sslc maths notes

CoxrE ^vrsA CTr 4 L 6 rao mrr?,y

FurtCTtor.t

S ivo

l acl

A-t-. Dna maK Atartr*.,2. fltro rn4n f{ A**Eon3.lwo rnar i( Ex^a)tdae AuaffiotI'{-' Fivg rnarrx guo,t:frao5' FiW nno.rr I E>cr;llr.!:e Aw)fir,16 ' ren rn&n K e.uaa Fn7 "lPtt rrraa R E]__ eidae &ualtsn

NAX,, A 4 if lRRhru AR i,t

r 0

f 0 o r &u rsT Iov

{ 03rr

3- 5-3-

- 8 1J

'PAhe.r,n

2833

- - - - - f _ - - - -__=_ ' r r \ . 1 _

I r i r R i h o r v o H E T R y

L! t-/EST t oN pApEfl, ?ES rCnN- - : - E : - :

(qq& trv ArE QeonETRrn nTRr"c E s

sFquFNcEs ^ tp sERiES or ftsta#sr4glt'J f ' lT rS7/cS

A{FrvSuRAf r o N

KOVUR SCHOOL,KUNDRATHUR,CHENNAI 600 122.

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6ap a

orn jta1u4U-A-

6aut q g.hdr_ ot

Point 7@1 q,w%-

fo 'fh!- ()J, d" anJfndh .t-,A,tlrb (tett$h of Eclr\g: h j 6.gcm) .

J;ot"ntU Loun- Ftom * poirnt P / 13 Cn ajtry fnornrh-a- fuso - +dl\truLt> ?A Md, PB ro ru Urd!-, ^d1-#to

cKe- a loirtL NIucA i5 Tn a,^r)TJ fron o oerlLre of fhe. Ci rdt_ +o,)iu sun, anJ Jnar^r rh!, fr,,to tatt6ettl io rnp_fAdL_ fnon nAL Foi^,b

/!?6*" cgdic qttadnilomoJ)

(,o,tOtuuct a c64ic q,-sJil-ta6^l ntscD in UL*cl. AB=5cm, f r ( = 1 U 1 , B c = b c mand AD =r+.?-un

ru11tuct ^ cgd;c q,rcJ*lotelJ paRS rrrith ?Q= r+Crn,0 R = bcm, Q s r)cr4and PR- -7 '5unCon+tauc,L a %&. qJt^Jil-l"J-

"rrrL Atsco ui krr AB= 6vn ,%c = 5' I cn

g?c = Bd an f , f tD= Q,sun .

CproY'tucb a. qrLc qp^J:r;lalpna F F&Fl u"rifh EF =5'L(tr1, ,/Gtr.= 5D', FG =6banA /EaH = 4o'

&rrVff,u.t q q&c

a , /ntso = B5 ,FD: L ,Lu,1 uf , AB l l cgtowl a C,6drc1^Jiltr,i l PARs,uljfh pq=6.sc, , 6-n --s SUn FR=7un, pJ:? s

'-onttut a c,rP,ic qryA)ilafuaj AWr: ff"v.rt t|ts= Lcrtt , &ELr 7D' Bc = gcm

/Aco: jo'. v

eu Thz two EargrAb frorn a-Conffie of a, ci\d!- of ra&.,u

f rw- can@

point u-tlucfi is bun adad frombun. AIbo, nL.abna_ fhz- W


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{ 2 3 5 6 l oa I It 2 0 ht- I+a

2,hR,+PFls/V144r'\,#.*

alu ^ Ahe^ f,t th!- ftLtoaifr tubte ^ l ietrLtiry ftw Vatu"frn

f-iQne, Findt'tw va,l,,re {t "thn ,L=4

D6ap .rhe ffih ,fro th!- a^b"ve .talle *J Lpnq *J fin|IttnL vil'z q A if ,x=4trlna valz S x if 6: tz

ffiaut Ih!- Aa"$ ",5 d - 2A , X, A > o,u4 tf^a_

and, +o Fin/t t uLw &=,ogdrpL rcfinJ, d **n,.{;

1l@ bsb of nzdf Pw l*tw '5 < ts Doa,u r\1eg4srt, ptnz z

WE.I1!- plbairy toOtz 6a fha- cost ut| rvmLw,6 rwreL.,o6,> bo$

N'oF'twP-boofr)

.+2_ + 6 8 l o Iz

casbH 3o b o qo I to w (6o

Wut fha fb?h ot,A lronq.0) fin| ffie- bst of 'Sewr nnfr-' booKS.gil ftow

W rwLe loooK G"n be bo,tnlfcfoa Qt6s

3 SETS AND FUtv'cltONSt

3h5

f of Lwo se,tt A and, g , A ug- A y aa.,J, onfi 4 / y#';B1AI_f A

,Afi E ^ 5

rf A= f+, d, r,B,rlA\(c\tArw:

8 =fz, + ,rJ c : 1,,r,3,4, s, 6J ih?, f?e

A v ( s n 4. Au (sn)

C\B = f ' , z, s ,b,5,4 \ lo,n,4=f',s,sl

a\ fcrO= f+ ,6,,7, s"fi\ | t,s,t= [+,617-,t,q,f

MS]

v eil)

Let A= fo,b, " ,4

Show hnl An

A n B

(nn $n araf

t8 "

fq,Lqn fs,4

b,

4,4) r

o3

fu,lo,fql at

An can) = b!, ",q n le_,.?=tta/

q ,

= fa-) KOVUR SCHOOL,KUNDRATHUR,CHENNAI 600 122.

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trr b,e yvut4u dpndn arld'

f ' , ' ' 4 , s '$lt, t, r,, ' ,3

tabte /24?taenld a Suncf,bz A= ls , 6, S, t ol t,h9L0?z

-f 6 =z^s- -r - Vin4 fi,a Valuss S a, and. t

F ( t ) : z a . - lF G): zp)- 1 F (D = L(D =t

= 7 = t g

R = fr tD C^, D Cs,rD C*,DJ Le a\. ' . X = 1 r b = 1 5

)1"/aho4 anJ 1?nd )12 )'AiLet

qr""1fe-t fs " 6, lo, qf

Q = tt,6,7,8,1 , I o, rt , tz ,tz\Vu.n d:^Ann A

ez f o,g, lo, tg g= fs, 6,T1,tE * j

[nve) (ana) [n -e)

f wtffion F= fc,,O(.,O(+ ,)(s,D c=,8 wr?t

- nAAk &uz&1ouvs?6vau) w vutl6 A\(sn) =A\d ufn\o


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De mn6an,s= A ' f ) 8 ,

Iru()s q u4l erv'lzl*"L'b"


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A67E ^L?t u= f+ ,gr tz , lb ,zo,z4,zs l A=16, ' r , rgvafu hrd' = AlrtB)Aru.'

