Download - 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.
www.rejinpaul.com
www.rejinpaul.com
-
6ap a
orn jta1u4U-A-
6aut q g.hdr_ ot
Point 7@1 q,w%-
fo 'fh!- ()J, d" anJfndh .t-,A,tlrb (tett$h of Eclr\g: h j 6.gcm) .
J;ot"ntU Loun- Ftom * poirnt P / 13 Cn ajtry fnornrh-a- fuso - +dl\truLt> ?A Md, PB ro ru Urd!-, ^d1-#to
cKe- a loirtL NIucA i5 Tn a,^r)TJ fron o oerlLre of fhe. Ci rdt_ +o,)iu sun, anJ Jnar^r rh!, fr,,to tatt6ettl io rnp_fAdL_ fnon nAL Foi^,b
/!?6*" cgdic qttadnilomoJ)
(,o,tOtuuct a c64ic q,-sJil-ta6^l ntscD in UL*cl. AB=5cm, f r ( = 1 U 1 , B c = b c mand AD =r+.?-un
ru11tuct ^ cgd;c q,rcJ*lotelJ paRS rrrith ?Q= r+Crn,0 R = bcm, Q s r)cr4and PR- -7 '5unCon+tauc,L a %&. qJt^Jil-l"J-
"rrrL Atsco ui krr AB= 6vn ,%c = 5' I cn
g?c = Bd an f , f tD= Q,sun .
CproY'tucb a. qrLc qp^J:r;lalpna F F&Fl u"rifh EF =5'L(tr1, ,/Gtr.= 5D', FG =6banA /EaH = 4o'
&rrVff,u.t q q&c
a , /ntso = B5 ,FD: L ,Lu,1 uf , AB l l cgtowl a C,6drc1^Jiltr,i l PARs,uljfh pq=6.sc, , 6-n --s SUn FR=7un, pJ:? s
'-onttut a c,rP,ic qryA)ilafuaj AWr: ff"v.rt t|ts= Lcrtt , &ELr 7D' Bc = gcm
/Aco: jo'. v
eu Thz two EargrAb frorn a-Conffie of a, ci\d!- of ra&.,u
f rw- can@
point u-tlucfi is bun adad frombun. AIbo, nL.abna_ fhz- W
KOVUR SCHOOL,KUNDRATHUR,CHENNAI 600 122.
www.rejinpaul.com
www.rejinpaul.com
-
{ 2 3 5 6 l oa I It 2 0 ht- I+a
2,hR,+PFls/V144r'\,#.*
alu ^ Ahe^ f,t th!- ftLtoaifr tubte ^ l ietrLtiry ftw Vatu"frn
f-iQne, Findt'tw va,l,,re {t "thn ,L=4
D6ap .rhe ffih ,fro th!- a^b"ve .talle *J Lpnq *J fin|IttnL vil'z q A if ,x=4trlna valz S x if 6: tz
ffiaut Ih!- Aa"$ ",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 $n araf
t8 "
fq,Lqn fs,4
b,
4,4) r
o3
fu,lo,fql at
An can) = b!, ",q n le_,.?=tta/
q ,
= fa-) KOVUR SCHOOL,KUNDRATHUR,CHENNAI 600 122.
www.rejinpaul.com
www.rejinpaul.com
-
trr b,e yvut4u dpndn arld'
f ' , ' ' 4 , s '$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
KOVUR SCHOOL,KUNDRATHUR,CHENNAI 600 122.
www.rejinpaul.com
www.rejinpaul.com
-
De mn6an,s= A ' f ) 8 ,
Iru()s q u4l erv'lzl*"L'b"
KOVUR SCHOOL,KUNDRATHUR,CHENNAI 600 122.
www.rejinpaul.com
www.rejinpaul.com
-
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 , -
KOVUR SCHOOL,KUNDRATHUR,CHENNAI 600 122.
www.rejinpaul.com
www.rejinpaul.com
-
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+/
KOVUR SCHOOL,KUNDRATHUR,CHENNAI 600 122.
www.rejinpaul.com
www.rejinpaul.com
-
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
KOVUR SCHOOL,KUNDRATHUR,CHENNAI 600 122.
www.rejinpaul.com
www.rejinpaul.com
-
?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
KOVUR SCHOOL,KUNDRATHUR,CHENNAI 600 122.
www.rejinpaul.com
www.rejinpaul.com
-
'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 .
KOVUR SCHOOL,KUNDRATHUR,CHENNAI 600 122.
www.rejinpaul.com
www.rejinpaul.com
-
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.
www.rejinpaul.com
www.rejinpaul.com
-
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 = ) . ?
