eoco - esaviya.com

8og @ AOz$O q.866. docsp ocf0{Dc.r6.

@ gozoc Eoco @QctcbtDo@aJ4o

q.Getr.Gi. (6.Gog) Storoo - 2017

r'

bo6ocs II

euD€ Qo@ er8ercOo

I

I

oocc 6dndop o6mazood1dod gecoCdoxo coqoc aad @to66.gocol/ ccorocd o6oro d€i8@O Q gQ6odors qqtci gpo oo8 eorodloO todg eroa-

qoc)zrJ €ooo,cBCOzD grC€d ag gtgO q1ta.

YS% ,dxflah orejka f.a wOHdmk wNsjDoaêh Wfoid úNd. m%Yak m;% yd ms<s;=re m;% ,nd .ekSug msúfikak

WWW.eSAVIYA.COM fjí wvúhg

6 Oorol 6torc oeorboq@dAO

q.gen.Gl. (6,.9c19) 6coro@ - 2Ol7

10 - €sogfdo codrDco

@eqq eoQo@

It eercs

A eoro€o 10 x 25

B oorOcs 05 x 150

ll crerco clqcor eo€soea e@

250

750

tooo/ro

roo

to - aogast' <o6oo n tgaSQoO ooel6o) | q.oor,a. (e.@e*t Oo:coo - 2017 | qoEiet 6dbob{D e.tr}tf fo€ eao qc6.



6 eoor Sorco ogoltroo@d4O 6toaJBE

daedoo mfl Pq-qed e ,x.nrg Qq"q6 nm u ooo@ul ogctao oqcfr,6eA 6dd soE0ad tu F e d aoUe Eod gefscr eg, &od ery$ p+o€g yo0oscsrrt rii CSo€t) a gBEAI@ €scc0gCI Scrdts @. i.pl6p coitpq Fa eq&6

6 e{soggt*rr

aP

cr{O6oO I= L(MY)) ---+ eoQogrf

$=(Amu-mv)-(mu- Amv\

a, 0=(r-I)u+(l"-llv

=,0=(t-l)(u+v)+ .L=1 .

e og P noc p qnd gd>rod 5ocg<6r6{o e18 odg" dOOlrf gsuod 6ogo eoQog:r} :

(a+v) =e(u+v\ @ :. " l;''e:1. e

10 - tooOa$o @lFt'(D rr (@|rQ4Dg@o o0oro6) | q.oeo.a. (e.oer€) 6o:oo - 2017 I eocod tsooolOel e6Aed rD€ EOO qzo'



6 @oor Seoxo oee$oo@deO 6o686

4€0 SrsoEsed BOdeoGd Obd qglocd rggcE f=0 fi ooogoe) 6rsS@to aa 6al#t Bdd D eoe0 ger$o aO; "f<f cO. ryCF, ,= f S Q @aftE\gd{6ord SAd A qdi#a oueod qi*s c,A. rsOgaoAtera dE

-Cc,6S Co aa #Da, e1aC Cg qd egrac, 6quo gpGo-ilc ee cr&*d eqlrar. t, t * ee0{g<.r eor g cs sasrfir,

stt=T

flo

frqo

AC * nc=Lr.BCs

o.c.AC

J =V ccp g'=

6,er8@ sa - oABgotsd*,ocJo6od6o : i(r.U)x"fr.

'#u.,

10 - rloodrD cDdt'6 II (CrO@€o@ oOelOo) | g.oor.o. (e'.@og) Otoxoo - ZOtz I eo6d oosobo graed 6)€ eQO qatl.



6 @o{or Dtoxo oeo$oo@dtUO 6er65et

3" ftctod P*BCDcgEdea 30f Scf E EseS qOC e0a ra6si$Op Fe'qt6, t&o:dDcanp qr" q1$ qgrhcrD Eild4p#"arl4o, rl"E P q$e S geO O6uf q qeouho 2ilrg EBAlg4edcgdq ccB. DCF*dilGl& SA fa,Cnrc e€Olsd 8a ead dn & CD €dd d. sqo q{6o tr@ccedO6bsQod 8o 6l1eil q.goA$Og 6#@6t s0d e seEdtu,sn}goo qca6o d$e6ra 66Se fu qdo*rr

x+2y = 4soacoaf =5'x+2y=0+2!,=*1.

4creq{ "8q .f s)c .F Eog66l "f =2F oa.

