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No. of Printed Pages : 15

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Part - IIIaouflpLb / MATHEMATICS

(pdl$ Lrgg Li garder ar g! / Tatril & Inglish Versions)

s,tl.'^,.=t'.q.] .. . suf.Ietvltolal.GoriFo.n$p Lo$ nGL.,ai.nsoir : 100rrme Ar toweLl : zl r Hours I [N{axllnum Marks : 100

gldluqeo,r : (1) st6o6lr$gl 6fl6lrr.is(gri efluris +!e+Lr uper n6l zcnenon oreorpeoemefl u ni $5lri 6a neionq rb. .et e+n r$ e$d lgeogug16 Lr lg oi,r g1 arrlris.dr,e 60flu_-a .. o ar eirrr,ns "g-6!iE6\-0(2) 66DLb eleleug s11Lrq eoLrugaren Lor@Go erqg51cuplELr Lruloirr@$pGel ain@ d I rnl oeir er:eorJeupf 6 6 uei;r$leb Lr u_r 6i[Lr@$g6)] Lb.

Instructions : (1) Check ihe question pafer for fairness of printing. If there is anJ, lack offairness- infor,. the Ha1l Supervisor imnediately.

(2) Use Black or Biue i1* to write and p€ncil to draw cliagrams.

gf1uq : @a;e$ern$pnoir pnoing Er,iaqseocnri 6lonai.rugtNote : This question paper contains four secLions.

(ii)

6(9g6rlro

1r rns\\ er ar Ute 1I rlrLtsstrun.,

(it Choose thc corect ans -er from the gir.en four.rlt-.rl1ativEs anLi w te theophon code ancl thc corresponclirrg ansr.r.,er.

dlflol- r/ sECt,lON - r

(rl9lr6lLr@ir.,s6ir:1s) / (ttart(s : 15)

@ L,r9 tor . e 6"16 tq 6sl5.dl-ds@ri(9Lb et a - er.]li o q .o

Cls n@rieu u r@ eircn gnoirg on$g ogcorsofid disqLio!)arraru$ Ggipclg@$g; Efl u5r@ rdr ogleo rug ar arrq rir

t6dllrL] : (i)15x1=15

s fl u.r r6ir

Ge rris,r

Note i

u,srw.ka.tv! sg!* I i,".,9,,T"lt{liqLrrls / Iurn over.

sslc - march 2016 - www.kalvisolai.com

5773

1. A = lp, qr r, s), B = {r, s, t, u} 6r6rfldD, A\B =

(er) 1p, q] (.+) {t, "} (g) {', "l (n') {p, q, r, s}

If A = {p, q, r, s}, B = {r, s, t u}, tien A\B is :

(u) {p, q} (u) {t, rr} (") {', "} (d) {p, q/ r, s}

z. 1,,L,2,3,5,8.... ereiirp 61pmn errfleoeuiloin I -6xgt L0iLlLl r

(.er) 25 1*ii{'iu";{n*e;1fu1:furvreu"' Gr) 21.

The Sdl term of the sequence 1,1,2,3,5, 8.... is :

(a) 25 @\ 24 (c) 23 (d) 21

3. 1+2+3+...+n:k erofleu 13+23+33+...+n3 6r6inll$l :

(.gr)k'? (+).r,3 (g) {1U (r) (k+1)3

If 1+2+3+...+n:k tien 13+23+33+...+n3 is equai to i

(u) k2 (b) l,3 (c) (fa (d) (k+1)3

4. x 411 = B, 3r - 12y = 24 ct6:n@ltn eLoeirrn@eafl ein Clpr6nr9l!1q

(gt ) Apr+e,El6tl erainarfldarsuql6i $riqseir zoirarem

(4) $riar @d6o6n

(@) 9Gffi[un6 $ria.] Lor@Lb z@ir@

,n 6i n Eriar 6l,n li,qa,ni .g.clars 6lai,er,n ocr i 6l,nri,cn,n il

The system of equations x-4y=8,3:t-12y-24 '

(a) has infinitely many solutions

(b) has no solulion

(c) has a unique solution

(d) may or may not have a solution


, "

= {': l) .",n, o' =

(*) [I ;] (*) (; -:J (6) [-: :) (") (: -:)/1 .,

If A: then A- ico .)