KOVUR SCHOOL,KUNDRATHUR,CHENNAI 600 122.
www.rejinpaul.com
www.rejinpaul.com
-
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 )
KOVUR SCHOOL,KUNDRATHUR,CHENNAI 600 122.
www.rejinpaul.com
www.rejinpaul.com
-
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.
www.rejinpaul.com
www.rejinpaul.com
-
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
KOVUR SCHOOL,KUNDRATHUR,CHENNAI 600 122.
www.rejinpaul.com
www.rejinpaul.com
-
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.
www.rejinpaul.com
www.rejinpaul.com
-
.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
KOVUR SCHOOL,KUNDRATHUR,CHENNAI 600 122.
www.rejinpaul.com
www.rejinpaul.com
-
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.
www.rejinpaul.com
www.rejinpaul.com
-
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)nt^Al t/,4* ori$'t ard.) u/-7 =0 r) 1ru:. 3x-^zy ^ plirw y ^ z;r-+ lr ?aaaea tlt*,-6* tl^o_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,t^ut
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-"
KOVUR SCHOOL,KUNDRATHUR,CHENNAI 600 122.
www.rejinpaul.com
www.rejinpaul.com
-
- N ( ' , ) /?nL #u Anlto?& et [TfW ughase valtcea ahz A (+,-)
8 [s,-D ann- c $,D .
= 1 4 Lz
G[*,t): (t+* &'ab r fu , +?.
/ , \L'o,D ,I3 anz,. (ttd 96 ^tkn g?nd, tl,w o th.eZ end.
r,y6 P,U)
o tl,ot aLJ po?nt ia (-,r,t)6?nd, lfu .dt ope of atmqnl[s,^D and Gt,E
l v l : 8 . - t t.x- -.-r/ - l
6-+- 3
z-3/" fi
, ^ / /
-
slfPe M -
Pro^?U tlu*W'Lhz Nlr
KOVUR SCHOOL,KUNDRATHUR,CHENNAI 600 122.
www.rejinpaul.com
www.rejinpaul.com
- STnL ltutl
-
fuE -26stt@ lt,u- p,ufE il,tuW
et br-qrdQ t,Thnse- venl,{uz dla_ ( i,D , (ar+_
,8, f 'xtt.*e,C-
pind th,a- eql^a,hnn ry theLW?r\,I'A Gr,D and b, ^E
;1nd. hp atze-a,and, (-s,^8"Arla:
11 tIlL N14o. et j/,/_ AAfu(s,r) B(-+ ,\ a,rl- c( o,n)
Avea-t
o
tlJ 6g q.utulb' And,tahert f n ot&)2, -lt z,
t!,!- \/erlta a-tu-
57nd -tl,e Vetrce_
b, +xr 3r * = ,r$
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.
www.rejinpaul.com
www.rejinpaul.com
-
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-
KOVUR SCHOOL,KUNDRATHUR,CHENNAI 600 122.
www.rejinpaul.com
www.rejinpaul.com
-
)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
KOVUR SCHOOL,KUNDRATHUR,CHENNAI 600 122.
www.rejinpaul.com
www.rejinpaul.com
-
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.
www.rejinpaul.com
www.rejinpaul.com
-
) 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
KOVUR SCHOOL,KUNDRATHUR,CHENNAI 600 122.
www.rejinpaul.com
www.rejinpaul.com
-
.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)
KOVUR SCHOOL,KUNDRATHUR,CHENNAI 600 122.
www.rejinpaul.com
www.rejinpaul.com
-
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
KOVUR SCHOOL,KUNDRATHUR,CHENNAI 600 122.
www.rejinpaul.com
www.rejinpaul.com
-
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.
www.rejinpaul.com
www.rejinpaul.com
-
.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
KOVUR SCHOOL,KUNDRATHUR,CHENNAI 600 122.
www.rejinpaul.com
www.rejinpaul.com
-
'#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.
www.rejinpaul.com
www.rejinpaul.com
-
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
KOVUR SCHOOL,KUNDRATHUR,CHENNAI 600 122.
www.rejinpaul.com
www.rejinpaul.com
-
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 ol^anVLav2 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 Tl^er1fuitvolu^a ane in Potios
Surface Cmea of i oo SP/1PYQ) aYQ in ?qti6 of q I 2Efl'^e-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
KOVUR SCHOOL,KUNDRATHUR,CHENNAI 600 122.