F *" ma ,/ far P:

2mgcG)

/=-\:_

cF=ne. J for Zmg:

T -wgsin30" =m-f

2mg-27 =2m F

rO - oogdtD @6o6 II (@A€goO ooo:Oo) I q.oo.a. (e.ooeD Ottl('co - 2017 | eO6'eS aooolOo eaqed tc€ trtDA q6tD'



6 @oor Otoro oeer:boo@deo 6eooc6

itkc fl gd ddd e*be*'m.kgfl Fcdiidd au€ Sdd oodd Q6d qr{s<os' oS eotdcegOEd ddcd r00 Eoodq€t o€&,?!E€e & o*ongg +otuaorc8.-OrS ddedooroodcd0$rooO , l,ld$o lm og;cee,l(>e)6oacc6. M

q BFd ddod S!r6p rgda e8r$ rSF pk\V tu W gd ddao6 @ tos6*se$oo vms*r68. @ q qco6to SAars +##g* ao olr#ra.+ rnlY

+

-->

^-,Jrrc-

vms-l

+F

g-oao 6e,- F- 1009P i/ --------..-- (l)v

I nnnpqial (l), (2) o, (3):+::-* - )M ^f : M -fv

1000P M=

- _ IM _T =:={T_hnlvln

1000nP-I=

---'--- Ar-

(M + n)v

F-*nq -+ farM: F-t"lvl-T=Ml'F=ma -+ forftri T-An=wf ----------- (3)

(2)

tO - 6oEdt' G)6t'6 u (OOA€@@ oOo:Oo) | q.ecn.6. (e.@o€t Sorcoo - 2017 | go6d esoorcdael epOed io€ EIDO euxt.



6tor06Gl

s.

C,eA AACB e rsSQ g o18 yarilrc q€d 8SOB 2tO.

dmi q6rncr : OA.OB =(-i+2j)-(2ai+d j)

;. A0B =L.2

OC =OA+ AC

=ffi+ffi=(-f + 2a)i+(2+a)j Ofr , y- qaSuco @a 8€o8.+ (t -2a) = 0 C)*o*+ (D

to - ooea$o aD6o6 rr rcpesgo@ oOefol I q.oor.to. i;.""ei a,D.t<l - zorT I eo€rid 6offi ef?il€d aoe eQO'er6. 6



6 cptor Ooro oeortroo@doo

O/ oo OFcogqfu cgaasB xr& c@8Ed O& aderc eq{o 2ceno 6d Wfl Afi. ftclcsJ crdq

Ade o

w

^17AOB =:, d16erf A, 0 nw E g,6wcorsr 8dc$S&oAB pEr Oadzlecd odulgcc G 88.A

.". AG=()G.

sAAG=oAG:a-

A0 uc BO Qocf Serlq:locezrf

T, =l{ cosa.

Tz =W sin a.

ro - €nogdrD co6oo [ (@tD€ggo oo0106) | q.oor.o. (6,.oo@ O6]CD6 - zotz I eo€od toosoJOo e6A€d ti)€ eAO eztt.



6 @"iDr 6toxo oeorboo@deO drmncl

7. ,4an E a:g Q 6cqQ qOroecacsa 8@ @qFdS iSzB aD6g. g6qg ; p(A U Br=95,

P(A'U4=* eos P(81,*l = | 60 Q qrrs.P(A)oo P(B)ecowsrds!-

A'v B'=(AAB)', 6cco P((Aa B)')=l - P(AaB) eD.

:. P(AnB)=t-1=L.66

P(B I A):!!-,'4- = P(A) ='+ =i @(-)P(/) 4

P(Aw a)= P(A)#(B)- P(An,B) + 1=Z*r<n\-!(,

€rzrJ

O(iers, oo6 arOoaS +Ouq oS. dO088f topdr$ I $pApeparo 995cl rod e18 qrld 956 &6d2e"6rr'acs ggde zsd qED. d6@ O Odso drs S(6d (i$@tor6O OdEezd:sdb gO$O<cE 41o4.

(i) AeoO otd erg9 eo$ eqcrit8 &$eo eorld 8oQ,(ii) s0roo od ogg rorA AeoS €sqO rt$i ffi,

e@ro€arrO otsrgghti.

432 |(ll) Ue?t6= -X-X-=-987 2l

@.-\' ll-/

(i) B€qd=;,.;=*

10 - roo6di' @60t'6 n (ero€€o@ eOo€o) | q.oo.a. (e,.ood Ooroo - zotz I eotod tsoooJao qr,tled oe trtDo qao'



6 @otD) Ston oqertJooOdqO 6oac6

@rnorJ aootDbqO.

a+b=x AAgf'E ab=y OO{

@Orsrro 6cor,2a+7b+ x+ y

:.3a+3b+ab =21

rsss Ssrflrt 4;tt.b.;bile, e yd; qOBc,6,*b I orn S&g oa, +sd d<,€6. @OO osd 9carcad q?

€CI@ @toro rpa 160 yFO Q ftHt oocs OOmro { oa2

th&, as &orEccfilra.

ec

=7 *.2

abZ.3.