(u) (:: ;l .,) 1',1 l] (.) t l 3) r.r [l -]l

3 5773

5. ax2+br+c:0 erdnp eroeirL]nuucir qgoeura:ooir eLoLb 6refiei, c -ein o$luq:

L b t. t:*'in 1 ,., ta'-ro /Fl r.If ar2+br+c:0 has equal roots, tlen'c' is equal to I

bl 1.,2 b b2/.) i ft) 4" r. , -;" (d, - +,,

z, y--ai9lgg $eoanuriargLb ( 2,5) 6tdnt) qonofl erp+ Geei,orgtLc,nerGpn&GonuLgoir sroeinrn@ r

(g]) r z:o (+)r+2=0 (gr) y+5=0 (n) y s=0The equation of a straight line paral1el to y-axis and passing through the point (,2, 5)is:

(a) r-2:0 (b) r+2:0 (c) y+s=o (d) y 5=0

8. +ru.rq 3 +salLb, y Clorr@$5la;n@ -4 +s6rlLb reirerr Gpri&Gsrurqeiir +roeiun@ :

(et) 3r-y 1:u (+) 3,r+y 4:0(6) 3r y+a=0 (n) 3r-+y+4:0The equaLion of a straight lile having slope 3 a1.Id V - intercept 4 is :

(a) 3r y-4=0 (1')) 3j!+y 4:0(c) 3jr-y+4:0 (d) 3x+y+4:0

wwr{i.nffi uohfr #,**T*oro*[ $11uqo / Turn over


5773

9. AABC -6! AB LDD0rLb AC serflc)ldrar qciroflscir D LoDPLi E 6r6iru6n DE I BC

ereirpor ng o eircrren. GLogtLb AD:.3 6le.L6, llB:2 Gle.d, ofELb AE:2.7 Ge.d,

6r6iJl6i, AC =

(er) 6.5 6le.Lf . (qg) +.5 G+ d (@) :.s Gle.r-6. (n) 5.s G1+.16.

ln AABC, DE rs to BC, meeting AB ar,.d AC at D and E. If AD=3 cm, DB:2 'm and

AE:2.7 cm, then AC is equal to :

(a) 5.5 cm (b) 4.5 cm (c) 3.5 cm (d) 5.5 cm

10. AB, CD ereirr ein g1g or ru$$loin $6 pnainseir. eeoer $rruLr@Lb Gurgl

P en e$$ri6leirpar LoFgjLb AB:5 G14.6, AP:8 Gle.L6, CD=2 6le.rf, craiel po=

(el) 1z Gle.L6. (g) s 6le.L6. (@) o Ce.Lf . (r) a G+.d.

AB an.l CD are t!\.o chords of a circle which when produced to meet at a point P such

that AB:5 cm.,{P=E cm and CD:2 cm then PD:(a) 12 cn (t) 5 cll.l (c) 6 cm

(fir) ranro

(c) tan2o

(O) e5 LE

Then BC=

(d) a cln

(r,r,) cot2e

(d) cot20

12. LrLg9d. sin0 6r6rfl6b, BC:

11. (1+ ran20) sin20 :(sr) sin'?o (g) cos2o

(1+tan2o) sin2e =(a) sin2e (b) cos2o

AB(sr) 85 L6 (+) 0s

In the adjoining figure, sino :

=1517

C

d15

i

(.) 85m (b) 6s m k) e5m Gl) 75 m


5 s773

13. eO $lai,rlo -96o[&G6r6r95l6ir o9rrrb 2 C]e.d eroflci elpdn Gon$g qprLrqrq:

(+ll) 12 G6.16.'? (g) rzrr Ge d.2 (@) +r Gle.rf., (r.r,) 3r, G+ d.2

The total surface area of a solid herrrisphere of diameter 2 cm is equal to :

14. t, y, z ein $luLa9la){ioLb t (r6fl6n, r +5, y +5, 2 +5 eir $lt orlieu&oLb :

(a) 12 cm2

5(u) i

to) Izn cm- (c) 4rl cm2 (d) 3rr cm'?