- - . - i .

AvB = fs,t t , r$ v t+,t6,zo,zBJ= l+ , B , t6,;o ,i+ ,2fi

Ard, B = l6,ti,z4z

> (,)a . . / lUrB) = v /AvBI

= [o,g, tz , 16, zo, z t+t ^E\ t+,gr t6, ,zo, 2 h_t^r ]={t4 \ l 5

A r , / t /A t = u\ A =f_+,E, rz , lb , Lo,L4,Lr3 \ fS , tb , z f i>( ,= f+ , tL ,Lo,z$

B = u \ B = [4 ,g , t z ,16 ,Lo ,zb , "E \ l+ , )b ,za rz= [. s, tz, z+J

n= t 4 , tL ,zo ,z$

,lrt

8

+)A ' o g ' n I a , t2 - , z$

) t ,u =fa,b,c,& , a,-f ,t ,r3 , Azfa,b,-f ,t an&

De magarb Lants ef umflennilat;s',.' =

A ' r t B l

= lo,b,f g3 , lo,b,q

, - . , - f ,s ,E\ la ,b,c ,J tc )

_r,6,rJ \ to,b,st={cr l , . ,nJ

ts=tn,L,4

(ArDA U B

A , -


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PA|Tt: ^ Io8,8\ { o, t ,E,J

,3J ,

{_o,t , c,d-, e-I t1?, fr fr td,,nJ n te ,h3

z

+6D

-f

JC

JL

)c-O. \, ,J

= 3 xa-/.a= 3( t i la: 1 5 - t o=6t

( r r

s r

( :

(? i.D[+

F

U\B

A ' r t B '

o ' " fD

r. f r&r8

>t,

: fr,- { |- ( L ,= ( D

( iDJ tD&) z_ffs) - sg1)

ls ,.

U)F/O= t ; - - )= z ( } l: 6 - r= e /

FD =sxz - t o: 3 ft+f_t o

= 3 (t6)n: 4 8 ^ t o= 3 6

3 - 3 4 = - z t /

Iz r 3l + , ,

rirt FD l f : ct + l

v- 2-ic4=z(D -t: 4 ^ r

5

(it re

A fund,b* JtD,tl rR iA dg?d aa {n))8,,r4

7?nL tl,r-

_r&

0 Fts)

F O

-t@ =tr)rtt)-3JFrD a z(ts)- 3r, ) Bo - 6 : ,r+/


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LU n= f6 ,1 , t5 , ts ,z jdt4"nzd,b f tD=L-B)an ;; ^"r;tff) a tubteAna:

A 6 E ^ nB : f t , L , h t s , Q a d . J : A - 7 8 b e -.qe?ruu',I

_f b6^fiD ^ set of otd^eszzd pai?At'*) a 3na7h ,

Nou.t, ftE =r^ ^/ r\

t ( b ) =f ( i l :

a F \' f l t , ) -f (tB) =- / \

+(a l ) -L - / -

Jc_- 33

6 ^ 3-

re3

v3,3

! 8 13

z t -3

L E A

: l

= +. E

= 6

, a . \

1 , , ) -

n o itrr) A Tab)& -

f,a 5 I t5 I E z )-Ftu t L 4 5 6


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?A 6, ^ l L

o ol 'Do br,)

o (,t,+)

o h,)o (t,)

3 6 1 tz 15 r8 2_t "+

z nltnbez qt AUrJzrt ta i n a,rto,rAAna:

A,% ortl,6 loatba/l?t% lrild Hoch7pt% 0,,,t6 Aiih eI

futn Ptfl hoo+ V aid, afia+*atuaA 4fu fuue y@ * o(Anen)=,

n(AuBuc) ^ n(D+nb)rn(o ^ n(nn} ^r lunD -n(ar)+=65 f +s+ 1L^ zo -25 _ts i l8

n(a 'anD

=16o 6o

%

6

5

h

3

L

I

n ( A ) : 5 sn f a ) : h 5n ( 0 : + L

n (Ani l : zo^ n (an) : z5-

n 6 r A ; r F

o'. /) (n, Br D = lo


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'Ah E ^ t3

ln ^ Aclnd et )toDo 6s1^afunb,2-0o0 knnw fbelnh,Booo kna,catul, anJ, 6oo krww llirtd),lfizo krwU fralr) aAd- Tarwt , Boo

knnw Tten'ct-t and, 1l?ndi,z-oo krwU f antl and' H?ndt ard,z 4 '' % sf tD?ze tangt'2arU

ltt) t1FLrJ MalW ft.nout AtlUAb OnL tan4tnp 7U o O

krwwhrwu'knn ut

Bort', k rwwEotn krwufuth KrwN

krww

Ff erL*lT arn4Jt|?n d,r

fteltch ar6 taillFten& M Ylfrtd^T a.il;U arl& H?nd,_

n [A) = Looon ta) = Soooncii. = 5oon(nnQ = tsoon [nnD= 3oon ( sn )z zo0

all tbw- tanyugU n(nnUt)= 5olt'] a scltooJ stululd lJ =t+ooo

krw- all b)"e- ,tl,nA Wg+r,a4u n (AuAu)i'e, n (arAvA - Un) r n(a)t o (c) - n (And _ n ft^O - rt[sn} f

=L0oo + 3ooo f 5Do ^ tSoo -3oo -zoo r l r tOnAn)^ 56oo ^ Looo= 359o

) Do nnt k,ww tu(/( the thr1ze larVta4rt : l) - nCeuBtrD

Atteat krwu

= ITooo -359o^

+5o studlrlbonz tanyagz : (,t (AvauE =35io stu&tt-d .