Z2

(l) =+ aD <ozrJ2il 3rsf o0sQ?tl qrld

zraq (l) a.a+b<6. Ol<a<6 dcer

a=2 b=3 *D.(:)

;1, "r2, . ". r .rlf €rta c$oo$r qposd @lp}Eto ps SOffiCI AE&SS IS iro 9 6O. r* {soaDaa OSffSEOtsf qg geg E'rs 6pfu tnO€@S qerdls IOe E qtrn s@O re.Ct*r aooers go€Fsgo

t0t/-, X,

@or:nxo=lO 3 4{ -16.l0

loY*?lr*i

Eocrnco=9 +'=r -102l0 = 1090.

= l0^og$ ooo0>l 9I @O:smvc,r *10&

"Z*? = eeo'

og,S coosre 9 E Soellso= 910 -t02 =t0.

=99l0

I*ilbl

rro

to - caoE6$rr odooio u (@A6e,@O oOol€o) | q.oo.o. (e.@oe) Ooroo - zotz I eo6ef aooe0Ao E?,Q€d D€ EtDo e6o'



6 e"or 6orco oeert'oo@doO 6rD666

11.(a) 4,o a p Ed ed.66 ooq6, 6dd oqieepO @!s g qdq % 05,tldrsorocdoeaoqdro C q(t!. iSdS gg@nJEA 6dotsrrJ

9n9e, i ezoJsodal asCIEocxd to8a o 4po oel$ g6*odo zoop

er@a, (d1€d OetlJar-) eoe, qdrrm6 oAod &u06d Delrrc S

C Eo R gd6u l croc,ero g Adal rse@€o8 afls. elf - * R - t] a ^ AE0lhad6<c O6rrt R 6e€ C,Olo OO oeldOurtra.

,4 o o0 g ftg,o6nJ Eq.ro.o, ,f , lrSd u:O, og oq6 eeO e40r6Ofrr @ +oeri&oolo edzllzr.

(f) 5 nrOd o€rde€€O r trn h-I damoO oeoerad ra{Goll:8d {teo@ rropo zodE.r? oArOgOts AO AoE$d M'0, Jha,6da lrrz0 6sEro e'eoloood E @AiAgD,'r*2o

ogOsr a @€co'€roA vturh-r&omod o6ooerrJ odg o6o ooaao@:rJ adB: o@6 lsin0 < y < {. dS" zrROili esd e$o cm sed os:ooOa:cjO {r$#cozr9o:rJ Ct8 oea4Cctracl oaoq€fe @m @rr !r1€ ood oqrs &ScrlASO esqoo go€)ea {e tr6eo€t &r,e qiueolo qerr&D.

eero@€roo aooddoO oA$AgeO oo cord O@o {no celq qrrd 6zst6cl r -2a OO ocl#al;eoa d=sin-t(ge!o) €o-

eOO @trd ogo {o<d o4O @O ff.roo o@go op gpzrr ee, e'((' rl roc cr(c! lrco18 eA$.

t, + t. = alycos-o

aD et'?fi,o'al.1 ' ut-v"

s =fi ++at2 oceQo@zrf.

-+lsoBqzolor: n=ucosX.t=# (@

t e eo B qdoc - a =ttsinLt -f,rr' -------------(2)@

(r)o, (2) + -a--R-+rT C= gR2 -u2R-u2a=o C

10 - 6060$o aDd0ta6 rr (@a€g@@ oOofo) | q.oor.to. (C.ooeD OtoxDo - 2017 | eotrd esosolOo Eaoed oe Eqo qro. 1()



6toaJs66 @"rDr Oroxo o€entJoo@dtzo

u4 +4uzag2,uTR-

@r.'R>o) C,4u" >tga. ogo o6$.

16 )i 16 r)9

g'o- +Tg-a-s8o, ft>

4

3go*

+ R>2a..'. coe @ercze6O oncOloO.

(b) r/(s, t') =

V(8, E) = 1,

Z(8..S) =

usin' <v <u

I/(8, ,S) = Y(B,E) + Z(B,S) C=V(E, S)+Y(8, E)

=F0*6=PR.

eDsr)S ozoJ*o = RtARz @=n-2d, e@E, QrtrRr=". C

10 - rcotrdt' cDdtDo II (@cDeg@O eoo)oo) I E.oo:.a. (e.e€e) Storcoo - zorz I eOcef ooocdOo qzqed toe EtDO ec6' l1



6 Gx;€D Ooro oaooboo@tao 6lo664,

I I /(PR, +Pit,)at J L1 -I L NE ND NN DDPnr PRz P\,PRL

PR, = Ptr- 1P,

;--=--------:-=ucos? -"Jvz -uz sin' 0

PRr=PA+ AR,

----= ,/ cos 0 + ,lv2 - u2 sinz 0

lZucos9J.t1 1t2 =

u2 "os?

