COPYRIG1IT RI,SERVED

_:N+ =r.L qEiq{ rffgfufir

aTq*6 d lrf Eme,a

lIuU Sigraturc ol Hcad Examiftrl

iilllruilfl

lFrlI stanatu r€- of Eemtne 4

-5...r.H::l 1:i E :. - l:.

2c\1

@.-1t+F.;*.-l4 ) lr

2015 (Al

2015

qr(iicelc

MATHEMATICS

19th FEBRUARY, 2015

FIRST SITTING

roio ] c'

Cl d 3o o 2q-\

(\ i) ,6 0 al 2

5ir4 8

a224

iq, c)e, I 5

0) o 3o o >o ItC) t\>cr L b ,((\ )_ t 6

C] 1 & ,((\ ']' b h0 v I

1nl

1

qqr.l qfiea6 6r qul rFrsra

ntT.n

1

ut

ryqfreflfut

cE-dwt \r4 effr4$q-fi f{+Vr

+ fflqr qire't ,Id., ,i EF -a re t'g+ fq'Tl 6. se Fq E lBi i{€tda q 3rqi rsn cr

,im- i- re ,nar c.ar, +a io ,Ro \o I - .rE aiB- Td{! lryr ra T, qEr

* eiaor ge rr fu r

z. rim rel t rdw rr qii fiE€ BFfl.rt + q,ftftfi Fti Ssi sFrqra Fi Errrr 3rrltifto a:msfr * qqq qrqr qrA.n, rq aerq qirn i trqfoa 6{ Jiq cE n r

s ffi ct qkfufi t E { F6 srr fft6r qSs rqq t alE{ d cn is+q tr aC cftqcrfii * EK +.rqr qnT +'rs{{fi \.j effi tr

+. rqo crr 6r .tr{ ,rc * +i rr< i; laq scdEE i.fi sl.r it d t r

qinqrql rFr cF{ 116 rin !k_Fr $ en+<o ge w <rt qarq qqr fifiq *m qt .:iH,rit q +ff q'T{ TfinTtF&xq1n'niE siha qrqr dr+q aq qfrsfl rqrEi 61d'3 +fi qcfr t 3rR F,fi rr-{ s6 rar gRmr( q67 {A 6retd t, { rd ffi *t ctrlr'ff +l qifl cq{ t' Er6r qri +1 qqfd rff + c]q

sF ri" {F6r}i E ?itrd au ffie *a. q }ra gli ?qsr/ 6r IE i+ }

qfi?r+i * frq

*er6i + frqEtxr qqi- a ,q+ .to-ft"' q car o. {- fu +: }, ri {Frr-r n +

r. r*+qr<{gt * {rqi d ,cri r{{s{em !fu6r +gq r,aqi f<q qrl t !16 !i!rqi6qi:E6r* ert{ Elt f clqis +1<oi or 3i6 sib-d 6{rr t E{Erlr + fu( .:r,r e{4 {irqrr.i rz oi* irai i, a] lll r * r+rqi i6Ti *Eri;iz si6 cq qEra * qri t r siF fud,!q il lZ 3r.R ffi e{{ I a 3iF cln di t, ii Fdrt t q eis srt< Eed it o :i* 3ifu-a

iFr, sgtlO4l ES r.d6R na{ ffi e{{ i IIq sin erq Etn t, * isTi G ftT,i +it *]9lr C ll.'q Fi itq :ifun 6i, c,n tOlO

z. c6 er{ * filq fur l."ii *r crRi6 +c$T id xY{ * taq :rFitri FFr n aifuF 6t3. + !r{ ii {fi H,ri E}, w w< ier * vrl n< p + +it qd firs (x) 6r ki

qrn

c hF wq' * sm 'rfi fri 'd t, 3q+ 3-fl + fuq itrdFrd L6 elr{ si *rs ( x) ai{ { r

s. sm + {qi6{ t c{srd r€6 9€ s{ clqis rtr{ 6} qi nr.F offi ii .rfua #t r

Eacl

lbral ,vo. o/ SrestonsyEt al Eid ri@r ,

,l ,l "