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8 . 9 In 6, SunJ%- of utivot;aiy Abtd.etuto,6b h,al ba"1uMa,th!,rnarlb5 u*,ile. q + t"oit bohu, on?uts> sduu- utD?ae',

-8 hnl fuat nalha'nal'r% d/d-na.ttA and em?LLtoL scisnu-,t@ and'/gata @u)Ae anaL

t+ hBL ta*vt il( ,hhz h"8 @t//7aa 'p?nd' tl''e' rtnmLatL p?nd, /'nn na/?6 h^a-A t*(u

0% n a,tlwnafrtot 6^ot tha e.0nl6 tumput,au srlet)cz pyhaeonb P)ga?u @Lhrae

A

^ . L 1

n(D : 5+n b ) = q +

n O a D BB2th n*tlurnabd and pW3^ bthaet n gna) = 2-BBOth fna,thzrna.b,A aid, compulu> sf,znczbae)n (nn)=2GSoth hn?u1a> ,.Jdzrcz- arld- ptt6aiu @uz)ea n (anc)= Lz

A lt tl'12- tD?lL b//u% rl (AnBn) = t+.'. ln & ttuU oS t,nivazbltd ALutarltb = n buerC

ntAvBv)=ntA) +n6) +n/D - n(AnB) -n(anD -n GnQ +n{nne;: 6+ +Q+t f iB -28 ^ : ^6 ^ 2?^ t t r= Ljo -7f= tS4 shtlut tO

HoJ tahu o nL brl)4a

- H6d, 0^.e- hL.nAe 1flk ?L+t6o122 =lfl l6 Stul,lnA, KOVUR SCHOOL,KUNDRATHUR,CHENNAI 600 122.

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ln A alle4z . 6o studu.td uut+lld. fl, ahrJnbty , J+-s fn Ffuara3o ?n b?olo66-"t5?n CIreniary arld,Ptg$ca ,)0 ?n?tt7a?a atdtsidog6-,o i n bioloy and, qrtLun;at1 ^N0 onz eruTDtted, in aAbrt?!!--Ffod- l'wto *% a]?- uhd)U ?n a,{lZaat onz- AuAied.Avta:

Erlno)led, ? rt Ctnhta7f n h) a 5oEnSwltel,

Ennpttea nrc) e L6on O a 3 otsoth En;d)d. @ ?Wra nfn'ns) ^ lpBotb Erlhn'ttd,

gobh Fruoue-a,: dgio'1065- n(Ane)ztod a',znLnJ nfun4a g

ErVLlfle& 1n aL( fh)!41- sui'*t O(Ana,lO ^ 0

".

Erlnpltei ?, n a.ttA,at Onz_ AuhSect .

n [Auov) = n (4 r rt(il +n (O ^ n (nrtB) -o fnnq= 6 o I + o f s o 1 5 _ t o _ , f aa l 3 o _ 3 o= loo Studzruh .

-n(Bn4fn(A/tanD

ln ^ toun 8,9-z q uu fapre speah urt,r, h0 y. s?qrA En4t;thvn 2-oz gpeah nindi - Atso, BLz spa* En#/;ah ar1^d, Tarul ,o,u.r_\ a , - o t , . . O OEPuh Ta'trul and, H7n41 and, l0'/. 3guh" En,t:) anA n?ndi

57nd" brz ?o?ne.nhf 0f pupte uyllD un utp*^

aLL hh!!-

I n o - , hwn = loo / .SePea* agion L 6er,S?eaA T arv;J : Es y.S?eaA Hin d^ > Lo T.

tsoth spea\ Tarnil aid 6#h ;g L /.Both iPu'\ Taryf,J olw 1l?ndi : L3y.

n f t U B v ) = t a on|A) = +a

n@ = Eo^n CD :20n (AnB) = 3Ln I n n 0 = ) . ?


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Both spuh E^d/.t, fu" H?"d^ n hnC = lDsPeaA at'( brz tlrruz larylladra 7 s- /

n(n ueu) = n (E+ n(B) +n(O-l oo =+o - l - 8E 1 20IDD : l4S - 5 f +a-l 0 o

I o o - q o - r cto =

"en(anao) = lo Z

ln a. vil,W tt tzo 1ryp112 ,43 yani,Uit uae SircuooL f oab:k,fr^+5 fatfr,tfu IlAe pivewood' ond, hetvsettz',L1 parn;tiza u/re *tro"o*wril aafriry p ,zr fatntltu ube- aokTrg W and F",t" uoo& .find, lrr'i"y uaZ f?rc-(pood- , kdtasdnz- a{1d. hoki,5 Jtu

,buAe 6?aelsaod, n U) = qg

n(AnD -nftnD -n (snO tn(noBn 43 z , 3 - t o f : c

CI

BothBothBoth

we keswsenl. n b) = 63uAe cooh",rgffi n0) =+o

Me'f?te11sood ad ftthesenz. f l(nn$ =)+S) S"^ n rcnA: z+re lpood. n(nn)=zZ

, Uae tuLr bu "ilO?le n (AnBn 0 = x

In ^ v?ttay in gamiLi,t n[AuBuA= tzon[nvsuD ^ r) tt + n td *n (c) *n [Anfi ^ rt Bnd - rt (in) to (a.

= q 3 f f f i f h 5 ^ t + g + z + f z y f ) ca zol - qb ix_: loE tx: L5v/

l eolzol2o,L

Ert )


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For % tD?4Q- seto A ,8, n[an6 = 6,,0 (Arril=t

E ^and,c

* n{D=t7,7tD: /v , n(o=/7,n ffin) =O and n tArtUt D = z Sflrd n {nu*uc

tn (0 -nhnD - r7 (sno - n [anD m(aou,i- 7 - 6 - 5 t z

nrcJ=u-n t )=6oo^ tq5= ZoE

a f - \I )(AuBu d ' n (+) +n tD= 1 7 f t T + r z= 5 t ^ t 9+z: 5J _ls=85

-" - r) [Autv) =25/

Given n /4 = LB', n tA = )qE n tu) : gao n (nu| = b/o,,r?ndn (n'n B')A rut

a [n,) : U -n tA)= 500 -zg57 z l 5

n (auilI+ Io :

n (Ans) =

= ntD +n- |a285 + tq|2 8 5 + t q s = 4 - t o48o - 4 to

70

A ' u B '

-rt (nnDn fnnO

(n n B)'n (n', a) ? n ( u ) ^ n

] 5oo -To(nn Q

:+30.," f)(AruB,),

+zo/ KOVUR SCHOOL,KUNDRATHUR,CHENNAI 600 122.

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LI

2

3

4

2

5 TF &z +bx*c : o h"t qu+[ sroofS ff,.o4 c. )s (n* , t- )4 ^ lEq"-! t"

r$ t= o, + c dh-sn

t$ g ,A

"d&ja.bE* p+easran ,il

{fin- ctn "S,{o n o n

glt $sf M g t$lg* -- l l-* tel i la^d,otr ,^,,hn &za;+1; Ai.r i&A bJ fr+ 4b^8:3,

t 3*)o''a' Ual *r t;e ct.c.d- oF 6'nns '. x*)

1 I * L ' cu oF # roR+bro*o5 u lhag KE^J - t (n * : aK tS)TI,e ture'e f ,oob of 4 (*-r*J+1")^

* (nns,

-C*-Jf)

t^ri*h- L ,#.ranb-a-

t ,

l + 1 * 1

O +g +t2-, +* + f

r,rr l.'.pt *7+ * -lx - Z cr.t

_?