o -(u2 -u2 stnz 01

2lucos0 . ) ^=## ('.'cosz P+sin2 e =l\

,o - *&J, oo666 ii'i@hffi6b'€or61ili1 4.o-.a.(6,odeDrgceooo - zolz I eo6d ooocfiOo *trd 'oe

Eao 9q'



6 e"ol OtD)<o @eo)tttD@OdtDo 6tocgr56

(a) srsqo8 AFS@erD r{8CD6ffioA, *OalDo hB goA edrbodAaSrra eCrt*o od:dbo Fdad q6r &*J odaio@ ldDpe

o6bo 66r q'e tr"dB--2A+ BAD=a l&,

o$8 O < a. ! u oosd = * *. *O*eE{66 EEe 6dat

o6@d oo qrSO Eil086 rDa€) CA@. qF l(>b)P arqfgepgoa'} aalqo$ d6 8OO eetr goe n6rd cad CId) q,,!d €6 Ad 6&€Adata alsrdOo arp. PqcqOEd q qeint$ 96eA@ q q1g q1o. 8ooc3dilfoozo rc6q PSep AR8€@:o tlqD q.€o n{O6(cBda€booed Aa 9e o6p god

so80e: aocdddP 'eAed &da;o fAZg m eetsFa qOcaEA P A dd{66tococc$erlzt.

ne q P q€gD A 2$& €ec 69tr orJroo ** lg ao eoedDsia.

(h) B qes o@daffi,q,po.

urrrl4cl6,OA:o czdoarco gr-E€ elr$. lil$zdlo.n0oo @ ag q0eE@ q'oftloa coao@ C*!o{s6 Cq"qe SISE S ,,lwa Bqr4" OeezrJ g Ad{ $srl6 eeod eAQaSapood6o o$ai ae qra, csdg A6EE$ 0,t)e$Q d tg"qoo ecidg<,: @6 do Edsd rDcod g a@o Odoceraod egg6..@4. C qoqD crodertr f2=&1t_gosa1 AAotr:slOzta; og& d rogl sO.-

4

e = ! en 6a C qoga, eoJgxn qrffrtc cflD ACI, Dregdd aosbz$rl,

p

..L(a)

/--\l1-/q (P,Block) = "f 7 oig o61p.

ooq ./(Block, E): F +o80 q(P'Block) = f <+

10 - t'o€dta cD6066 II (cro€€oo oOorOo) | q.oo.to. €.oocD 8ro:oo - 2017 | eo6d toooo8Oel gEagd oe gQO q?,o. l3



6 @oor Oop oeo$oo@dtoo 6ocec6

F - ma: eoQe@rrf

HCQdffO + Q=2mF + m(F - f)+ mf - "f

cosa)

30= 4F-.f -t"1)

'f=+ -'--(1) @

:> 4g =5f -SF +5f -3F+ 4s =rof -sr (Dqlaf (l) = 4g=25F -BF

4

= F- s.t7"

(l)=+ /= Iog"17

@@

(D@

s =ut +Lat2 :2

ocoQe9::rt

o=o+! fi2"

/

€oqor :

ro -.ooedto @6666 tr (@6i4g@O ooopo) | egooo.a. (e:soet) 6roloo,: zorz I qOad ti"€etQQ gegq oe @ T?. 14



6 @ptD) Etorco o€orboo@deO 6oac6

(b)

rl1

I

oal6 co.ai86 6o@eorrf

! * z, * 1a072 + z* l* m x (a0\2 +2'2

+zao2 =-2gcoso*zs @;.gz =Eg-cosg).(I

2mgaas9-mg(k-a0)-mg(k+a 2mga

l0l0ation 5

F=ma:

(: a,Ev',o /i R-2mgcns?:-?m.a02

+ R=2mgcas9 -Zmg(l-cosd)

=2mg(2cos0-l\. C+ 9 oi6 oar Eo Rqg oa gad

"o"e --! ozs'r 5o R = 0 eD. @

A =! o-Eo C oodgo to1d o8.J

10 - €so€iilrD o60c'@ II (qq6eoo ooorOo) | q.oor.o. (o.@og) OrDo6 - zotz I Eood 6o@@f,oeD eca€d 6e Eao e6o' 15



6 @oor Oeorco ogottloo@dqO

dDreoe8lo Qo c or gmaocS<}:ao &trrsrsta tzg A qqd€ gpseedO .airhXga Ord eagpdail gOO€dtd os&orso 3a cccd @@at ftc.r fi6n B qoqOao lfi? qil$. q.@ O

"Ard ggd

ar$qo6 Qar "rcanlrr, aex < 3a cq4 l+{6* Za\=e qg6€:r} ao o6uftx oO@odg q6DbB oglooos odnk{s *o.ur}*

* -

ooFQ coOo {D€g 6€0 end g"qoO cr{o€S it€hr€ tqu odg aodgE ge669c, 96E@O6IJasx<3a erqoc i2 = &-(4ae--l)@ otlsbzrJts.