3

srcrq Frtgr :

GErIERAL II{STRUCTIO{S :

A[ ouestions are comDulsoni" r"* ;,or- i- EG e,s,c n o q i+qz- 7 En= A,.- nrs+ r :ia qr e-c a i.iE r{{ rA6 2.sai 6r !!o< c q (s v{c rAfi: :jsii 6r nq E c o i qiq cai cAfi e 3i$i 4T tThls question pape..onsisls of30 quesrions divided inlo lour Sections. a' B' C

and D. section A.ontains l0 quesrions of 1 mak each, s.ctio! B.ontarns5 qlestions of 2 mdks each, Scc.on C conbi.s lO questions ol3 ndks each

d Scction D contains 5 queslions of 6 mdks each{ajf + Bfrt q fr4fi 3tEi <

On.\ slre !l--s rc 'o

oe F."'gr+ 6 rfi{ laa 6 !T!r ir( ,rI E", ; x'dr+ ! A zAnsse.s of lhe questions musi be in lhe .ontext ol the irstu.tlons gNeniherein*.F r.r =r" rvc-n6,sfl gF-+l + 3id i jiq.r{ Ffr ci ff a1Bq, srq* oi +aDo all rough {ork only on the last pages olthe Quesnon cum_Answ€r Booklei

El!-g - a( nrr {lqr 1i ronFr+6 l3iq'6rt )

SECTION -A{Question Nos l to r0.drv I mdk ea.h)

qdrg,l fu * qft.iq {@r + s{ni{q cqn Fid i qr 3rsia qr{ff tthe rationar numbe. S v r have

non-teminating repeating de.jmat

a te@inating decinal

IErl

9 +1 ""fi-3f{ ?b .i- fl

50

ilillll|llllilil

"r;o il --aT'tt a

t[llruilt

2 f{ rq rrt s=p(x)t{${p(,)+rf4+l+1d@rftfissL

lorynonial p ( x ), fmm ih€ given

t1lllililil[IP, T, O,

Eq

o.

EiR

flililtll

CoJ 4 qa

stt\l9n-4j)

1- +il (10'-o) : c's 9;

bs q.3-

lilillttfll

ilfluilflt

a.rd{

fr q"@E si,e,< ro #i'. + r-rorq '-- 6i' r

If the perimeter ;i a senicncte is 36 cm. then lind ib didetc

ffar ? 6dF- 61- q€Qrg'-- 36c'bi

>r '-31x "r + 2T --+'

\ -.- 33.T. ] Gz 31,\'....--- *

l-Lr 17r 2- 3t" X+^/,d ^.qd-1 u '"Lr"

+ r_r :36 cE

3L L*96

,s!,'4r= -T\a,"{D" ^i\s- 12F'

ill0llllrll t-nj

ro

eqft d arlac tr qfr ff =9 qh ec= +s rl* d er an +1fiq

B

=)

-)

arrqff- +,DS uBa- ertsD'.e ^

D g-- 5 .r-

De gc-

'@-, EAs Sc-

9 A+.A 1,8

ri,SXsz 8fte&{" -) 4 s xg -' -tl-'

---' *

A-MAiH @

rrff-t *a ec= +s... r.a a_e.

." Fe

Hiltrfl[

: t.9

llllluilliltl

-JAC-

a.

€fdr t}1r;r

rlAl-

irrn gr <i' .atrfidc ffi {qiir si d i} {€& t zWhal is the m*imum numbcr ol pdallel hngeds rha!

eaqr " r " ql rrfoddT <nk Ea{r " E TS" +1 $frkr 6r +r @r dFir ?

