XncpØv ˛ ¢m v 10

A[ymbw 4 ˛ {XntIm-W-anXn

Bi-b-߃/[mc-W-Iƒ : sine, cosine F∂o Af-hp-Iƒ Dƒs∏-Sp∂ Pyman-Xob {]iv\-ß-fpsS ]cn-lmcw

Q.4.26

Nn{X-Øn¬ ABCD Hcp NXp-c-am-Wv. PB = 7 sk.ao. Dw ∠PBD = 40° bpw BWv. ∠APD = 80°Bbm¬

a. NXp-c-Øns‚ hoXn F{X?

b. NXp-c-Øns‚ \ofw F{X?

(sin 80° = 0.9848, cos 80° = 0.1736, tan 80° = 5.67)kvtIm¿ : 4 kabw : 6 an\n´vv

A[ymbw 7 ˛ km[y-X-I-fpsS KWnXw

Bi-b-߃/[mc-W-Iƒ : km[y-X kwJym-]-c-ambn ImWp∂p

Q.7.10

Hcp s]´n-bn¬ Ipsd ]gpØ Hmd-©p-Ifpw Ipsd ]gp-°mØ Hmd-©p-Ifpw D≠v. as‰mcp s]´n-

bn¬ Ipsd ]gpØ Hmd-©p-Ifpw Ipsd ]gp-°mØ Hmd©pIfpw D≠v. Hmtcm s]´n-bn¬ \n∂pw

Hmtcm-∂p-hoXw FSp-Øm¬ c≠pw ]gp-ØXv BIm-\p≈ km[yX 38 BWv F¶n¬

a) Hsc-Æ-sa-¶nepw ]gp-°m-Ø-Xm-Im-\p≈ km[yX F{X? F¥p-sIm≠v?

kvtIm¿ : 2 kabw : 2 an\n´v

D C

BA80° 40°

7 sk.ao.P

A[ymbw 8 ˛ sXmSp-h-c-Iƒ

Bi-b-߃/[mc-W-Iƒ : hrØ-Øn\v ]pd-Øp≈ Hcp _nμp-hn¬ \n∂v hc-°p∂ sXmSp-h-cbpw hrØsØ c≠p

_nμp-°-fn¬ Jfin-°p∂ hc-bpsS `mK-ßfpw XΩn-ep≈ _‘w

Q.8.20

Nn{X-Øn¬ O hrØtI{μhpw PQ sXmSp-h-cbpam-Wv. PR = 18 sk.ao. PQ = 12 sk.ao. Bbm¬

PS F{X? hrØ-Øns‚ Bcw F{X?

kvtIm¿ : 3 kabw : 5 an\n´v

A[ymbw 10 ˛ Pyman-Xnbpw _oP-K-Wn-Xhpw

Bi-b-߃/[mc-W-Iƒ : hc-bpsS Ncnhv

Q.10.18

A (2, 4); B (8, 4); C (10, 12); D (4, 12) Ch \mev _nμp-°-fm-Wv. A£-߃ hc-bv°msX, kqN-I-

kw-Jy-I-fpsS {]tXy-I-X-Isf ASn-ÿm-\-am°n NXp¿`pPw ABCD bpsS GI-tZ-i-Nn{Xw hc®v

aqe-I-fpsS kqN-I-kw-Jy-Iƒ Fgp-Xp-I. Cu NXp¿`pPw Hcp kmam-¥-cnIw BsW∂v sXfn-bn-

°p-I.

kvtIm¿ : 5 kabw : 9 an\n´v

PS

Q

OR $

rrl6rn1(I)o

CallBJC(ldOIOo

g;;cn0crurdru'- x

flroflxnli]] O,lBjrlBJlfll Ocrudxm J01t0T olfl m0'liD'l (SCERT)

onBlcBdad, d)e.r)o, otolero@dloo 615 o[

c6rdcQtc,Jo,€@cs

Lcrjlcacdrnoil{djl, "€lmolor56BUi, ftlldaaruoorJas8, cDccuj(d)6glos .r)5roilo)o, o{d)csl

oro6oil, 6rxooldrB6rBoA, eJcd('illDlo EDrlsor6ntoor)o, (rudl{ot oiorcodo6rnad "Ocm1