X=x*2ho18 o6$ot qa€ouD g$rod6€ -asX<atoqoo *2 ={(ez *X2)eo.ooe"rol eraoo

rodajrn: @oE I og 6UOo 6g ge &6rc o6.e<oFO "qS6 q?

q'qo e€" tr91 olrlna O'dtd prn oopg

s"<seo cs $d oeh'cra -asx <4ecQoc *'=*(e -*t)* t q*,o; sds B og oo@ arocod6 q€ObA eets@d 6fucc rsq Se Sc{aodo e6.9o6zrJ Ddod rsdar et 60 qd too c.$ qd E€ qge6g S€etle qoqO e€anQzD pd rorsts5n li3-{g os et:uJdaJro.

a<x <3a: tcq6b

7=wt-a) (D{,= nra: ooQe@zrf

ln fngfil J; mg-T =m i

+ mg-W(r-a)=vria

+.f+€(, -2a)=g.a

i = 0 g6rj odalgo eQ{l gloO- i.e. x =2a .

\:,/

PE IO

S@ Eecc C, I oalrrlgo eO6" eOE C og OC:2a g O@o Eddo eo@rrf BEom safeors8. [E]

oal6ee.dg6.*ofrl I 'rzm\ga)=r*-

ga : *2 - zgx + 81x' - zax + a' 1a

*z :2gx-Ex' +2gxCI

| (x-a\z- ngx+img ,

10 - rooEdt' @dBt'(D rI (@E€goO eOerrOo) | q,oetr,co. (e.@oo oeoroo - zotz I qOed tooooJtDea ezAed og EAO ezt'. 16



@ @oo) Oetl(' @€E)oD@€)oeu

a<x <3a

X=x-2a=*=*rroq a<x<3a e -a3X <a.

Yz =&ga(x +2a)-(x +2a\2) @=&14o, -xr) for -a< X <a C

.'.A=Za @I

*y o€ o1Q9O eerd g"cgoO goOo6 ogoo orfat.

6oorf ocd grr>cod doooord oiQ@o ag soDocs l,fA [ " =1|)

X, =818, -Xt)a

X =aOa Oe ;i =1,@ oo.

go =E1B? - o21 C_8=.,6" @

10 - esogdt' <o6tD@ II (@A€g@O etOerrOo) I q.oor.to. (e.oo€) Otoloo - zOtz I eo6d aoooJOo e.Agd loe eeO ezo. 17



6 @otDl Sroxo c€orboo@dtDO

lg, It Etllrr =;, 5t€0r [1 =lla J J c

@lg, E ,rrl-I: =;' 5l€0c ,2 = -la- 2 - 2

5rE".\+tz=e{;

ro - toogdrD @60n<o rr (@a€g@O oOo:Ool I q.oor.o. (e,.oog) OtDo6 - zotz I qOad aooodOo er,Qgd loe EAO g6t'' l8



6 O"tor 6roxo ogortloo@dqO 6eDca66

l4'(a) 'c'

eoo B ee@o da oUoosaogpo o +oe ge,cad q€a{air-,,t A o B ggnr- B,rdor oqroar BEp€ooq*zo 8€6oei'raEqo b oo' oqg'doocod c gge@ eeg*roo r =(1r h)n+)rbcs18 o,Eg; @@E 0<t< I @O.

,+-deor d6' eoq8a a, b eoo i ftSedzf gzs$cs ro6rdo.g a6d, cgradoro ,48 6sab odoar r&n ggoar ffid ,{c: cB = r: (r -A) a6d oc:a}or:ial.Azrl, OCe{t0cD AABela*w caxlert:ialzltcarg Sop1. ftffa.c; = t"tit."iuJd €s66, 1<*erccs?rftD,

(b) fzootaB ABCD clp ,4B = i m onCDEop eaeery 61orsdow6.Ae e€e6)€,rrf BA, DA, DC, CB, CE.wl

gtrJ, Bn at DA

91806or adqge,ro€. r*O o{Afu Fraogdoce 600 ggcda agter$O€025'?rt5 our oO,

o@@ to gel ** zi --aa\-- -- ,- ^ , a- A

z ed tog AA ogorn gzda>cco ,4 ga ryrE 6d

"i*a

la. (a) Oi=a,OB=b *r dE="r('l\:-/

AC = Ad *ttc = oC _ OA= c _ e=Q _ A)a + Ab._4 a;)