(+) f +5 (6)) t (rr) tyz

If I is the standard deviatio al x, y, z,is:

then Lhe standard deviation of jr +5, y+5, z+5

r+5 G) (d) xtlz

15, e(D 6DL-ruEl6l 5 6(DUl1, 4 Glereireoor roSELb 3 dlaruq ppLr r$5laeir rcirenen.eroerruruq 916opu96n Gpn$Gp@rils Lr Ll @ nr gO rr,Egt 6oruq ppLons

@eixu nLo o!6 Lr rpf e nar S)s!_rgeeq :

(g) (+) 12

(6) ; (") :

II a ball is selected at ranclom,

L3

t(,) a

5

12

(sr)

A bag contrins 5 black balls,4 white balls and 3 red balls.the probability that it is not red is :

(b)

3(.1) ,3G) i

4(b) i

,wY[,:i d[ $6Lrqs / Turn over


tqdL,-.1 ,

Note:

6

Eflo] -rrl SECTIoN-Il

(o$uGranseir : 20) / (Marks r20)

(1) upgl a,lleornrisqgrilg er9eoruofldaoqLi. t0x2=20

(n) 6fl6.irr 6r6iin 30 ri(g sa:orLqLlns e$eoruoflriseqLb. GDpd! 14 6rll6ir]ri6dfldJ

6fC.Egt oGg@rO 9 orllernrisareng Gpieq 6leuru-rqii.

(i) Ansl,-er 10 questions.

(ii) Question nutrber 30 is compulsory. Select an), 9 questions from the first14 questions.

16. A:{a, t,y, r, s},B:11,3,5,7,-1Ol ererri 6an@dorjuro6ir6rr s6irnlE'6(!D;g,se&rrat s 6{l6ijr Geriuq 6lau,,eu nelrgt, L.lflLln$g !airL-1 LatLu_tgl rrdrileog +flL.l nririseq L-b.

Given A:{a, r, 1J, t, sl, B=1.1,3, a,7, 10} \,erifv the commutalive propert}, of set

17. 13) 6rdns. /= {(a, y) :1/:3 Zr,)i.A,A:Is,6,7,8) ; B={-11,.1,7, -1A, 7, _9,

/ € Bl 61601 6)r6D[u]mr{ia,LlLlLfi)6rr6rr.F

(i) / -ddr Lolur l66o6n 6r(rgt6.

(n) 6rles66 [email protected].

LetA=15,6,7,8j;B=[ 77,4,7, IO, -7, 9, -13] and

f= l\:t, v) : y=3 2r, r e A, r7 e B|

(i) lvrite.lo\..n the elements off(i, lvhat is the range ?

18. .D, 3.ir, 5!2,...6r5fr0 c,u@$ Glgrri errflaoeugein rz.aor5t rEtLrq Lr.r gt

Find the l2tL telll] of the A.p. jz, s",1, :"i:,.....

wwrfji.%titeiefas&tr***


7

3-to1q. e(b5(q5:-- ^+;-

11 8SDTDIiJT

-

+

-

- \-2 /- t

20. c{, P 6r6iTLr6ir 3a2 6x+4=o 6r6itr@16 6lo6i,rutlL+eir (lDorolsei 6r6ifl6i, ']t2+p2 6iir

lD$lL.rLlri srai,r6.

If cr and p are the roots oI the equation 3l - 6r + 4 = 0, Iin<l the value of o2 + p2'

21. Lql6i,ror(Jor@r6,rflfleu elod 6lu196od eleoTu-lE:Bsull@Lo[6inr6D g]6)lD6oD 5lr6ift]5

,a2l' " -'l l-" tl14, o,l,r

r..l

Find the product oI the matrices, iJ exists.

/4r)12 o -t) I o ,Jl4 -1 o r l_, ,.]

,, ll,;l =

l:]..*.,', ogeb z -eir Log)L,qoooor snaino'

5773

Fincl thevaruesor;y"".,- [i 1;] |;]


5773

23,

24.

25_

E

Lj6ir6rn (1, 3) E DG6GsrrL0 6DLourLorsri Glsirai-rr griGonoalg$en @6 g:orereen(- 7, 5) LoDDrLn (8, 5) 6r6ifl61, (lldGsrrarmg$e;r goeilpner5] geoemaoud srairsIJ the centroi.:l oI a triangle is at (1,3) and i\,vo of ils vertices are ( 7,6) and (8,5) thenIind the third vertex oI the hiangl€.