+15*

: :cL

: t2-

+t+x + 5


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ptov a dti (t-,1 rA c\ I o.dcot oo l T ) - L x z + t r *pc rQ= x5

_6 r r+ t t x - Lp ( , ) = r - ( + n - 6 t r o (ru

" be $,o.1 sur'

"f U.,0.coe$FcfoLf '

" { O /,

6)

T1"4 ( x-,7 +3 a fo.do, oF pc-)S , ' . n p t i f 6 ' , ( x 2 * q c c -

bxz - tzt- ,6 x L + 1 x

= ? r - c z t + z )sxL-rr )< 3 z< tx-+)

' *

x. -+ .

r i , ^ l d ^a 6 . c ,D d f d r * To t t a

L t F iJ fl*ottut o.r).A oli ,i&/ bU z.-- 3

I i ; dg , * G ,c ,D o f

simpli l6 Elo-

-77 -+ 2o

(x'D *r a. f"cto tlasn+ Jo.tors *S

rc3 -r x +GF a ctorize :- 'xu- r, ; r '

^6 ero a;nJ"ri u, hvt 3 x - - 2 * n + " r - s

X uoJr,a-t'c en""h-,

2 t

31

4 ,

> s b . 4 d " 7 , 3 s b ' c s , 4 9 " \ J ,

De].r,*; dg..e ,-i-t" o t r o o b s o f d F . o -A l+ , . '* zBF -I ty\ : a ,

f o * l

O + l + l

-6

z / - / o ? c + 2 +

-3 -,o

+t -z

* , 0

+ +

^ -lL I L

rL+-l 't-

+ L ++6

I

D - f i

0 ^qnd T\n*csetrg'-.-ar- 4r A./i:.

+6- 6

OY

= x L + x - 6= k+z) @-*= (r-r) Lrlz-)G+,

+ - 6 3 o KOVUR SCHOOL,KUNDRATHUR,CHENNAI 600 122.

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.Th^^E'th"T7

ckov (z+Dr - a - l o

o + LI - f

t,! q :faclo,(x-a)

0 )t+\!n fo"t"ts = *-x- la: C2c-4) (r+a)

a3- 3r1ro,E' taar= (x-t ,*-+)cz+r)r n - n ? c + : , | L + , z x z + q x 4 , f ; n J d ^ ! s n u o o r s - T o o hS. lu,hon.

Ay-(uve +k polyaor"i*9 in dr#ff o^rdorq z h r l 2 : L 3 + z g r a - n r c + r n .

3 + Z + 4q * t z + 2 8 - n + r n

q("+Y, t t z +2 -8

4 t : - + h( ' )

6 + \ + +

o I fol ra,,r) 7'

o F t

+ 2 4 - n

+ ) . + + r bi m

+ r b

o

- n : 1 6

n : - 1 6 .

Sluor.s- o $

nn : +16

e c h - t o x ? f Z l x z - 6 o z + z L


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E ^ zz

+3r - 6 o

- { o- l o

+t2- - 6o+ r 2 - ( o

z ^ 5

T"r.- 6X urors- roo I

/1v

o [ + ) - r o z 3 aT t x z - 6 o x + 3 6 :5 t{rrt$.'-

k^/^/^-

s 1grasrs. yoo I o ! x+ -6xo+ )1xu- go = +a

t2- s r- +6

t (o*z:*-z^!E

(o*:+f-s+ 1

. 1 t

2 - \+?:(+ I )/

r i"J

,cl'rJ

F i^dhrv ;

{,+* =

s X t r e u o r o o t o f 4 + 2 5 2 " 2 - t a x - 7 4 * 3 n t 6 * 4

dfu st Lta'ts ooo t . [ +*1 + Br3 + g*+ 4^+ r (nr*,. r-

dfts .S?|dLa' Too I c [ 4 a 1 - t ; x 3 + z t * n + q r + b

a , " - 4 - u f + \ o n ' - t L q , - + ? LdL! Snus:in- foo t

6t

7)8)

12

l Q t

$ " J o r i z e

F aJor i ze ' .

z *9- 3xz

7 ' 5 + r g f

- 3 x + L

* 3 z L + z o

(n,tS = k+D(x-r) (z_r-ri)

aTuo,.o voo [ 6 "

b, x L+ - \*3 - f ,oxz_ or.+r_ (-a^oix+b p* t ?a z r l L x r * o , o

ra ' fo r i=e ' ,73 - s :c4L1o f r r , \ ex - * ) ( x .+=-+uF;"4 dn_o

: r z 1= q /

q xL-6x.+ 3 6

t * _79J

t1s

fru 4241 , KOVUR SCHOOL,KUNDRATHUR,CHENNAI 600 122.

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T72"

?,qaE- ^zlVETR

rl,a. nidqoint op llu l;rw jolnn, (a, -D *t rco,BD-

thz czrtttoi& et bu tnat7tz cu?th y@lf6aa at (_r,_r),(_r,,)anA, ( to,-D h ArV: (z,DAteo, s(t ttiand.k- fabmad- bg pointa (o,o) o,o) ant (o,r),M'. L sq,.un)h. V

rhz po?nl ? uel,fch divTdut(r, -) ane Btt,D inlavwfl

lfr,2 ?arallef -h

SL\W /,uu h:"t 3T -tL = O ?rtl.aaeda tl,re- X "azia alU

0qudiculall

Sind Uu(t ,+)

of tle diarutu>la /^ M [o,o)

+ tfu)ntÂl t/,4* ori$'t ard.) u/-7 =0 r) 1ru:. 3x-^zy ^ plirw y ^ z;r-+ lr ?aaaea tlt*,-6* tlô_pol* (t,)

of A b eqre( fA Arut O .61o\)

nL,

lrrrL 7y -zx- =tt ,b eynt h

q fuLab- b Ct,D .tJ Dnz end-b al (tz,$ ttzr) U.ra- oil,tût

nlL poTnl sf ffra: s d*&t jo?ru)a fih., pdrrA ft,o)ana,o -

/ V t ) 6 ^ o - t - / . , "' ,,wrutflt u t*a) l

=

na-"


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- N ( ' , ) /?nL #u Anlto?& et [TfW ughase valtcea ahz A (+,-)

8 [s,-D ann- c $,D .