=(t_DQ_q_).@

)*-AC = '" -CB

(r- 7)

i.e. AC:CB=),:(1-A) C

10 - cooEcSeD @dtD6 u (cro€€o@ oOoroo) | q.oor.to. (6,.oerg) Otorocs - zotz I eO6d rcooojOeo eracld cD€ €'taO qao. 19



6 @otor Eto:<o ogortroo@deDo 6lo6a6

AOC =,C,OC

a-g=lqllclcosa

b.g=16llg lcosa@/-T\\-.1

= ffi=?^ C+ lb.l@".q)=tal(4.s)c

=+lOl{(1 -t)lq.l'+).a-fi= lql{(r- Dg.h+Uhf\ 6

(r - 1) | q | {l eI I h.l -a' bl = I | 4| {l q| |b.l- s.' b}

(r- 2)lal= llhl

+ ).= lgllal+l4l

('.'q oo ! gEalor eoa d*oodEo ourroo..)

jo - r0oEe$o codotlo rr (€|cE€g@O eOofol I q.oo.o. te.ooe) OtE)(D6 ' zotZ I eOr!€S iirooosaeo E'tted roe OOO qzo. 20



6 oorol Otuo oeortxao0dtuo 6r'6s6

(b)

J3ar. @

X-tw

o{Odca gd@oznO C,ea:zlor Ozr:6ear,

+ 3-5+Qcos60" -Pcos60" =0

3 P-Q.=4, oo' C

P=4 and

t -zJt -4J1+psin6o" +Psin6o' -o C

P+g=12

io : tro€do cDdtoa rI (ee€€o@ €OeFco) I q.oo,a. (e,.@o€) Ooloo - 2017 I e0od oos@JAo qaz€d roe etDO ec.D. 2l



6 @orD) Otoxo oeo*5oo@doo 6o6o6

4'# {3,4

-+

4I

x =5+.i+8cos6o'-4cos6o" =lo @Y =2,13 -4,13 +8sin60" +4sin60" =4r/3

R = a/ioo* 48 = 2J37 @

Ff o€ Qzul ^e 8,4, eo@ggzdaeaS $cor 65ffi a$Oar gzsfor:o o18 o6$.

D-;.''E +zJie+a)+,'6(:* 4-2)=o @-6a+2+

7q=-m.4

10 - rlo€r$t' cDd0r'(o u (@tE€g@O ooof6) | q.oo.co. (e,.ood grE)o6 - zotz I eoGod tx)goilOel egcoOd oe geo eErD. 22



€ o"rot Otorco oeortloo6dqO

15. (a) AJ Woc elrlbrzs etx ?a Olst drsmd cs6)6or$cd zgO6caud6A EdeJ o.o6@zst Oo oOl qrrs. ad ZW vt Qa ?a !)da*od AB qdOro A olos0d Add so8e@6 edelrca*jg@O <ogcs qe0 od 916 qpDd gerD€p6 rsolroecd g0eEdeC pgsozoa ded$O 06 @zdrrbe,cJ oa gto. QdOod@d csa: SdcB a6cs qO6ed AO Edd $g,araO gOAO:sr gnd er{CAa tlOqSaruOoa{ trO6. (q{r€ gderx#aO eoe.ex <f1ocl OgaJaJ-) ueutsrnbd q0Ecs oc dOErJd eo6@ Ezrd o5a.g caoe62$<e p@_ tt >.6 OOocrzrlosJ6)-

(D) <oragOdO@crJ Sqoe€g otd8 rodra eq Ag,BC, AD, BD at CD cs1o16fg qrg erogrrloOai8a <5c$ cs16qf,gd d2oocl caoglOg.AB= @66 a at BC =6Od Za A6 d& P

aAD = eDA = neD =3o"eo.ogo186fuo8 A e l50N at DE E 300Ntocd 6coce c1ro.6rs AB at 8C Edd Ozsr erBQ Bpoopp3 A axC 8 Q ocs4ar eQ p.*J e A6d Ag eqrodalcrOe<J rodgl gi6l 8dc3 rDe<eD es@p$o0 fio-P=25A N iiO eerrJtldar.eoJ gorozn* sr€a,'czrj 'g?irE"a€ esoornzJ qrq 6 o6!6 eco$ o t€oe grDrrae oacec goo cpun6q oodg@ q csalor gnore rodolzo-

r2w &

4O5o*qr, IR,+Rr:Sy

4OO.o €DEsJr

->F =.1

@/-;\l:-./

10 - t0o6eftl @6tDrD II (@A€g@@ oOorOo) | q.oel.a. (6,.ooe) Otorcoo - zotz I goad oooojOo e6a€d 159 €eo qz1n



6 @prD) 8ro:<o oeo$oo@deO 6roesaE

AB e,gunsxa-2w,+=o @.."s=.f:nq]

3

ij

t5ox2o+soo(za ;) p3a=o

+p=250r'/ @

10 - roo6do @6o6 II (OrU€€o@ oOo€d I q.ooo.tr..(e.oo@ 6ocoo - zotz I qOtod ooooheo entDed rog g4O qao.