agro(l)jc(or6iB!6 oraolo6nt:Jc6id circBlGooor(oo 6)E}cocdoll(otS)pEoj. .oHo o)ooroi

eilolgp G*rnj6m./d d]oloIT1.o' g./Eo.!sl.6'd"rd -,oil dl.rJ6rd. d)o-rJ.6dnploer

GrqooQJ6sBglo oco6lDd,glo 0€)l(6)cor.)cgo olD6cBo.Do(orerco e)tcoq68 go4l domi

"rolcuoc(rjl€ol(r])caocosc o rdrdorcolos orpd4 a,o5rBrdld)cni OoJ6collaolam circRl

6rtBglo ponos0ol6rd. crO(,oo6dBglescolo orc(o5rDeg)csco)lo .rJl.om Lorc(ojccDm)c(l)l

(6)6910 f6rd('tloog Ldleilloc .€r566BElo croctc]ll cridoc6m.croioq i?c(ooc6n;. ((})toc6(dlo

ordjlafS olerJotd5mco LorcxdoDmorJo 5]ol .rool.r.)rd6romo ('o(m(orc6rd .OarD

oco6meojl(dE c.!6rDo @(6iloco arua"l.nooccri-

ojlojl(x cDco(o,6sBglcsolo rec6t6soca\jL.o Lorodcnaeg;csoolo grigcoLo(r)o p|5 ole{

crild6m(o) Lorcudadoo6sBCloa 6loolDc6rd. {t(mcruoorJdglo .srdocomlruollo r,t}Erd

o)olo o€1s6.!lo ojloi'l(]) pjcolcDlco) ffidrjlcdndl"gl. oo.tr.c0)coml m)i€Dc.to).xJo

goAc!(blemrc.d a)t olai"] "ro14 crq0olor6EBglos GDcrrcojor)o L"lcoc(D crr(Ijde

6€Bglo ocllo)oH, (610 Ld,l(o)6glos n(ol o)oo "rl.l)dorccomro;raceni msao;croi.

porooooco] d,cd4rgcd oJAJrid6m(o) Lnrordolo)o5irBCil6SaoJsl dlscmlcolc6lcmlcua

circBledd6 6rq)coc€o)cmrc06 ooorcoi raroojcooc:g!(63 (Dlmj .oroml"rc('jld})

Dc(ot cdcBJ63B0A eodogs](dE)6mo.

cjrcBJ6sBUi atrtoo6roo)sldolcoucod ('Doroo .roilo6rD1cds6rco)c5nj.

5rccoc ol6rrjlBlcel(oJJo or(oocc!or.orococcr6sBUi o,ilplloillol6roodsl(m o).D(olo)1l63

GdcRJGoJdd Oq)COC€OCOi LOOaalido6mo.

6lco GDotro.dojloq .Do.m sr.rderota,o circRj5sBod cdcBjc"rd.t68 gdog

sJ(drDcl1'ilollaocaS LUD€rt.aolocHc.

rOSr ]]ler1l\ D dfitlF.gp d Jil@.rAdolo poror?oo{ orrD r.rm o dos'lelJgp

circRl6mod 9(j80 dsl Gldro6n3 or D6rd.

t6TdCDJ9(0)o +

6cflee,camdloil

isord@aRLd/tUrla6mo,ud : cocnnloiF sine, cosine ,,oaml axlud,ud c6r6lrd (6rag65)cmlEg o!"oJ@,ud

Q.4.1

" ill|iDoroilo8 ,a, = 90' .e,lscoo) ,48: 10 oox.o1., ZC -30" @d)()coil

B

a) ll co)os orogoo,rodt

b) lC, BC por(o)los a)lgo "Oadj?

aJc.scd :2 .ruoooo : 4 ,D1o'15

GDoaorgBud/oro6noud | €6,c6lrt6r(p sine, cosine .Oml cxler@,ud €6c6lrd cngoocmegg 0u06nJ6ud

Q.1.2

"ilL(')(d1l'nd PoRS aol ruo"r(J)llooc6nj. P0 : jr cDeoccS

ar ,tU .xlood mlso oo(rd,

b) cos45' osmaocao;a.nJce)d : 2 .ruor((Do:3 01.n15

tgtdrooo8nud/ulco6no,ud | 66c6ntoqd sine, cosine oilE6'oE €a'c6lld cBg@ocoegg fluo6nJod