= 1 4 Lz

G[*,t): (t+* &'ab r fu , +?.

/ , \L'o,D ,I3 anz,. (ttd 96 ^tkn g?nd, tl,w o th.eZ end.

r,y6 P,U)

o tl,ot aLJ po?nt ia (-,r,t)6?nd, lfu .dt ope of atmqnl[s,^D and Gt,E

l v l : 8 . - t t.x- -.-r/ - l

6-+- 3

z-3/" fi

, ^ / /

-

slfPe M -

Pro^?U tlu*W'Lhz Nlr


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STnL ltutl

fuE -26stt@ lt,u- p,ufE il,tuW

et br-qrdQ t,Thnse- venl,{uz dla_ ( i,D , (ar+_

,8, f 'xtt.*e,C-

pind th,a- eql^a,hnn ry theLW?r\,I'A Gr,D and b, ^E

;1nd. hp atze-a,and, (-s,^8"Arla:

11 tIlL N14o. et j/,/_ AAfu(s,r) B(-+ ,\ a,rl- c( o,n)

Avea-t

o

tlJ 6g q.utulb' And,tahert f n ot&)2, -lt z,

t!,!- \/erlta a-tu-

57nd -tl,e Vetrce_

b, +xr 3r * = ,r$

n / /z*l/

Atea' ef tnagu a = +ft- ,gr**,br, >cr u) _(,

= -

= l r :- T Uu* iE -to) - (-a ^ zo_rt- , f ' - tsDf

, -

.-a =7:!l*

lZ6 = 6a+z*1 3 6 * t z u , = 6 c r

+ l Z - 6 * c l . - KOVUR SCHOOL,KUNDRATHUR,CHENNAI 600 122.

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Shnw t|.,et .A^/. pointa A("8nA:

Atreo, q A AF,c

{1,.o) aiJ- .(s,:) auw_ bt)?npdb.

- | r^\

z- LUJ

7r* 7o?rtt NL.L 6p11irceilt

e.uaealafuial 1pltase- Volbi&b a)-e- ?s,D,frnd, ,Aa(-0,-u) (+,

Atree % awU*taleul

Tind bu ill^ q, bu(s

,-q) arLd, (^5 , -Dvet*o't q ttian+ta ttlns eA)wo, tT q,"uruh ,A.u pfn)

JotlneL b4 poirr.A ( E, 1,

[o,C ( +,,8 and (e ,r]) artA fu;U"4 va//.tz- $ a" u e

= *[t-, s, tcc, y

Ez

l - .- z )Us +s+ur r )(

l f- z ) ( s s ' ^ ' i

c' ) 'L-;DJl r ^

- - ; l d 6 lL t _ )t - )

_ +> >on.utu.Cletiae- Suma

.t;uat6n-


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)JS-IFvI/V

/1J-

L

) e ' , ; ArB =C ]tA!/"

fhen fhp- nu,^teH "f ,I*, 3

(u* ' 6 )

?A nr -28

L x 3

IF

BN4 " 4

a

u8

rf otdaSL 3 x+ *J ts u3 ovds?L 4x J , JAp':, df* atdah 4(n* : rf* C

tr *x (f = ( i ,) ttan the or d-elE e f A"d [n* t t ^4

(ro) ,

dtwt dftc vahrc- ,j f -s [n * , - r)

r )z)

( ?

B ,a [n * ,[_J

z t 3

A - / o r r t u t 7 q " r 3

\t l\ a Z t q z z q Z Z )

= l " i - 3 i 1 , i : t r z l i= l z ( , ) - 3 ( r ) l : l z - 3 l t i - r l 2

- 1 2 c , ) - 3 ( ' ) i . l z - [ l : i - 4 1 :: lz() - st i l -- (z - q) : I -r]

A / sof n

Tuso moak q.u.llthor,..vl-1.e -1A..tl\^,a -(r&!\./W-

Conbkw* zxlty or.,t : \zi - :1 Io v rSol"fr,m :

at& t t

( 1 2

of audoL nnxn or.,J0tL B *,l5 Possib)e

J A nsu;ex-g,'.Ur,a v-la.^^dF/16w@

| , r , - l \ t +-rno.lttx At lo^f \ UlhoS el.-!,rr\snj4

B '}J of s6 drl P *1,",f {n nn "- m=

t \ \- + J "

, ,il;Lt;t''\

? t n : 1 t i

Gf\s ! ruertU

2 t

4

- l' ' )

4

,

+

: J

=lLr" ) - sC) |a l + - 3 )= l t l= lt l , r3


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z ( z ) - 3 c 2 7 l = l + - 6 1 = l - z t : 2 ^Il z c z ; - 3 ( 3 ) l - - l + - q l - l - s l , r

*J c h'f

= S ;

: . A : l r 4 7 )t r 2 s l' f A : ( 8 s z 1 r r - t : - Jtr -3 ,* ), fu $tad. n-5, j *h'u.t '

A : ( t s 2 )\ r - 3 4 /A T - [ e ' \t ' ' [ < - 3 I

\ ; t r /

r a r t T - [ t 5 z J\ f r - [ ' - r 4 J^ , f v \ 1 6 - Z x \solve : l 's*l " (.r] .; i )

t F . '< ' l , l ' - + t r--

J { t i?r_r{. t r j

l Y l l 6 - z ^ \\ Y l ' ( . , r u v ff : 6 - z r : > X - 6 + > a : o

^ > 2 r * 3 ' 6 = a3x -- Zt+uy :) 3 x-- Br- g): o

: ) g x - 4 l - 3 t : o

- r B - 6 z

a ' H : : 4 KOVUR SCHOOL,KUNDRATHUR,CHENNAI 600 122.

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) dfr* i;^l ad&' l ive in 're>de o{ A- tf \

- l l

\ r

L \- 6 /

[ z x + ? \ - / ' f \t r c - 3 r j - ! ' s /

,A = (;;o tndo['f.re lnue.ue*rqr[ (.rr)c, -r)s i*l; .

[ -6 r )c ' -1 ) , , ,\ ' r 7 r , \

[crrl ,, c-r) x ,ilJ- f t z - a z \- t l

\ - 6 , , /

e*9#"'-* ..lgs.j-

' r 1) f" o \ = [n o \ il&r, ttne vil,o1 3 s / L o 6 . ) - \ t o )

5 r

o J t r f ll 7

Z 7

3, t1,e/1 zlz or b-t ol ,,-)ricoa ^ = fu) Then [;J rF q = i )

golue J.v *-*J $ ; f


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.seIl r q ' !