6 @oor Sorco ogorUoo@dqO der666

o100

CtI

I

150

I

I

o+50o

I

I

.,alt parO, @

edc gado ozsdg@AB Zs0,l1N

BC zooV3l -rr)\_-/CD 4oo/v @DA s00N

GDDB rooVaiv @

10 - roo€dtl <o6tl6 II (eal€€o@ oOorOo) | q.oo:.o. (e,.@og) Otorcoo - zotz I qOad aooolOea eza€d o€ €tDo qcA.



6 ooror Oo:o ogotbooOd4O 6er66Gl

16' eahdS,o C or qelcs eg qtso oadrtriold occlon oloooal Sd c6$ dao*scd zso6cls ctb?rft) edrlgo,fu + gdSzrt st6 oo or**grdrrl.

c,:raq dlerr+cs8 PQ,PRa S7op. &oa Qoa dacr$<c p g 46 daoctDad

o06co6oi zocrc rorJ tsdg eSSo tsrO€ S?116- pea pRloiO€ eqaq f,7o

..

@OEO-g dazs

{rozo darsloo kp g 4E desceooo oOEcdaJ ceqr od otdo&ro Oaoc

q6@ a I gbO Oerdar**rd OreroS; oO& &(>0)dcarD{id eA. SUTC&AOruia:ozocd zoO6o PQRaee<t Stoc Iepdor:ele Q SfesOSoO escc3oo d1r:rx3 gdcaOar Lqaal ogrs@s <Jcpo 6xq' {prn. z8 eczoat) o&rfgcc ,* (t!#); ,ou" q1B du oezrfordo-

ccaOg dlcaocC tae3aleb qr6 oE LaOA d.€O, 6S Dadr,czDod eorOclcl@O Edci 5d8€zs oo Bdccc osO Or€(€€@ ggcdOrd rrd6 dd E6Ego<o60ro daUco oOBar', A8 ogca AffitO gOAO eOa@roO q1o:^ L@o

Qcccrodan og p,reg r$d I > ] ao .<roO.rt o,

ftzrf k= I c48 o8g- Pgdllrecl q d6ob6 mOrrr qo<god LO ta0&rbzs€ ern q eE rsr 8AA@O O ro@rgeolooO o0*:reozrr &" m <3p @oeesJoriJg,r.

o9€6erozrJ. oCzsrerlO ozsfzrfgr.r , G , CA @a SEOB esE)

p 64 darzs'rQoar eizsralO<.e o18 oE$.

oG=r @

l0 - tootrdtD ctdtDo II (eOS€o@ o0o€<r) | q.oor.a. (e.ooe) 8to:<oo - zOtz I qo6d toooobel e6aed co€ €,qO ezo. 26



6 @ro€D) 6tom oeer$oo@dtuo 6t'66Gt

2

=! tcnso doVJ

_r,

d8o Ln=a(L4)p N=

,|n

ozn8zrl c,JzoaJa oz*afgo C 8o -gddul ero8.]L

=!.sin2

uer4u dz$2rjOo Ed 96, P 8o dmaJa Iod:rJeoO t

PR ap) i@PQ sp -@ [email protected] zsp _) a /----'..,t L:-/SUT Trakp (} a2a_+-

2rc @eo"gafal OeCqO (++ n)ao(3) 7l

10 - rDo6s$t' cD50o6 II (@a8e@O c'0€006) | q.oor.a. (e,oo€) Atamo - 2017 | go€od ooooJoel gz{D€d oe OtDO gE.''



6 @oror Oorco oeorE'oo0dtDO 6@sGt

teg66ocozri Z 6 oJazrfO odzdgco P w O os rod6o&dcO grl BEO8.

edzoofO onlalgeod q6d ndEO g66f ,

(4ap + n a k p)a =zao*f,+2apxl+ ru*o*(;.+) @

+ (4 + r k'li =! + o +' o k + ?ok'22

/ , ,, -\| fic++K+51O+41 -t-t-' l. nk+4 )2

Z dcgO eo@q@zrarOooof oqan 6q SEQeg 6600 , "i Eo 948.

fr

. (,*+4k+3\a a f-\t.e. l_ l_>_. t J )

\ rk+4 )2

t*+4k+3>rk+4.