Q.4.3

"-nL(o.dlon(l'a ZB- 90', L4 = x, AB = 8,BC=6(sDcocoi

a) sin r, cos r @or 65lD@ocaole.

b) sin(90' .n): cosj' rorqoemcni raroorz; .roco,lcml. ct6sBglos GrdclL"rce)o

mica'cd

BC

noc.;? rDod(D).ll€6)16.

r4oDo(oo.5o'l(r)'ld

rstottd0OgB(d/rUco5n8,Ud I Loicoc6m4lofl gdcorcolaJqra'lo)1o, L !a"moBUil "16'l.n0166llml

Q.4.1

6l(0] m)oie)sm)cocoo)olla,oroloae ao] oroooroilooe mlgo

40" colo rargerd. GDo-r'lool oro*goi d,fiDaocaold.

(s;n 40":0.6428, tan 40"=0.84, cos40"=0.766)

7 oo1)o olgoJ. 5]o] c6c6njloot cng.r-

<njc+cra, 4 {l!ooo)o : 8 ol(r)-15

Q.4.5

r0ond(0)gBUd/ujto6m@,ud , Lolcocsnqloil 9"r€o)c{til2iLdcca)co16 L"Jrd"m6BUd "rol"no'i€olm .

-j1L(rJ.6rojloi -8, c/Aorooojlool orlcm)ac6rd. BC: .]. dlsco(or orjoro)ontooe srqaoo -R GDla,coi

a) "jt(J)oloioi ,14 oiad ot;er3occor cac6ni €.0i?

b) #7 = 2R .6roo6mmj ojlell "roorlo.D). coll6sBplos Grd(e:lLdrcco,o n1])ad? .ruod(Dnll€o16.

crtea,cd : 4 mdr(oo:8 0'lml5

6rgrd@@Bud/uJc06notd : Lol€6r6rDo;lolgd600JcutlqisJcailofloJ t rd"m6Dod.ro1.oo16oem?-

Q.4.6

j-nL(ooldiloi 'O' .!J(dr?')cd,La3o ZAOB =90'. lB = 6J2 oaD.al. 6)scoo) ,.-BOC = l0'

a) Lojlc6c6rno O,1B erlos or(odgoclcd?

b) ,roldeJeo OABC s\a. orodpoi 66m6ocaole.

micacri : 5 olD()o : 8 o1.n1<

Q.1.7

rgoU?orgB{/d/uroSmoud : Lnrlcdbc6m4lojlqrA6ts 0!onr0)colo)c6ts qc4l(d)loJ [rltrd"m6RUd .Jol.oolo6erm]

" lll,o.6rtJ1(o8 'O'.xlcoroca,LcBoc6nj lC= 8 oa!.ol. Z4=40o crg(o)coi

a) t{i'ic6c6mo OBC ccDlos "rodgd "Oodj?

b) Lojlcacdno OIB lo,los "r@dgoi "Ood?

sin 80'= 0.9848, cos 80'= 0.1736, tan 80' = 5.67

sin 40': 0.643, cos ,10" = 0 766, 1an 40' = 0.84

mjeacri : 4 fiuoc)o : 8 o'lo)lE

GDUdOJABUd/UJco5m6,Ud : Lo)l€o,c6rr4ilo)loleos mr"ncorql[tocos Ecqlof@ Ldua"maB{rd.l61"oo1o6laml.

Q.4.8

A

90", ZBOC = 40". dlsco.D l3 = 5v5 oru.a1. cto(orcoi" nt(ooroiloi 'O'otsoo,cd"lxto 4OB :

a) OA, OC qota,l5is o)lgo oO(1.;?

b) BC o)os mlgo 66m€ocdol6.

sin 40': 0.643; cos 40' = 0.766, tan 40' = 0.84

nU'cacd : 4 ftioaoo : 8 o'l.rti

s0(n(0r6Bud/oco6noud : Lo'lcocfmalojl rulerord gudo,fisem qcalofo) L.lln"mo

Q.1.9

anc"

nt|Dorot(i'a lBAC =90",AD = 6 oa!.o"], CD =9 6$).a1. L4CD = jr crolo)coi

a) tan.r ooon olororol{o)?

