3kms. per hour faster, he would have taken lhour and20 minuts less to ride 80kma. What time did he take ?

:p^t*T ,1Td*- porid 3r.arc. darr* dertdo_ dJDended, g0e.aoe. iso dDder l+od

2U neDd de* di{d)doC:re d dr. aor6aO elAJr q,oSni*, ddd:food 'oodd} , ,

KSSSHMS & CPUCPA Mathematics - 2015 ...* lz '

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35. A committee of 5 is to be formed out of 6 men and 4 ladies. Inways can this be done when'at least 2ladies are included.

6 gd:ddr -bq 4 dlb€o$ood 5 rdd neD.so$q dcis3e6"nd. dOd E?rcbad> ieDed$$ dt"3iuodo* ?

Dhow many

*bSo$odrd

3

KSSSHMS & CPUCPA Mathematics -2015 . . . . .1 g

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t

D36. On dividing_the Polynomial p(x) = x3-3x3+x+2 by a polynomial g(r), theQuotient and remainder were (x-Z) and (_2x+4) respectively. Find g(r).u&ddoil

f(x) ,=. x)-Sx3+x+2v$- g(r)sod e,nni,rddood r,Jd:d {'Drre4u d$u> seidl{,;bann (i-2) ;b$ (-?-x+4)qjdd, Sfilq dodrEsaos'o.

Or/qrC;roIf both (x-2) and (.-+ ) are factors ii 62.+5r+b) show that a=t).(x-2) dr{ @-+) eOir+, @xz+Sx+b)o$ eriddrdrtqianen- il a=b .rcdr EDee.

3

KSSSHMS & CPUCPA Mathematics - 2O1S . . . . .1 I

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37 . Calculate the mean and Standard deviation of the distribution.* an.m oddpd icnio abdr drodd adEdrl$$ dod:b80300.

CI 5- 15 15-25 25-35 35-45 45-55 - ) - f

55-05

f 8 t2 20 10 7 3 4

KSSSHMS & CPUCPA Mathematics -2015 .....20

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38. I f two tr iangles are equiangular, then, their corresponding sides aProportional Prove.od& 9qbcsrlg: i;b *oeOeo3lrlqrunqd, eldrls ernbdrdd t,oo&figt iiinnbanddE-&d d aoul>EDQI.

(v' -e

4

::.::.:.21

Dre

KSSSHMS & CPUCPA Mathematics - 2O1S

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Dof39. If two circles touch each; other. externally, the centres and the point

contact are collinear. Prove.addl drd_rlSr r,:odrarofl {Ararorl, ddg., deo{.,rld:, abdr igt Eoub addeavorlSaan&d-d

aoc$ ToQtu. 4

KSSSHMS & CPUCPA Mathematics - 2015 .....22

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40.D

2cm.Construct two direct cornmon tangents toWhose centres are 10cm. apart. Measure

two circles of radii Scm. andthe length of the tangent.

deo{.,,d$ erodd 10io.aoe. .acbd Sio.coe. d:d: 2io.coe. Srcirrlg:$, dod.,rled. add:radndo n drddsdl dc:,. i drdd *qdq ,iorro.

ded

4

KSSSHMS & CPUCPA Mathematics - 2015 ...,.23

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