o. Whal vill b€ lhe addnion of the probabiliry or incidelt - E ' dd inciden

il' G1++ €t 16S1 *r eITTTBI zflsr t

aJa;\' e' * & r,A*t P IE)q.4-

PG) + P

X&"ozr 6r

' 6 #\- u,af}'fl P (Er €

lc.\- ,,1 sl

^MrH @tllIlililfl

lflllllllllll

q4q

Etlg - B( rw riqr r I t rs ir* rqo z.3isJ 6r t )

sEcfroll - B(Quesrion Nos. I I to ls .ery 2 mtuks ea.h )

rie -?dEr6 ar .iar ' -szq * q DloJrr5 d =

,tgu o< <+ f Et

'. o(+F ,- -sotxP = z-rA-oq-

'J* 1 <x€

€-.r-ra-

= ".L + gr. -t p.o {

,q

o

] F r- .*= i--c: i'-6,l?," r;-r ri._F;l;]-ll Wrne a quadrattc pdtynomial to. $,hich the dum or zeroes is _ 3 sn

ruil|lil A.MAT'I E

o.

ef<,-a=f ,ti -"a ei "o"""e otqr{flrddFqt

Irto'a=*,tL.n ma,r,""uluesorcos, dd cos.cA.

rfl

'gg ^ rec-, aaa^

A cL:

q0 qGr)-l3)5

q

=F4

bA0

c.e3ec * a:i, - h cl- 14 c.

ilillllllfll

faqrt:

+.rn A = gC

\B. 150-'

ng' 4

i' Ls=

tq) +t6 +

\

?

IP,T,O,

o.

:3iR

13. qiipr'gr+lXitkq

lf the distanccs ot p I r,

1:ilre1-:.+1r.lqniri,

poinb a 13,6 )and ,9( 3.a

'P gs),q)()

i?-ar+p Bp,)

-/\, @r\i

Y\ -XY.)

(s,a)"+ (t-tf: dt 3-"r 114 -D

pf 1.q.x+ r'+&,'-1 , ,+ 't-

-- esl a-gr + ;Y

i ?.**at-n}+Se-+24 a1g- ty

, - L\-tt4

:'\-+l&1 - "'d .#14r-t-r(A(- tL

i"iEEn

a.

Tr6fq--z-\) 7t I - cJ1-

cl- EL

'i/V/+'1

2)L

4a

l[ililffifl Eel

Eacl

€ar &;-6 +s.)a'i I'

ft-aqr er<r

)tmm:

, *tsR)n+,c ^' a PQR-

-. -l\ Agc : ^

polL

P.ga- PqT

As1-

,q- o rsq i.-

rrAi 'S

& -1" as.) = *+'=<3i *lrqo-) ' PQt=

fi- .."e 6 46i +;rqit* ai"r .r,,rfi + d-+ +arral -)-tr Erl

B c2. nc)-q Pa= PAI

_L5r 34\Id '44

a/4a1tt l 6tT

t:P4L

[l 2 -t'st,ql. Ag

Pq/-) Ao-- P4 €ft* o.{a FAt< g.: .r&, Ac: pQ-t

qA- -A F Se

ftB -- pEB. - .!(A( - P( '- ..=i qlr B-

ffiaD".. sss fr4 Prgc

= 6pE(rt"tl

lffuffiill

1s .ig A frrx'fq{ fon;t 6r tn c]q sdld* t Es*1 er qfo+o t i+ eo.*qt+qqfifudqE+H 7

slcrdr

Find thc probabilitt ot gening numbcrs havinA difference I in throwineirvo di.e simuli eouslv

A cFi + 116 Frq H q'i fr c{ 3ni Erd 3isi 6rHfffidr irdfitd(Pihu tosses two dilrerem .oins simultMeously. Whar isthat she sot at leasl one head 2

fi6GH) [rr) (rrrl Qu;

q-a v@rn = 4

ftr Frr AF .d-

erlg-a- c{Q]irq :3rrAA+r = etut

rrrCqadr

" g&- e-rag;a' qQ;g{d3+

d{ff4

@,-O=F

&- * Raqr sn"-r#'rq.v*- q tryq-

S zc')r€rtdr-

= s u6t

lilluflil1

I

l

tilfliilrtIP, T, O,

El!',lt - C( q{a rirq ro ri zs r+ Fl+ : sidl 6r i )

sEcTIOl{ - C(Queslion Nos 16 to 25 carry 3 mdks each )

ro gEac favrar forlftr:+ or rqlrq*' +zo fi izz +r ncrlra +lBq

f{d 61fuq h 7r5 rfi qqf-+4 q@r 6 |

t6 Find the HCF o1420 ald 272 usirg Euctid s division atgorilhh.OR

Prove that 7,6 is d irrational nunter

{Fr:Sg z6 qft}q {-6r q.. +.rs =\ (t,tr)