b) ,18,4, erlos Gngoorrd;

c) lD lo))os m19o "Oo.;?orjca,od : 3 mDaoo . 5 ol(r,'ld

Q.4.10

cDlaaj6slud/Uco6noui :Lo1€6r6ms10r'l@e6rs m"ncoJBomcos qlc41o1c, L 0a"m@!0d "t61.o61.€61m1

" nt(d)orojl(o8 O colmocro cllAadroolo oer acaacal; AQB, L4OB :120", IAOQ :60', a,lsc6),.t)

Pp = 3 o(ru.D"l. (oD@coi orlorooloiloal (sr0.00 .OL@?

oricdlca, 3 olJooDo . 5 ol(r)lq

Q.4.1r

{sOUaa0r@n|dlocrdSIDo,ud r f0il€6,c6nqloila4os cruoocercrotocos Lolc€@c(,16,L"lrd"m6BUd "J|a?.oo]€olm

6l@l ooorolo0l cnloo, ('ood(di otoidolcm aol 6lt 40' eoloicdcmrjlol 6c6rDlfDl. o(oomr'lmJ

o'oaloJcoroddol 20 al8d msmojl(I)l4@.,eio o.ooIo.ioag (6ntU)o 80" cooica,cdrDlletc6nj a,c6m)cmd.

5roJ og}a,c6(n;lLoo .,rco:] oooll)-iloce pccDoo 66m€oc6ol6.

(sin,10'= 0.643. cos 40'= 0.766, tan 40'= 0.8,1

sin 80'= 0.9848, cos 80'= 0.1736, tan 80':5.67)rnica,cd : 4 nlloqoro:8 Elml5

Q.1.12

isD('d(olgBtd/Ujco6noud : Lo €dbc6m4loflqr3os ar,)"oco)onDroE L,rcc[orJol@, Lol@"md6]l.nc6o

o(.l "rlgdooool(oi otoEdoJm ".o1, ool6cool.d8 cril(mlo 10 olgd Grddloel(crlpp 6loJ s(xoloal

asrilcoo 20' cor.68ca,c5ntoi 6c5rrl(m:. oo)aDloold)lgp cec6nt 40' cooic6c6nteJc6nj saxajloai

crilci)o 6c6mlmoj. ooaolco)lo, Ggcsrdeollo, sorolo 6rco co6lotorc6rd. 6rcl "{]o,c6co"ill('o cilcolj

"rl grolos o/1oi a,mDdocdrol6.

sin,10'= 0.6428, cos 40'= 0.7660.tan 40':0.8391

oricecd .,1 cuoero : 8 o]fit5

(0D!0aJdtnud/ujco6ID6,ud I l6ils@,t6n4loto4ds mr"oco,orotntd ldrsoJcolo I,roltD"trdll"oco"

Q.4.13

orJ.Dlmjo po)(?olgp ofi; o6ts6mu3 (o)zailoi

Sil6i rnmlo o"r.ilo oo5ils.ddilooe oJduiec(,o

toi rt.m)o c/eilor o6:ils.6otooA zl6-.qecao

a) 6r(.l nEdlcRU."illo)o .}lod6oJ6

b) o"r.t@ oeslls(dldUoo3 gcooo .Oroi?

c) oe,i(o) o6tsoio-io01 peroo "Ood?

(sin 70':0.94, cos 70' = 0.342,ian'70" :2.'7 4'7)

I 6 olBd .lr.dlaol6n;. orejlco, o6ts(orotoo6 "llor45" cooic6oc6rrjlello, oil.illD oasils(dlolo(d dlor70' coldAcdoc5rDlprlo ac5ml.ml.

mica,cd : :l ruolo,o : 8 o'1.I)l5

r0O(IdoJanUd/Oco6moUd : Lolcorc5rnolol pdGqrJol2Jl"Jce0lrol6L.lrd"m dol.ncoo

dsrdEdo.oo,lellgp ooeld no.],,Tulml oJd,elloi ot(oSdolcm 6lcol 6)t gsellellgp Brol 6Ho8 20.6"1dc€oc6rlt{di 6cdm}.m}. ooerd..i'ftl(d8 mtrDl. 100 olgd crdd}oei rtoi€ol(m 6r(ocu3 ooelddolcffol.Dl 1216gilerlgp d,]toer 45' co68coc6r'rilc6E 6c6rD)(m). dOF,ll.ra

a) oJ.rdslpE o,loro6€Bop cosllrDncmoc€6il ooj o0ec6oo!_jll(o)o olocoi@old

b) ooerd.ocrulool eaoooaad?

c) 6nl.d8 6oqrjl68 rilmlo ng)t6 cJrdaoeroc6rr?