5x 2! 9:A, ay + 2r i1 :0 gdlu GpnGan@selr geiirgB1g g6i,rE 6leni19$gl

eroflcu, a oir Lo$lLreorri onaino

Find the value of'a', if lhe straight lines 5r-2r7-9=0 and ay+2jr-11:0 areperpendicular to each other.

LrLESl6b TP eO Clpn$Gen@. A,B eroinuor orrr$$leir Lfgoiien q eraf)adn. tBTP =77rDDg o AtB 1' .6if6r -ABt pe + aiuo

In lhe figure TP 1s a tangent to the circle- A and B are two points on lhe circle. lJ

-Blf-72'"nd. {rB 4'" l.nJ. ^EL

26. gO AABC u9eu 6lsoGsnomLb 'C' -Lrllld) =r6DLDUru

CluDpn cos (A + B) LoE&Lir sin

r \ + Br 6dr , $. -jea er.i s- riraff AABC is dght angled at 'C', d]en frncl the values of cos (A + B) and sin (A + B).

27. e15 5l6i!rLD Gpirerrr zlgare,nu9eir ererorryrq Lobgllb .9tq6e$i!6ir6ll 0D6rt Gu.r

4400 e Gl6 rf u:!pLb 110 Cls.d. oreri el, eleleq1q56enu9eir rufp60gq6,el!)rr$eopuqLb snai,'na.

Curred suface .uea anLl .ircumJeren( at the basc of a solicl right circular q-Lndei-- are4-100 sq. cm an.l 110 .m respectivelv. Fin.l its height and Lliamerer.

w-$f wr&[3{ri5*!fl*ffi l&* "o


9. 5773

28. BO q6n6ri oller,q$$eiil rorgrru@d Clo1g 57 LolgLb $1rr crglao6eLi 6.84 6r6dl6i,.e.trg s ".61x1,;4 "1

g

If the coelficient of r.ariaiion of ir collecticn of clata is 57 :rnd its S.D. is 6.8,1, then iin.lthe mean.

29. 20 SL0ecrfl6i 1 gDpd 20 oi6ofu ]6ir6n Or(g 6rdifl6dr (96165rLrL06ir6n6nr. eLrlcxtlurlr ]u6nDL,; 6D n, C f a Adorrutfdlci me,, .g-ror:nnr el daa,uLl S-r.o eior

6T6iA :

(, 4 d, LoLErens 6)(gBg

(ii) 6 -6ir Lorrusro @dueunLoel @(!5ria

+f . fls+&f snl"ir F6!]re eots 616 ii. s n.dd 6.

20 cards are nurr.bered from 1 to 20. One card is drar,!'n at random. lvhat is theI'robabilii_v that the number on lhe card is :

(i) A multiple of 4

(ii) Not a multiple of 6

30. (+;r) 180" 6olourr, Gsr6iirgDLi 21 61e.1-6. gqgLb Glgnair-rr errrGsnorlr 6r+6'E6Dr60r

$gLnq$ psr4eir +trEr6ar6n 6-*pgt eO &.rbll L(Dorrr&slru@dlpgl

" ot' d, .ga + b9dr 1 r$a.p e-6rlr6

secg 1 - cose

(a) The cenhal angle and r-al1ius oI a sector o{ a circular disc are 1E0'and 21 crrlespectivelv. lI lhe edges of the sector are joine.l toge+$er to mak€ ;i ho1low cone,then fhrl the ladius of the .one.

(-+) 6oel.

f -i sece sin2e

(b) Prove th.it:

1 l- secO sin2e

se.o I - ( r)se

OR

'irwy.kaM?El$iit|;1.,o 0..", r gleL,qs / rurn over


577i

Note :

6dlnll: (i)

10

L9flq - trr 7 SECTIoN - rrr

(o$lLrGlraio;acn : 45) / (Nlarks :45)

Llleirrerigueoeraoid qcp@r nr 9 er!] errn6a1g16 g o0eoruoideol Lb. 9x5=4S

oll6iTir 6rain 45 sqg oai.nlqLtlira a$orruofldeqLb grgd r+ efilernrieoflolg$g B o9onn&oeoerp Gprierl 6euru-ler1Lb.