G =-4+9

q*" S ao arqqfu *r@1 t

+G

.u{

tilllilfiilt A MArH lsial

tt'

flilllllllllII, T O,

-, i-''r. +.{= !3

,- 3 -'

{+s=19

2-AL

9*- _5Y_= _t, -"Aa-2 t+. -t *

-l L-Q) iz*tle[. ta^-@

lq} .,tr

tlLl2)L+ tg -- +8

lzn ztL 2 ?+o

2gL : ?+o8o -21-L

Y

-L,tL

-)3I

ror+lL

['lL.lrc

l*'lo1rc+t-* tr..oi$

:r.13

l[]wilfl tr

..: L

'.1

a

TnI

18. nlrntq lcfu i {d +ifrrl :

( I€ d@r 2a c{ r{tr flli iq{ 6r qdq dfuq )la. Solle graphicaur_:

4x !=4I use (hc eraph paper giEn on PaCe No' 24 |

z.L-y-: z _# G)

q.^-? ' ,.( qdf. O

$4F 0 B' ftr2!L-

3- = z-(

q'fi- ol t-a-r-

r6 L

* -tl ,1

o

hr

tlllluilll[P T, O,

frE

eiT( s i n1 rqi iFa{ ,r< i 3irl 3iar an @r i ?

the nFl rd the lasl rerns ofd A.P arc It and 35o

.ommon .liffcren.c is 9, ho* mdy tc'as a" ihere

2-9x 3L

69+3

ffi si*,ri,r+q i.fr 6 ,irc et 3ific q< a!Ir' rz qtr gso i qii q'i

q2\V *.a^-> 350 ) d2 9)n=? , S^"?

at= a-t Cn-r)4350 = lt +L\1-l)9.gEo.-tt 3 9Y\-9

':3?la -" gY\ -93Az \ 1> 1\3q2 > 9t\'rr = 3qL

31z 38

Stt = ! (a+r)

r++

sJ

nuruiltIP T O

/l,u

I.H,s =

_l l+s6A 1+<;Al- rl'tA t+ll,rA

F._-.'d f r+ (inh)._

U )1- si"-''q

.t-(, +=F.tz-N-

I - <IALA

(,lA

ie{ A

Cr t si." n

Q..H 's : t<{ A

l[illllltill

lJacl

:ur rs fu< o ii<crio nrd 41i:qq + k<3ii 1,r, c):ri'rls.sl+iqrd 16dc 6r ijjfrtfi 6c i : r * :r-:vro i fuiri+a ;n-ar i r

,l lind tho ooordinares ol thal poili Nhrh diidcs rhc line scBne'i jolninE

thc poims 14, 3land l3, s l1n the.a!o or3 : I inrcrnauy'

1n\rrn!13:1/'.. ,r.\ P ,^-.\ln'-'' h. +) (.? '5

)

"c\,V ,,'', tL

,ht {2 t 'tnL'aclx:

3XS + rx I .zLt + t4

,fl+

'-q ''

3+l

f- f4r ?2 + YnLyl

5x1+31

tvee) r { -9+

tFi{ * G&iB- Q., q

lillillililfl. M'TH @

,,, FErcsr-4l.1n /fq h- Hlaj d€ +,17, 2 ),1s, I ), (3, t)

22. Find the value of k lor vhich the lollowing poinB are collined :

t7,2t,ts,rl,t3,&l

I *'r'(s ...)