(tar 20'= 0.3420)

<nicocrE ; 4 rldru)o : 8 nl.l'q

60Uaor6Bud/uro6m6,{rd : sine- cosine o0rmi rtleleud g0do.lsl.m sJcql{Dl(0) t Jrdhts]]ud

Q.4.rs

Q.4.14

" nl(Doffiloi L4 :40", BC = 3 orD.o1. (oD(oc1oi

a.) tdjlc6c5mo,4rC o)los dr@lorjorD(Brooo 66tD@ocaoJ6.

(sin,+0':0.64, cos 40'= 0.766, tan 40'= 0.84)

b) aol L(dilcec6rD.dJlrioq 6raol cecdrtocB GDgoj 30'(6rg(o)coi

l0' c6c6rrtcd d{)cdioo(o)lgp orooorlo .d)lp{oc(o,ilolao)o "Offd

asnra]L"rcooo C\lod6ro1ao)6.

fi$c&cd :,1 .rDDero : 7 ol.nlE

oordaJgBud/ocofno,ud : sine, cosine ,Oml Gogoreoud pudo,rjslarD esJralo)lo) Ldua-msBu' do1.nol66llml

"jlL(')(.J6ilcdE L{itic6c6mo lrc aJJos "rolc,rJ61DcaLmoc6nj a BC = I ocrD.o'I. eo ,a, = 70. oolo

ZC :40" col. aoDoocol

a) orcolorloro(xjcol)o o,c6ml6

b) ,18 (o)los .rr"lFo e,6rD€oca6)]6,

(sin 40'= 0.6428, cos 40'= 0.766,tan40":0.84,sin70"=0.9397,cos70'=0.t42,tan70.=2.747)

c$c6cd : 5 auoqoo : 7 o1cD15

GDo.iooi "r.d'lorl

(dro GB o c,llo

docollaor "rooo)lml. mt6oBP)os

Q.4.16

Q.4.17

{UO0?[)dtBUd/UJrO6m6,gd :sine, cosine o0fin1ongall6ud gudbl,iJsem qc41lD100, Lol{6"odBUr} "tadl"o.dil06eml.

Lote6c6mo PQR 6Z PQ : 8 ocrucelolgolo PS ICn p. ffro6rd. lQ = 20. oolo Zn - 50. oJoaorE(o)coS

a. o(0l .{}drrcocojilLoo .!roddol6.

b. dS ooi (r)lso sr"Tn)e.

c. RS oaa m'lpo d,c6ml6.

(sin20':0.3420,cos20'=0.9397,tan20':0.361)

aica,rd I 5 0-l)oooo : 8 rtorq

oOUa0)6BUdlulro6nou, : gqro0,(!r?o,pro ng)fit(x 6,6no6rc66c{rd LlDlc6c5m4lol dngrxl6d

Q.4.r8

aol ddle,loae oi\!6o'l(f3 ctoiaolo-D 5rocu6 ooerd doc.ruione oldoieccoocm) 70" cooicec6rrilalo 61dccl,6.drd) 30' dlldcaoc6rollpr)o 6c6mlar]. spl.D1oFjl.6tr mlm)o 5 olgd olaellercolj(6Doi cDl{oidolcrDoi.

a. 63@] d{]6cB@.jllo)o droqidola

b. 6!erl oi Tlfnlo 16\.0) 0ro6oercor5nj ooerg'en n"1 .

c. ooerd d])|D fi\,jl oa3 poroo 6c6rDl6.

mjea,c6, 5 auo(oro : 8 o'l(r)l5

lIjD0aargBgd/oco6mo)vd:10',60',90'so,c6mgrxeggLoflsoJc6m6Bglos(x0a8Bgl6ts{srddua6nknrogudodslmL.]/d"m

ffX/dDEC

Q.4. rsEe

" nl1o)ololoS aDl:rdlola$)cmd cDfirjlcaDcorDoradlojloi

"rorc6nj.,1BCr 61(?l ir.D)ooc5rd l, = 15 o.ru.o1

a) .r(lJ)lcoonjlo.{ (r)'lgo 6c6ml6

b) L6jlc6c6mo IEB erlos oopc orcrodBgJo 6c5ml6?