A - I ) I"

- f - r h

Btc) 6, Bo ,io zz , hr4 U"e vaniaa y_0 j: z'8 ;1, ++ ,6L , 6a ,A A,"o.:-..lzga; b ;A h''e aLanaped' aurrrr*ion ry b,6,2 , hzrt ,tfu 'bad*u,d l u ? a h o n x t 6 . v + r " ? r

'7,5 , &+5 rzts * i W,trvreaft 6'rd atan'&z'L dr,u?ahon ry ^ dazlq Nzz- +g and tLT%Pec.hvelr* "rhe Co -e-f:?atnl

+ v Nlhden )a Arut : zgC,rff;"

^'Colreohan q tt ?ternU , LN_ __tzL , il,t4 tU ^ntln*&

A r t a : t zVAfLi-arcL $ c\ ;tia-s& t t rta/ uh*a,( rLutna)^ *4 .fur_ ! a'TwCI rnaSils AWttyoru..

ah,a TarW Dp ,h,Qc i

t1 t2 .s tzq ia-Y iusL ln P f r r r * rwrnbhA z ,3 ,s ,7 t r ,13 i t . .

.Ant: zt

L

'aLe -btaqdatzd- daffia,bw4 c5 3?ast lB 66atuth-f

SLattJ'an+ d-eu?atian ( f)


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o f pirs I lo rt atunal rutnbelz

S Lantaa-J J-e*?aho" (t)

_

___

^ \ 8 '25. T r ^ n r . , = z ' 7 Vt rLp- I ahau t va"r,ctp- i rt A ta)rec.ko n a; da/^ )) 7. +4 . r-ftV targe ,i,o L,z6 , tl,erl Jyd thz Srna.tlzbt Va,ttue- .4ro:_

R ry , Lagzdt vaille_ -s rn a,Ll^ut vah,e.+ T"b) _ srnailllt Vahlz_ =z,z_6

sma, l l la t va l tn-= 7 ,b+ _2.265 na;* ?arat = 5')8/1calaila.tt bu ALajldabd da.ufatipn 0J; fn t rowir_ft da.lq.l o , z 8 r l r , B , 3 , 4 ,Aru'.

X X.3tIl oly

LO

1l b6 4

l n a22-5h o o

5.=60

f i = 6

= I n'- t

-f,,r;V t u

I L


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77nd" HrBo5 liat I a u?g dfrto7Uu.t^;"

I i s tz l t z \Lr l - l\ j 36 t 3tu)-

\ I =3zg ,z_\l

.----

1' 1 2 -

135,h6 * t7o

v- r L> x^Bz f L . LJ;d,7oTt78E861o

I

35TBlz-

I L

- 8* +

0hE

- l L

-L+

- 7 0

03 Lq 6

l + +l q z

8 0o

l L 87 6 5

Ls,t Lfd-=lz

32.++rf -tu e h . 7 l r

r-\- r / /{ KOVUR SCHOOL,KUNDRATHUR,CHENNAI 600 122.

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.E

xL5 ,

9"ff.o8n8lLlry-

ri 0 ;" on ?nfossibte e,uenl , tlun F(f) _ Aru: aPbcbah:lit& of Sww_ e,v erll *{@ ' I7 6 s b Atz sanfle spacz a5 a_ ban-dontlun pD= Arta: q

a- tandon epa.+rrut( ,

l\ffiffi.q twTi*^^'t?tt scaae c-eato,n 7ncturL{utn 1r)

fu + TL ptohLi tryf H'',at l'u u,fitt rwt scfre.

-T r'0 rp d''L af,Lz Hh ., hkda-, Tr,p- pdobaart ;b

\ Tttrff a dnubet *4 g -l:*a'

lg A and- g ffizz nutua-lh: Ud,ua?v< euuub and.s ia L)^z Sa-mps s?a: sk*h thet ? tu):J._lrf$ ar* s : A ug , d,.etj [> tn): AU

,*

_rLet A and- B arLA twp e-u*tts and s be .bl,afot}%?"fu^:fr," spau- . Tta- p(Ana):Aru : p(B) :p(nnet5 /\ aqLd 'ts Qfi-'- LUa ev en4 srdh tla,r p /a) =[ ' z s

, p b ) = p , 0 5 e n ] - p ( n n 6 = n _ , , . 1

hu f) . tL ' " ' . ' " / - o ' 11 tL*p( auD=1"2 Otd. hmu h1 -?rr e,br?)

"u.*o-lt r:

bandan e-xpez*vnt T%u/-bl a - / jvg swea444

.L ,r,ffiL"{ P''v'','n 'a'4' {pb obabTlrt b5 s,t-c1p44 h au %T i::'Ytra

that A,k*? #m- hsvtt ),.a.uev r J-6taagA gb 5s sat -'^a & s/r


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'#4

TH,T73s = f l H ' H r ,f)f$ : t1

)-et A be brzA'[urtTHrHIS

A / \t ) Lr ) =Let be Hr,e

0 (A) =31>{n) - n / n ) 3 ,n (, 4-r

&ond an%. onzH4. pbe babT r'b

ie divisibte $ rlD"

= l Spt SpQr,y q c,L,oesfg a-atte W ,

A fn'5 = J 1 , L . 3 -( ' ) -

n f t=ba' . . / o r l

^ r *+e/n {n) : lc

Twa uira at e- l,ottU l%ttADL, ushn| b flu Tbobbi th6oJ: AUL\U at nast onL i1,ad .

W*1+

l L + 3xr ent

Ptil = fi(a) I1 tznz mi'xd U-'.th tz

brdan . rtlla,t .)0g clna"T6 tatten %t?

A trchet A dhac,,, ,?r( a.b,:"? The_ bfa+U alLe_ ruLru

-4J3 na,udhpA . uglwt jz

-t U Db.hnA?t?/t,u,tl? A ,,uwnben ^divfsj bt e_ brJ',2'!*7/rb' a5

oi Xlt7ry a.t mnst one Az.^d.V Uf i (A) =z

n : f i c , ? & , 3 0 l o n KOVUR SCHOOL,KUNDRATHUR,CHENNAI 600 122.

