think90plus.com...created date 8/21/2015 3:21:22 pm
TRANSCRIPT
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COPYRIG1IT RI,SERVED
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2015 (Al
2015
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MATHEMATICS
19th FEBRUARY, 2015
FIRST SITTING
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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$i 4T tThls question pape..onsisls of30 quesrions divided inlo lour Sections. a' B' C
and D. section A.ontains l0 quesrions of 1 mak each, s.ctio! B.ontarns5 qlestions of 2 mdks each, Scc.on C conbi.s lO questions ol3 ndks each
d Scction D contains 5 queslions of 6 mdks each{ajf + Bfrt q fr4fi 3tEi <
On.\ slre !l--s rc 'o
oe F."'gr+ 6 rfi{ laa 6 !T!r ir( ,rI E", ; x'dr+ ! A zAnsse.s of lhe questions musi be in lhe .ontext ol the irstu.tlons gNeniherein*.F r.r =r" rvc-n6,sfl gF-+l + 3id i jiq.r{ Ffr ci ff a1Bq, srq* oi +aDo all rough {ork only on the last pages olthe Quesnon cum_Answ€r Booklei
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SECTION -A{Question Nos l to r0.drv I mdk ea.h)
qdrg,l fu * qft.iq {@r + s{ni{q cqn Fid i qr 3rsia qr{ff tthe rationar numbe. S v r have
non-teminating repeating de.jmat
a te@inating decinal
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2 f{ rq rrt s=p(x)t{${p(,)+rf4+l+1d@rftfissL
lorynonial p ( x ), fmm ih€ given
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If the perimeter ;i a senicncte is 36 cm. then lind ib didetc
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o. Whal vill b€ lhe addnion of the probabiliry or incidelt - E ' dd inciden
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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
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t6 Find the HCF o1420 ald 272 usirg Euctid s division atgorilhh.OR
Prove that 7,6 is d irrational nunter
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( I€ d@r 2a c{ r{tr flli iq{ 6r qdq dfuq )la. Solle graphicaur_:
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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
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r++
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,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'
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,,, 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
-)
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- B(r rR-3J = D
+ 6.1 3
-1 9
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=)
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R
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e,/ .2't6t fr44h
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+
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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€.
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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
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Saq- ae- €; 14= eegzTal: dP gk 6Jq, osA-
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C. "rqffr=>
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'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-$,..!-{
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o: + rn iF E _@Jg a 3,rEl r E6r- _r-rt
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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
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artai€-d fifq- 6r- .l+fErAtqdi e€ qr alaoa - A..r,1,.-
4-s. ^(' - I {.rI n /et-rr\:ao.L )
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a c, 6_i-&a"=-
1
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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
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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^
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a Bc-n $
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t"',l q(" = fAqDc-
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eT4- _A Ac, +,
9 la. co' - 4cDC
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,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.
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+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
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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,"\
9l.]trr7iT 1 ?
(t"'t'+ lr)'+=*,+
3,34.+
t--,,...-t
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n+, (n'+-J -")
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Vfrq{d : r++ q,14 > tll.+d '(rl + "{_
"frflarZ
H-{f + fr-}1si<- ro. I rt+ _l-
nrr5.98:fl
'::-x \s / !P{ rea4-
> 2r X ts,X tq+> q Ealo .1n3
2 \te eto
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3. a 6
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#*a rtr ar{ * HI FOR ROUGE WORX ONLY I
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#+omqr{*tr}I FOR BOUGII WORX OtLY
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