B

pedao1o8o6c5n; aDqcocaolcoJ 6tao] mils.)elol

Oo lrtc = 30' 90 Grq6ri.

aJca,cr6, 5 ouoo)o : 7 nl.n]i

I

Q.4.20

rgord0DgBtd/U.Jfo6moud : g@oo, (Bn6ero n0amlax €,6mooc€6cfid Lolc6c6moloi lgngoloud

crulojan 45' co63c6oc6rdoi ac6rnlcmrcod oooitnooi otge,ll:d 6 olod CrJlgol6nd o{)s,ll(6a

a) oo6{rnoq goaoo ec6aDl6?

b) ffD)ojoi 30'cooicdc5rDl.dE d,c6mlccDjcoi ffige,loog mlpo dot('coc(ojloll€olo "Ocd 6c6rDla,?

c) nneenoc! m"lgoJojloi oroJm orJ.6rjcor)o oOLo)?

c$cd,cd, 5 oloaojo i 8 [l](r)'ld

Q.4.21

(IQUaa)gBUdlulcrdSIDo,Ud : p@oo, {srdoprd nofirjlrx 65rDooc€ocfid Lo)ll86c6m4loi srdg(I]Soud

6](b) oo.drdiloaa o).seile,jlo'laoJ.m oocoi o@oiojlo.{ dlc!5j(63 atmlo l0 olod .srodoero)lge 6!{0l

dccilocr) 30' 6,1dcdoc6id(oi dcflnl(ml "O6llcra

a) o)o,oiloi rjlcm)o "OLoJ e(oro.drdjlelc6ni aolococcd polaolcmd?

b) 6lo4l6).00 o)ccad@d @o6dBlcoJcoo.,sio €rooc:d GToe{o6c.jlo.rJ 18o 61dcdoc6rrtci 6c5rDlcmlo18,lod pcJ rJd r0.ool8 d pco4.6lo,lpl,eni'6r.ri .r rem;o

sin 18'= 0.3090, cos 18'= 0.9511, tan 18'= 0.3249, sin 72":0.9511, cos72" = 0.3090.tafi2" =3.07i 7

mieacd r 5 al1JlDaoo : 8 o'lmli

6o0?00rgBtd/ulcramo,{/d : sine, cosine ,Oml i8rdgorloud p"J€orcutgfsJcqlofor L Ua"mdnglos oraloocod

Q.1.22

" nl(o)(i5)onnt3 PC : 10 oruoglalboolo S4 P.l oj elo6rrc,rJoc6nj.

csrqlo)c.d8

a) IPQS 6'q (slagoi oOL(r)?

b) 9S ooa mlgo 6c6m)d;.

c) PR oa3 mlgo 6c5rol6.

sin40'=0.6428, cos 40'= 0.7660, ta 40'=0.8391

ZPQR = 120" ,x,ta .PRQ : 40" srla

a

cnJcacd:4aloo)o:7 01.Df5

Q.4.23

60Uaa)aRUd/uJro6IDa,Ld:ttngetrtpudo,flslmLor€orc{r16!'lnd"msDge6rsd6l"nj6o

elo6nloc6nj oOFl(oi

a) ZOPA <\as .6npoi oOLoJ?

b) P,1 oo)los (rJ"lgo dOL(')?

c) Ol aolos mlgo oot(')?

(sin 54':0.80q, cos 54o = 0.588,tan 54'= 1.376)

mica,cri : 5 oloao)o : 8 iDl(T)'I4

Goma0)anud/Ulco5md,ud r po}6d, lsladelo n0rmlol 65r0€oc6ocfid Lo c@)cfn4lol lsrig.!A6{rd.