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fl7 "

5- rnNL t

Ana:

" fr,r,rTLt) ru A Le uu

t;D rct c be tlz,c = { t ,n ,b t

P(0=n(Qrtft) =

I.4xt & ftetil cilL t^r1 tt yt e{)d-etfu i^ a-25, tM ,i:Doba"bf),"U

4t aQ atu) and _f ov ?_f f c"A11,('A

o,s5 o,td. t\a_ p,T;-p^AiFf#f L,,at ? h kt ? )r aeb 6ath *he- ar.u ariJa ;a o-tb-

eL/ett % S*tirg azaq ore ta,dIt (D:z

4 =! , /

H,T, T Hll n fs) a l- ,,t_I

ttoo Iwa.A A=0 {fr) =t

PrA) = nt4),6

: _ l , .r/

{ u,Beuent of Nt?U


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p?nd il"a_ pbotubilit6 tha,(()it 1rfil) Aet uttpcrtt )nz aj Lk- tua a-uad6b{)it u?tt y on fu- or1-L aJ ttq- alndtJ)Arrol

A- y ry auas>JB - 35?*a kte o( stu)

?@ = o "LD ,j, fD = D-35 P fena)= c-tCD ?rn ud =?@ + p@ ^ ?rnn)

: o '25 t 0"30 - D" i5= o , b o _ o - U

'(n) *?hnrt + ?@ p(nnfi= 0 " 7 5 ^ o - 1 5

+ b , g 6 _ D . t f= D - 2 5 t o . a 5= D-go/

Et',uldrle sww,

h b a* et tontatq 2 p o?ple+ 67/Ld la oD a"WJTu.t Pt ,^91,;eh 5 ^?PieJ and. g 6b anpt anz Vetl en "TJ o- P e/ao n takas P Ut orte- J y LuZ a"t ba,ndafo,7?nJ- H^!- paba$ /?b that bke 5zuu,t ,4 eitl'e.n04 anl e oT A, ffnA Jr dl

" ,5 Ha,agrs Anaen anJ

b d)za*ttn a* TenJa.ry -h,a,t tl

'Aht -+7

t0 ttrl ertAuhaLiyn-

rnoak attrllti on)", -Xe ToLd SuvlacQ awa ol a so/iJ fu-,*splrsye of olânVLav2 c:n is equa) toM: ' 3 f t c rnL

rhpTorioS of U,LRa?ecftva heg]Ls and he Ru?a-citve roJ';of Tuo cglidprs a.re li2 ond 2:t ?uVectivelg Tlêr1fuitvoluâ ane in Potios

Surface Cmea of i oo SP/1PYQ) aYQ in ?qti6 of q I 2Efl'ê-iv vo(urM aha itt ctra Rafio

&D: 27; t2E

tlL

I

rf Ae. 1. S.Ais equal Lo

" -

SfLcr3 '

I thp- c,tteq ofCllyn Aa volwra

, - g6 Ttcm3 '

Monk Otrof iorr; :-;nc[ d,a volunB- of

3o oztlophtI

ol a solid lunuspluve ls tzft cmL, TLun ibs c s /

lan;sp/^soe arc a of SPhsYe6F sp L.srE is equa!, to

Elindtv uhosa radru,\ is thw *J

volrru of solid calin&r ,v = r-'v'h crr'uruts-

'

, C ' - t + x / { x a b

= '['rxlQLX 30

q-S B 8o tT un"

2-r S 3 6 t L C m


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md,a and sIMt L*gtt oF R,TI,h find U,a. C'g.A .I rn I ' -

circulah. con0 A-nA I3S ctrn anC:I, 31Un

Y= 35 CrttI-= 37 ern .

f l ' E - a

c . S . / = f t r . X s + ' u n r L s

= #x 4s x31

= 22x 5x377

c . S . A = h O T D C m " .

if tlrP- Ci'rcumk^tetf,e Of

t2Crr1 , find' a^! c's' A '

@ :

S. fun'r; sPl'ur'e C's /

slarrt Aeghb is

civhperarlcQ oF col.ro: 2iLT = 236 crn

fLY ='9L

f t r = l l 8 c / x '' c ' s ' l

= f t Y l s ? ' u u r s '= l l 8 K l 2

c S.A = thtb u' l FinJ rs /

m g - c . s ' A o f a S . h ! . r r u S p l r a r c i s z 7 1 2 s % . c n ' I t w

I

a conj'- is n6cm and

= 2 f t t - i - 7 1 L

Tt', ' = l3 86 o*= 3 fvtL sg,'truES= 3x l83t L- sl 5g crn

( :z)

?.S. A


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]!\4 Lo etdl oP a frulturn

of a corw hh en

ct^ T\^-rn dnpt| rs thu'tflhw )f ts pind 0''p- vo!*a

f ^ ruhtum of voiu^e = )4 x (n"*t'+Rt) cu'cutits-(v

=8 Afrt = 8 . \ ,

2--1- , ^ t u t l

ondftL|etg [-tr49:-

,l oluira ,of fru.ttum= + -',rh (n"+rz +frt) cu unic s

=!* +. ,4( 1L+C.r ) 'n(zx I , ' ,

= L x 4 4 ( f * U D ' + t ' L \ )?

l , t - , ' \

9 ^ 0 ' , q + 7 q 4 + t 1 b q )

le strrn4:'

iht T,adl ol Luo circu,tan endt of a ftugun sl"pnJ

uckd oJle tecm and yan' Tl $s AL?Lh "'^ 6zun, F)nd Ala'

aWiL! of Luckzt' in l;tro5

B crrr and L.-t-gllL t2ut)lzadslroK each ofbe mad.!?

t

r S

Frurrtturt = lh08 .570n

4mn1 - How nntyJ lead Shoid cart

no,{in's


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7t,

b'orrll-

In a fgme,L,p Ag - ro5'

flrtn ;3JPT =P

- , 4 -

A M , - / 5:

' t f .

I ? , = L E ,l__u

e r

L C = 2 F , A * nfn ttiotlle)M". AB =

D E

IABc Md o.F ,

vfF

in fura ratia 2"3 ' d''an:lrrlsi&^ af turo sinuliar tfian3le) anerta\y o.yeah aJTe in fahi o

&' . - 4 "q

7n ch! aoLioirurp'nlsrceVX at ? Ll

fi9 unecLordl AG aAd, c0

t 2 w

a stvaighl linz iMsvczPl'c*d, E w)?a'ctiuulg ' wtd is

_tqAts.

and Ap>?B, dron

i nD

1 1 ) : .