Ansrver 9 questions.

Que.rr-n nt,n ber 45 i\ .ompul.or1. \L e. t ..r\ g .lu(.t.on- tr ,m th*1{ questiurs.

(n)

(i)

(ii)

31. BO orrrcl6ur60 $leneoud, 190 ror6dir6r,r56rflLLb.el6!i.sdr el!115LbL.lLb @areugeir6r6o566i)or5 $foreride BO 56ftr$6l5@LrLl pLpSLgr t1a Guf Gofr,*$$lur@eo+eo u u-.11i, 5O Grri"6lndlu $ooeeorqLb, 41 GLrir sirprLs @eneaouqo,14 GLri GLoEs69lr $tareeo u-l,q Li dlqndlr @ar+aouqlb, 15 Guri GLo!s$$u.r@areooLrqLb oripnra $o+oouqLi, 11 Grri oiprrs @eo+eoLrqLb dqndlu.r@ooealrqLb LoEgLb 5 GL.ri. g,beldrrp @eoeeeocnqLi a9 19 Lb Ll6l6irp 6!rf.$d.aso:,' ooJ)er, ,-jg _ d. 9. .o,cr_,enp e "one

(i) 0r6irpr erens $eoesaronulLit o8gLblnp rorermerrisafl eir erainolfl rioos

(ii) g)O 6)16o15 @)eneocoer Lor$6 er96Lbq6 Lonolrerrisaflein eraineu:flEeoo

(iii) dlfrdur @eo+eor oE6LbLll GLopa$$u $eoearu ogirqrirng ronarerirseiflainarainerofl&ecs.

A radio staiion surveye,:l 190 stu.lents to dei€n ne the tvpes oI music the], Iiked. Thesurvet'revealed that 114 liked rork music,50 liked fotk music and 41 likecl classicalmusic, 1-l liked rock music and folk musi., 15 iiked rock music anrl classical rnusi._-l llike.l classical music ancl IoIk n usic, 5 liked all the three ol nnrsi.

Find : (i) How manv clicl not like antr of the 3 tvpes ?

(ii) How marv liled anr h,\'o trpes onlv ?

(in) Horv manl- like(l foll rnusic but not rock music ?

w**iilijilBfat re8ilt' w vr'1'lr


\-

11

6)r ar rrurg.is ! u Lo6ir6irgl.

f (3) + f (-1)2l@ fo)

5773

12. a t:l ,7t- R f!6ecin "r.9

,i(,)=L;

;

Gloinoul5orenerlenpri snaiirs : (,

I t,2),. ,t"

141' l

i",_,

l2r r

2< r. <4

(i,)

A f,rnchon/: | -r I R i. J.h,red ". lollor*:

f(,):

Find : (i)

; -3<a<2; 2< r: <4

f( 2) fl1)

f(3)+ f (-1)2 f(6) f \1)

(")

33. 7 +77 +777 +....crgjLb Gpnrrfld gopab n zEuqeerfldn e,Op6 6rains.

Find the sum to n terms oI dTe series 7 +77 +777 +...

3a. eO 6!L0E ClgrLfl6i 7 0:r6rrpu96in 7 -6)19l LotL] llir 11 Gr6Dpugl6i,r 11 6).rgt LUtLrLlLbsLDLb 6.6ifl6i 16 eu5l rpLrr9loir L-o$luq ggg)ub ereor @19r9as. 6sn@riolrru@eilcnqeirofl e$arlruooieir rq gpd rpLrq LolELb Glung o8$$lure$$eoor& anemr

SugLor ? onpeoinb a'poqLb.

II 7 times the 7ft Letm of an Arithmetic Irrogression is equal to 11 tirnes its 11& term,show that its 18th term is zero. Can l.o" fi"d th" flrst term anci the commondifference ? Justifl, vour ansu,er.

$rWW.kalvli0lai.com!r-!i) lr.;r"*1{}3i * lf:* llu *'*r

| $llgLrqo / Turn over


5773

35.