- _s-

/ea 4 ,qr.[<( 6.1)

tu<6t-

*b,td'#ft@ +..-l $;rrr = o

{*"(r-"r')l = o

n - Fa) + :fe-t! = o

-)

")

- B(r rR-3J = D

+ 6.1 3

-1 9

"., h)

=)

- ,-h..- :

/ ?'K.- --

R

-1- -ll8

e,/ .2't6t fr44h

* Ir<tt" -h)t "t,tp,1

+

\

K_

t-l':[+

d

I2t/E

ililflI|ililI

dftc

a.

tBnq-s dfuS 3i1r s{i s, s o rnn i rr<.fanfu-a

o iq1 tuer or w En diiq s+* ,i;< ri ro tfr +1 {i w ro fu.{ reifu-< dlaq r ee fu1 i gd #r rqii 1€r Tc dFsq

23. D.arv a lile segmcnl 4 2 cm long and dn'ide il lnicmally in the .atio 5 I 3'oR

Drav a circle olEdius 6 cm. From a point 4 10 cm aNay from its cenire,

.onslru.r th€ pair otr gents 10 thc circl€.

/

I

ilililurl

Iilfl|] l[

o ;

to-q dtuq tu sru fr< t Ttr qr *S 'ti sii topii +1aq:.fr qoct

arS trP.ovc ftar the lengfis oI tanaenis draM frcm d eicmal poin! 10 a

Ed T<_ p.F 4?i- D

"e +i d#i- >ryr'E

Saq- ae- €; 14= eegzTal: dP gk 6Jq, osA-

G<1-l8r diqf--* z onr eri eDBe = qd E

TXTF:

L;!-fcPs--6- s sp o i, -bF = rs CEd a+ tA@l)

C. "rqffr=>

f€ar A ," ii{*-

'o zrzm uraq T6t o8ffi $

a)er J,-+fi A-S rrqaa +' z$*r ".-qr t--ri* $

It?o =,,8?oP* -- (B Cc,e c.t)

. pa-$,..!-{

l

l]ililllil[

o: + rn iF E _@Jg a 3,rEl r E6r- _r-rt

3{Xt-[

As iii{ cD +q onrn kqrsi :r +4 :i{ z i* era sr {idq q+ +

dtul r

s,o

Find the &ea oI a sc.ior oI crcle urh raiLus 6 .m rr !ngl. .r ih.

OR

AB Md CD are respcclvely rcs ot tr\ o con.enrnc circles oI j ..r ri r I .mdd 7 cm md.enbe O lf Z4OA = 30 . nnd rhe dea ot the sh.,..1, :r)n

o

!,

3

r4zrl €- B:30Gc,Te* acl$

.r. +ch(Du.rqs un+?

@. a+oa.

tilrruilt

artai€-d fifq- 6r- .l+fErAtqdi e€ qr alaoa - A..r,1,.-

4-s. ^(' - I {.rI n /et-rr\:ao.L )

-'wQ2 l. 1 r1

fler^F(err -G)-J

zy' (trr+*t Ic r ->\?a\\- '. ,,)

)t''-19

a c, 6_i-&a"=-

1

fua'3b8 4,t62 3 .-

illlmilt

lrilllllllilt

EISg . D( qt{ liqr :20 i so ir6 rtr+, a 3i# 6r i )

SECTION - DI Qucsrion Nos 26 to 30 car[ 6 oarks cach I

ffi c*-,,r:,,- -, - , = o * 61 hfet+l, 1r1 aar +iL.) Tt ffi {, sI lqnr' 5r fli rnil I

o

' 3IIEII

6:r dan( an +ti{ ti-q6r qrl zz 61 3iir26. Frld out (al discnmlnanl, lb) nature orrools

rormula olthe quadratlc equation 3xr- 5x+md lcl root, usins bnronial

Flnd rvo numbeF whose sum is 27 and produ( is ra2.

5'x +'L = o

),4--'5- t-L

EI- -4qLL

- b+ J-D p= -r-.io- L-rtJl

9-X 95+r

e-.< 9

s-\-!!.G.L

qo- q.r .rrgtr+q Er

- ('>+-fiItlP.Z

z

" e'r-26-

(c)

lrflrlrilrl

l,rAcl

,7 {c + qs fu{ s \'d ,o + :ni qai + i]llg w d,+ qfi iirr rffrn *;rq :at ftrqr;ir r*++ +r,l r,qn: 3s, 3ric *, i, qtrT{ +i ircT{ nrndtuq r