o"i @e

<+

fr=lor8 o69.t, -\

eso. x, :1"*'19.\r+4 )2

i uaP Aa qgri dzonfO emfdgoO CLA S6 ees o:dzs,.

r0 - 6o6do @d0oc5 rr ((gad4gog oOolOo) | q.oor.o. (O.oeO Aomo - zorz I eO€id toooaoJOo ezQ€d oe eqo 4ro. 2A



6CIr!666 croor' 6eo:o oetrboo@dtDO

1.

o8o llep+Es ilt^l;=(4ap+ro itrfi. .@a ft+op+na p)+*]i=(4ap+"" ,r(#);

e l1+op + n a p\+ ^lr2 =ap(n *T;

ap(r +7) aQ xz=tr+aoqoo o6,

eozr BEQo@ coo4@zrO 86A00 iri Eo g.q eD.

. ap(tt+7) a. a '

r.t.?---.------------.=I@ap+na p)+ml2 2

1,

e ap(n+7)> ap+Es p+m

e m <3ap.

iO - a.e'6ftD oOan rr (CO€€oO do6Do(i) | e.oo.to' (O'.o€€) 6t'[oo - zOtZ l eottq Goqe$Aet €tzn€d Og eQO e@l



6 Ootol Stoxo o€ortJoo@doO 6o6s6

.(a),4,8o0 t*tO qeO6gfgels*d bo & 2deeb 4d q Cod@e8 96 catg ,aed loi6 qde (flr+l)d t +0"e 6.0. Eded 68ft0c@ ond6reoes: OaozoO o!1 D qoglao ogee o4@ eAJg g,q!$r$ Og @doealgOtrrO oE er6&" 9OEA tod'€€A o6$eis 69 oo gBnO od eq0:a e@C6o lo€ EotD- o0rryr6ao

lg 6D. rz8 qoo oasoESzt.

s q epro oo! ogS 64re fi0,!0o Opm aod @€pnr sa{yo 6d-@ ? +16 Eo" Code o:lddr

ma: E6oO oftcti8rlso sos€i'ttf),

(D) Eol}csd l00rn tloanffi gdrr6r$eogslsd8€4d"{ oqEs0 6Oc ode;rq@e0Dod6ccooo &9<0€)8 gde6:

er6td sdltfta Bols 6"arsAI5

2-4 ?5

4-6 40

6,- s r5g- ls 5

eO@ €DudE{$rJ @)rtffr€o pam #o4Elo0tsel o 6fuio ro<ftda.

Xu- M\* * -T O6?d 4gQ &qe@6 rq fual 6dr&D; oO& Meg o*d8od@Out&)co eO.

tl

(a)

X og eg$ eOJgo Eg eoo oqO:n oOf,6lc6 ?od oet8 ct69

9d es@toeE6ra 6co@ooa}, .

P(x)= P(Xl A) P(A)+P(XlB) P(B)+ P(XlC) P(c).- ------'-(l)

p(xtA)=1"1=* @P(xtB)=i"i=+ @p(x|c\=--!- += -l'*tl. (lD' (2n+l) 2m 2(2m+l) \-

aoq, P(A) = P(B)= P(C) = +.

P(X)=4, no,

lo - 6o€Eilo @d0t'6 Ir tOrO@€o@ oOe€o) | q.oor.o, (O.@aO Oo:coo - 2017 | eo6d oooolao eu@d @ EqO qztl' 3()



6 @otD O€t)@ o€o)btDoodQo

. 5 4l 4l (m+l) |(ll= -=-x

f-X-18 15 3 15 3 2(2m+l) 3

5 8 (tn+l)=---=-6 15 2(2m +l)

,^.- n=2( 5 )

m=2+ P(xlc)=* @s6oe'i gegoooaf ,

Prc | X\ _ P(X lC) P(C). P(X)

3lr0 3=-

5

l8

=+r'@

(h) f, 5 f,

ee€ erdc6(! .IOrOl gdu>

x x' fx .f ,'o-2 l5 I I 15 l5

2-4 25 J 9 75 17<

4-6 40 ) 25 200 t000

6-8 t5 7 49 105 735

8-10 ) 9 8l 45 405

l./ =too I fx =4402' lf t'=zltof, 5

a,=#= 4&

=4.4

jo - 6oodt' @d006 rr (@a€go€} €roof6) | q.oor.c. (e'.@oo Etoroo - zotz I eocod aoooloeo ecagd oe eoo qro' gl



6 oorol Ooxo

-/'offic

=.[23{1s35 @4

2.tr

0.3=--2.tl

P- 0.14.

@

,?

e

ro - aoedo ('6o6 II (@lrD€gco ooloFd I E.oo.a. (e.€od 0t')@6 - zotz I eood aoooloo Eze€d tD€ eeo eEo.



eoco - esaviya.com

Documents