A3= l6Cnt ,?D = Bcrn

AP=, ? C = b c n

Yh!- )';rwPonelle'l

c

AB anlb o B C ,

vc of AAB c

aLan -E =h L


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Two ManiLi.or 8m','rtAaa

pare\lel h DN

0f a- TriwYte Tnk'e'rsechn3 thp' o,y' two gid'u' hln

sido'tLs tvid!'L

) ^ lo$on thsoran)

'l ^ lP rh! SLttcska oF8d iriangt -,e a r - A H ^ n n t t o

is Q+waJ' Lo ffiL surn af thL sguahe) ol: ffie- othtv

Targw ,MIW- ,_ ,, _n ,,^,, ,AoAL(otucircle),# \^'

ru: ,(= af hom t)â oninl of unI'acl' :,' ::Xrf':Û",?' ,to,f

',: ;,:;,'r' ,

crr tê- cho'L makos

urih tLa tange,L t;ru A -rl:l :1rYUYIuir\*T ,r

ttr.i*, in fru. corre6pondins oJt'eunaLec,o arY\Lnf S

v - ) '

Let?6 che fangents ': a circt ot n and 13 'a cl''ond l& C

be a poinr LBA. --s 4' ond LBA q= b2o atn

p ind I A3C

AT2'-AB ) cAotd?0 -> Totgwt

BAa -- L ALB = 6z

L J s A c 4 L A L B + L A B c^ o

$ z + e \ + L A B CLAr.c.L AbC

A1! UWtenwiltto SiJo) '

= lBool 8o

l S o o - t t bo

= 6lt


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- n 3 / -

A& vdw- of *

P n x P B = P c x ? Dh x : t : 8 x 3

X= Z\ '

pind u-,-a- v alv!- of ec '

f ) Al r r xPB =P CxPD

4*4 =(z +r)x z

z + x = 3 62

2 t L = 1 8

3a--_ 18 -2

2 = l b

r A Dn A A B c , D t \ \ 3 c \ n d

*

Tn A ABc , l r \ \ gc

.T l AE= z '1 m ' Pind E.c

2

-"8A I " A E

E C

3 . 7E C

2 -3

lrhrbi['''oowfl

E C = ; . E g h 1 .


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Attt - 53Exoradtte sutr.6.

-

ln A AABc , Drtrd- E Ffrflh art S?d*0 Ats rmd A cTtxpecht've,fu SL{h t}"^t DE lBc- .r F 4D: 6m, }8. gcrt andUAr=SW thln 6?nd Ac

CrnUe_ A Afid, B ah4' a r t | L + T E = r y o

A tvfaqt ln c*nileV L 7 = t r u n , A p : g c n

Arus : L

Ar4_: l

L

{-n

J .

'L-

) ,

I

+'?' ) '

Ae cu"d- c D NLa_ tto a clwtda 0 FLttwu i#etaect l ntenn t,

?B : zw tt,- pind, ?D *8 at P '

AB ^ '?4 cD fiu twn r,jrandq 0f A frauz t 9h;u ?ntuue4exbuzruil(1 p1 ?,rJ Bp=3un , (,F,6trn and (D-=z(rntW r?rtX AB'ABc"D % A euad)f,ta"terlal s ttuc| th,at a4 0(f {tb Sr,dp)t,ouch k a"at rj As: 6w ,BL= 6"5un a.nd c.D:Tan,than '|ind

"U',p ten6h D_f AD.n,Ininnvar',FTRv_

Arw rvtasr"h n u zt: :sln'zt, f mt ,o -I i ^ , in'.D 6sec'S :( , - (n" t ) ( r+nt t ) :S"'n (qo -S cos & + ks(qo _D Sin *)c-- ^ Cys& y=b tart * tW #

i A n t ) q- , F

, " L-k ; Au'


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6,7.

I

{

7 .

l t , a t l ^ f f - . l s e e ^ & :

Cot* x - s in4 x( t+ ba'r fi. s?nz *Tt;:o fnaWrpTovs tfwtAu',\-

.nSin gft$eP P

Cos &se-c & = l

II

(ns e flw *, n g. /,-2s , i; - ) tl.* edcv r.. .

&,,:t ^ veMiu-g L^.tc,nd, .Tlrz_ ;aot o_f the

*hom ] l ' ,a l t tnJ l "

r i r tA lLa I a-^ lh t ^ r r -Sbom ltd ruCt " Sirt| tl-e tW U ,o"tdorcj hlaen = x-

ANqq f Torn tfq uLalt Bc Zu /Aac Ccs aaa = W-

.IIz

.?_:

"-\_*-lj'e

,Wfu ti tnddm iA 7 M. KOVUR SCHOOL,KUNDRATHUR,CHENNAI 600 122.

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l - M s 9l+ ensp

Exud"ue sulrul,'pTov e tlra,{

lb ov z thet

ftL:

bd u7rua -rL+ ta p o;a.n 4 rnahe e4 ry 3oo

t'oez- touclW tI* g*tutdtlran g?nf #r! o,Clun (

= (asec & _ cot p[ * tp+ c*6e)= t -ss? f pu i *

f1

l '

ot nnA^

A llen'txca-.l ttez, ;A btohqttle ftez [auc]lu> btu groun-AL,iLl. 7t ^ sg t),L top 0j tl.etson aua(J fbctn ifs yood,I'W o|"h* buz '

Theal fuuclta ftv 6nualn r?gu A Aec- hs

f ta: 3ont

300= pg

Etohu of ( tu f tc =x_


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fr,i,t E ^ln t$t AAB: t ^t a,rt 3oo

3o- w

50: 3 c

-6: lo6

_: Z or{i/e :A scc & +'A ban & j 8= ^ tarte f bsec B- it -. -z ,,=(^ d?,)OVC " ' ()

- -'' \''\ttL' 1- u J(c (>" Syt0l J -,3

dro:l -" l t .s =i: i i

= ('a .SBc & ,+r- e ^ - ^ \L; ^.(, ;:^:H ,;;:rr uu,u)L

: cf -6a --' '

-J * b (Lan^O : tu.'n): - R" i l -s

u , L" H^s , R.l^l_ "s !1 encp , pyod .

Exenti+e cr t m,\.

AUTHORS, XTH STUDENTS, V.RATHNA KUMAR A.KUMARAN K.PARTHIBAN U.VASANTHA KUMAR

REVIEWR, S.MANOMANI B.Ed,M.Sc (Maths) B.T Assitant Somasundram Chettiyar BOYS Govt.Hr.School, KOVUR,Kundrathur main rd,CHENNAI 600 122. ALL THE BEST

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