12

sr[6r6flaL.rGr5g]s : jr3-5f - 2:r + 2.tr

Factorize : 1.,3 5r2 2r+2,1

36. &(D5(q6 :x2 +3x+2

1 1

1' + 4r + l

2

+

rrmpru\-

3? A:[_1 i) ":l:i] ,rr. .:(j:) 6r6in 6i, A(B+.)=AB+AC

eeir ag afl.lr=isorjt

, "

: (-; i), = (. : iJ ""0 . = (,' :) "".,i,,h", A(B+c) =AB+AC.

38. ( 4,5), (0,7), (5, -5) LoSELb ( a, -2) +6Lr gmremoeocrd; Gsnainr pnle;r$$teirrlrq srailno.

Find the area of the quadrilateral -hose vertices are (-4,5), (0, 7), (5, -5) ancl( 1, 2).

39. Gp6l6i! Gpppp-p erqg$ pgL9risatlb.

State and prove Thales theorem.

40. 700 16. rurq$$61 Lrp$grri GlonainrggrigLb 96 GpperlonLrrfla5lg$5l g6orn gn+pdld, @)O oeoysaflel GpGT$7ns rotuor S6 Gtrrl5rseoon 30., 45. gD6rE6

GsnaurrasoJld snaindpnn erefldu, g!floin.llso$eopri gna;no (./5 : t z:z)

A person il a helicopter flying at a height oI 700 m, observes hvo objects l],ing oppositeto €ach other on either banks oI a river. I'he angles of depression of the objects ire 30.

and rtr5'; Iind the rvidth of the river. (.,5 : t.Z:Z)

rl r {.i i}. i c; l{ i* I vi e; ri,u* xnf',q.


13 5773

41. eO gl6oL6saiml 6u E69 6D r6i.r or rdflrgl6ir GLo$qp LoflglLb =9E'!D ':'brEr66ir

["-fC. ,,t Gle.6. Lopp Lb E Gle.L6 GLogLb,4pLb 63 Ge'd erorld er5dtr

6 e-c.-.,.. . , ,; .' *r. I _

The radii of tlvo circular encls oI a frustum shapecl bucket are 15 cm and B cm- II its( 22.1

-.;$ r- or. m. fLnJ th" ("p". n oI JlP buck<l urLne'' ll"lon 7l

42. e(D elr6s6rx ErLrlfLD116.15] 16 arenu.g eir d5: a'Lbq 6eoerorBp a! Lq-6616\)

!tir65lul-*5 a,unqr$$6 6Lon$p rtrryLb 49 Lf ' etpeir errauu&s$$lein cdlrrLb

,+z L-6, Jqgeoenurns$$lein ru:1Lb 21 16, GLog1b 1 ed 6$pneir 5eoflrrQcin er0eoeu

? r2.so eroflei, m'L nqLi +larLorio Gparor tl neo 6l$pneir 5alflLrliair efleocleouti srarars'

I _ , rl lt" - I

Acilcrrstentistobeelectedjnthelolmofaconesurmountedonacylin.]er,Thetotalf-r"ign, of e-t" tent is 49 m. Diameter of the base is 42 m and height oI the cylinder is

ii'-. li"a the cost of canvas needed to make the tent' iI the cost of canvas is

2rlI12.50/m. rur"1T:7J

43. S$sairr errreuaoeorugdu Glon@ri,ou u r@ oiron qcirerfl eflorT$$eir prre$eo6o$oop& uarrri:61@o :

Calculate the standard deviation oI the following data I

3 E 13 18

7 :t0 15 10 8

8 .13 18 23

7 t0 15 10 E

t{$rw.kalYisola''Gom,., rJ,liidrr.lL oi.Ut|!'rV


5773 14

aa. eO CILrL+ulld I ClsudreocrLr LrEE6(gj6, 6 Sl6rraLl lrligls(gDri, 7 sOLrL.l ll$goqgLoLolgLb a $euu upgoqgLn reiroreo. qrGggtb g15 rpg aLoernuLrq goenpulileLr

. i,e--.;ma ei nna .g.nsr --t"snel+ 6Gro Clsn "as .l6 ,n pp, 60 ja !9s69a 6r e ,.ji e.