BII"'I\r{-sqrc a!i:r T{ rTS +nr *1 a1qr 31r fofa i +o cl 3rii.6 .iE} ?icr+r i Tqfu El 6' 3-rnipr 60. i qe+t so. Er qnr i r

3r) w=ii 4i ir5fTd 6('r + irq q6 F.d 3fiq (furl qnitra) qrd :rr€ q aj eFdrr furp or +r fuieq r

s) +ir{ +ljfrri nra 6Ti{ I r+r+427. From a poinr on rhe ground, ftc dgles oletelarion ot the bottom md the

rop ol a ransmrssi.n rower fxed ar rhe top oI a 20 m higtr buitding de45o and 60. respecrivetv. Fi.d the hclsh! ofrhe ruq...

ORThe shadow ol z !o{,cr s! ding on a leret grcund is tound to be 40 mtoryer whe. tlre suns alirude is 30. rha wh.n it is 60..a) Drawa sinptc diagrm (tigure)to demonsfate ihe question.b) Wrne rhc name of rhc rthr deled tiangle tormed in rhe simple

c) Fip! oul rhe hcichr oirhe roilcr I + I + 4

A

c,c +r4i' + fq€

ie4r 8; B "=-E;511.t ot{ar E

&4 n^

lrB:?

1ilil10il[ a1t

a Bc-n $

) J-,

t"',l q(" = fAqDc-

-) tic-_;!o yrv

eT4- _A Ac, +,

9 la. co' - 4cDC

\t3

\r2

A-a+8L-D c,

FS+ 2'.,

}o.fe = P.B-i zo

_ 2_n -_ Ag

-r) : +a

i-qr-< r-ff+z 4 --sTts\s!9otl3- l) .nn q

I

lflillilflilrl

2-o (S

IP, T, O.

il|il] ]il

lllllilllllilfl

o

Jtr{

llil[flfl[ Eq

,8 fo-q qlFq iF q6 FEr6Fr B.5a i +oi er +i nr a rp:ii * a,n *rl1r * qnal Frdr il

24. Pro\. rhal in a righr irianSlcd, rhe sqlarc olthc hypotcnusc is cqual rorhe sum olthe squees or rhe othc.lwo sides.

€4I F' .-^ 5

LB:9do-Er E-hc'- Fg-+ac' Fl -

,-!fif I

! rrq .,

^ sA- "..i A BAc;_{ eB-' (9oA : fe; \t aft6. { o rq.o (e*6;

& o. €izn "rqr-GrS' ea. . . gd t

A GA(

, AB- (uat dt;tfraar <a'z )&c-

ftB: &A. AC

4}L= bA - ,\( .-€fr OJ

6 8" s -zr a rre-i -

{Aec = looc (96)(*Le7 (Dc-6 -e*n> w;

rY

tF;

erlE! f

+r{'urr a+$ &Bac .'

ECee-oc-9c- A <-

gcxBc -- 6-e,

Br:L : o q.

nrBl+ gqL =

O zd- @ + cH qd-,

A€z+ Ac> - oA.AC OC'AL

qc (ox +or)ftCx AL

A-82 -; B.z = AqL

@ulaqrr;rar aaa;

.€fr@

,P11!14

A_MATH @

'-,

lillllllllill lP T O,

r, F- Lr- qdr ri, .;r..Jq-- .- q-rl.+ .+Er.h- 43ipdi i i-+ . ri a ) m;' i -r.r ?r+ .fl Fqr iqr 6r rrrrm ,t.q$:_# rr, zsq.iir 4040 q? +a "l op.pa- fl !I - -+.'+e qlr 6r {e nrd 41Fq (,=-f orir roooffi3=r#er)

:19 A ..nraln.., opened trob the rop and made up ofa merzl sneer, is in thelarm of a trlsrum ot a cone of hoieht 45 cm wrh radn or G lo$cr rndupper tnds as 7 cm and 2a cm respc.lively Find the cost ot rhc nn[shi.h can .ompletety lilt rhc container, at ihe rat€ oI Rs. 40 per Lrrc

1. = f -a rooo"-3- r n-1

,+ ALOe5'6rt4 4q t1('rcr- T -_ AR c,"\

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