www.rejinpaul.com
www.rejinpaul.com
-
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
KOVUR SCHOOL,KUNDRATHUR,CHENNAI 600 122.
www.rejinpaul.com
www.rejinpaul.com
-
]!\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 $s AL?Lh "'^ 6zun, F)nd Ala'
aWiL! of Luckzt' in l;tro5
B crrr and L.-t-gllL t2ut)lzadslroK each ofbe mad.!?
t
r S
Frurrtturt = lh08 .570n
4mn1 - How nntyJ lead Shoid cart
no,{in's
KOVUR SCHOOL,KUNDRATHUR,CHENNAI 600 122.
www.rejinpaul.com
www.rejinpaul.com
-
7t,
b'orrll-
In a fgme,L,p Ag - ro5'
flrtn ;3JPT =P
- , 4 -
A M , - / 5:
' t f .
I ? , = L E ,l__u
e r
L C = 2 F , A * nfn ttiotlle)M". AB =
D E
IABc Md o.F ,
vfF
in fura ratia 2"3 ' d''an:lrrlsi&^ af turo sinuliar tfian3le) anerta\y o.yeah aJTe in fahi o
&' . - 4 "q
7n ch! aoLioirurp'nlsrceVX at ? Ll
fi9 unecLordl AG aAd, c0
t 2 w
a stvaighl linz iMsvczPl'c*d, E w)?a'ctiuulg ' wtd is
_tqAts.
and Ap>?B, dron
i nD
1 1 ) : .
A3= l6Cnt ,?D = Bcrn
AP=, ? C = b c n
Yh!- )';rwPonelle'l
c
AB anlb o B C ,
vc of AAB c
aLan -E =h L
KOVUR SCHOOL,KUNDRATHUR,CHENNAI 600 122.
www.rejinpaul.com
www.rejinpaul.com
-
Two ManiLi.or 8m','rtAaa
pare\lel h DN
0f a- TriwYte Tnk'e'rsechn3 thp' o,y' two gid'u' hln
sido'tLs tvid!'L
) ^ lo$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)^a oninl of unI'acl' :,' ::Xrf':^U",?' ,to,f
',: ;,:;,'r' ,
crr t^e- 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
KOVUR SCHOOL,KUNDRATHUR,CHENNAI 600 122.
www.rejinpaul.com
www.rejinpaul.com
-
- 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 .
KOVUR SCHOOL,KUNDRATHUR,CHENNAI 600 122.
www.rejinpaul.com
www.rejinpaul.com
-
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'
KOVUR SCHOOL,KUNDRATHUR,CHENNAI 600 122.
www.rejinpaul.com
www.rejinpaul.com
-
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$eP P
Cos &se-c & = l
II
(ns e flw *, n g. /,-2s , i; - ) tl.* edcv r.. .
&,,:t ^ veMiu-g L^.tc,nd, .Tlrz_ ;aot o_f the
*hom ] l ' ,a l t tnJ l "
r i r tA lLa I a-^ lh t ^ r r -Sbom ltd ruCt " Sirt| tl-e tW U ,o"tdorcj hlaen = x-
ANqq f Torn tfq uLalt Bc Zu /Aac Ccs aaa = W-
.IIz
.?_:
"-\_*-lj'e
,Wfu ti tnddm iA 7 M. KOVUR SCHOOL,KUNDRATHUR,CHENNAI 600 122.
www.rejinpaul.com
www.rejinpaul.com
-
l - M s 9l+ ensp
Exud"ue sulrul,'pTov e tlra,{
lb ov z thet
ftL:
bd u7rua -rL+ ta p o;a.n 4 rnahe e4 ry 3oo
t'oez- touclW tI* g*tutdtlran g?nf #r! o,Clun (
= (asec & _ cot p[ * tp+ c*6e)= t -ss? f pu i *
f1
l '
ot nnA^
A llen'txca-.l ttez, ;A btohqttle ftez [auc]lu> btu groun-AL,iLl. 7t ^ sg t),L top 0j tl.etson aua(J fbctn ifs yood,I'W o|"h* buz '
Theal fuuclta ftv 6nualn r?gu A Aec- hs
f ta: 3ont
300= pg
Etohu of ( tu f tc =x_
KOVUR SCHOOL,KUNDRATHUR,CHENNAI 600 122.
www.rejinpaul.com
www.rejinpaul.com
-
fr,i,t E ^ln t$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
www.rejinpaul.com
www.rejinpaul.com
-
www.rejinpaul.com
www.rejinpaul.com