(i) s(EnllLb @elorrLoai GereirarenqLir S)darnLodr

(n) Eort-rLl .el606DgJ Cldr6iTa)6n

(in) 66!6ir6r.)6rr .sleioug floruq stdr6Dg ogtlrLl eteicu5l $arLb

A box contains ,1 $'hite bal1s, 6 red balls, 7 black ba1ls and 3 biue balls. One ball isdrawn at random from fie bag. Find the probability thal the ball dralvn is i

(i) neilher while nor black

(ii) red or ufiite, ancl

(iii) either u'hite or recl ol black or blue

a5. (€r) eLDdnLrrO (1 + m2)r2 + 2lncil + c2 a2=0 -dir goeuosei sLoLb erolflo,

c2:a2(1 +m2) 61601 6lgtoy6

(.eJ) 2t 3v-1=A, jr 2y+3=0 46lu GpriGsn@seir e$$li6Lb qonerfleou.JqLb.

(3, 2) ( 5,8) 4du qciraiscoen $eoerrrigLb GpnaGsnr@ g aiorqe;

p@ LrqdrorfleouqLb, $enelrri6Lb Gsnr@$ gairq<ir eLD6 Lr.rL6oLli 51cr[15.

(a) lf the equation (1+ m2)jr2+ Zrrcr + c2 a2 =0 has equal roots, then prove thatc2: a2(i + m2).

OR

ft) I1nd the equatior of the straight line segmcnt h,hose end pr)i11ts .ire the poinE oIinterseclion oI ihe straighi 1in-.s 2]1: 3V + 4:0, r -2y+3 = 0 ard the midpoint ofthe Ine joirnng the points (3, -2) and ( 5, E).

rr: t, i! . i tr; ! l- 'i; !". i {ir*.!v,.'ciir

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15 577 3

L51flo] - Iv / SECTION - Iv(o$Lr6lrar:riseir : 20) / (Marks : 20)

gdluq , gdG1er.:n6 erllemne9I Lb reiror $rraimG) orrfp e$eor;-risoio5lOpB eOergleonroerS! Gprr!6p@$5 $16 oglennBeqgdlgLb oSleoru.lofidseq6' 2x1o=20

Note : Ans$'er both the questions cho'rsing either oJ d1e alternatives'

46. (€r) 3 6e.16. 419eiron gg orrrri ereol$5 slpdn <oLour$$er5lg$gl o Gle d'' .

GlBnaoororglg1ciren 96 qdrorflenuB gflrio elLrqeiroflugallr5$5 er+$$pgGlprGrG6r$lsdr er..l6irrpgr erp6h.66nrirs6Don seunridlSa

gt 6D6ugl

(+) Pa=5 G15 6., QR:4 Gle.6, IQPR=35' toEPLlr IPRS=70'gdLr ercne)leeir

Gsriairr elrr pnfs[Lb PQRS or6it[6'

(a) Draw the f,\'o tangents from a loint which is 9 L'm atvay frorn the 'entr€ of a

circle o{ radius 3 cm Also, measure the lcngths of the tangents'

OR

(b) Constuct a c,vclic quadrilateral PQRS given PQ:5 lrm' QR=4 cm' ZQPR=35'

and ZPRS:70'

-ir " ".r5 sn6n.o I' L d" r:-' b0ereinp eLoeinurr arr$ $n6sq Lb

3161)6D51

Car ran ar u rrs afl ein aainaflBeos r 3 I 6 8 9 L6

pnrcoflein eraino#Liroo Y 96 72 "{3 36 32 18

gtrrerarearugei 6sn@riaulr$idrcn a9e!q$6lf sn6n ereoqlrL-b oleola

€rpdr Ur6Dt-b 12 Geleoeuunusoit eleiGorsi'el6Du l g:lSer5]rcns 6au.,lgl

gl4ris 4gLn Brirsafl dn eraineoflrianseoLuri srairs'

G) ;r;". the-g"'aph of v:r2 -zr 3 ancl hence {1 Ll th€ roots of -r2 r b:0'olt

No. of r/orkers n 3 1 6 8 9 16

No- oI da,vs y 72 ,18 36 Irt

Drau, graph for the data given in th€ iable H-'nce finrlr,\,rrkers to .omplete the lvork.

thc number oJ cials taken b.v 12

-o0o-

(+)

(L.)

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