Q.4.24

5l@l sor.jloo3 @oi.x(o6.BCllprccoil 6lco coolcojlo8 2 oo:ils6sBoA g6ni. sorcilo.i, oldlgi(d8 crnmj

1.6 o'lgra glDoolgc aociJa oa,5ls6sBop 20", 30' 6,ldcaocmnldlgilelcol 6c6mlml. sol.jloce g(oJoo

20 izlgd cro6ni.

a) 61.0] o4d,GdooailL(')o ojaoo;aol6.

b) oa,sils 6dB0A .dJzollerlgg .oro6ero sc6mla.

(sin 20" = 0.342, cos 20" = 0.94, tan 20'= 0.364, sin 30':0.866, cos 30'= 0.5, tan 30.:0.577)mje.scd : 4 oloaoo:6 o1.D15

Q.4.2s

oDl'n(r,6s80d/ulc06n6('d rsine. cosine "0.m1mEgol3ooij 9ud6dsl.m eqlc2ilol(, Lotrd"mslrgAos oralooor?o

"-jlt('oloioS Loilc6c6mo ,!8C (orlos dolortroroca,Laloc6ni O. ,BC or)os a(])jo (BJolc6nj ,. dlol.rlcro).srgoo 6 oclJ.flolRolo ircoro llB oJos c6t(Bc.$c6na 140'olo 6rgoc.oi

a) 5roJc5l_d lB o)os cn"lpo ec6rD)a.

b) I (oiloS atmj BC cotcelddolpE ero6tuRloo 6c5rDl6.

sin 20'= 0.3420, cos 20'= 0.94. tan 20'= 0.364, sin 70':0.9397, cos 70" : 0.342,ian 10. =2.71'7

ote6,jd r 4 cruooro : 6 Dlrts

rso0?0068ud/xcoSmoui :sine, cosine "0rmlcrdgrul6ud gud6r.lsAr0 qc41o)1[0) ldua"m6!916s nrdllooc6o

Q.1.26

" ill.d)(l'llrjloi Lcrtedr,c6mo lBC, ool "rolooc6ni. PB -'7 6rffr.oi1. eo IPDD = 10" l())lo (i3ro5rd.

Z4P, = 80' carg(orcol

a. dcoloolojloal ()]"lojl o0Lo)?

b. doloordjloql o)lgo d{)Lo)?

(sin 80'= 0.9848, cos 80'= 0.1736, tan 80'= 5.67.)

mje.o,c6 , 4 or)oaoro:6 El.Dls

10

cGt?CDJCQ)o s

o€JCDCdSol6gBC/A

oDudaJalvdlu]co6rno,ud : fi!4,Jotom"olDjl6

Q.s.1

20 om).o"]. orcccllo 24 om.o"l. dcolorlcoo.)llolgE oaol

6lo] cr)odo)loorlo cDcal' m)o"rc6corladilcd}lc6tt6EBglo

g)os o"lgo "oLo oocco,i aolaolo ?

mjoiro)lo(r$('l" ila, 0tdoil€ocai c6ruc6njl

o.xtocog)orol. L(ojlc6c5rD.drdtoae .xoo66B

nu'cacd : 3 ouoaoo : 5 o'lctlg

Q.s.2

{sDUa(l)aBd/Osrd5ID6,Ud : 0x4,rnr3o0u"('l Jo,

o1o p6rcca6ilao 61(Dl clo!-raD]@c$o):djl€,(o)los orcd@ro)o-laddilool crdgollagc6nj dltco.onjloi ac6rrjl

+il(oldol(moi. mjor;"j)e,,or;os "rcRorsolo .iollorlcoroolo "€)LococcojloldoJo?

arica,cd : 2 nuo,roo : 3 or'lco'li

Q.s.3

|sDUAATABUd/0lC06n6Vd : OUzdrolAOOUr(Dldjlo

42 ocD.al 42 oc-D.ol

61.0l .rr)olr.d)lo.rD'6lone.rjldojl.eocoi c.!6ml oc6nl() oolSilocoJsloto rDo"l.D](D@idjloc4ol" .r)ce:

LCDlcoc5m5BBglosrDlo crdgoleu3 d'll.D(61otl(d8 dlc6rDl4l(b'16olar). @ot potccoccol+i oxod.oJl(bmj(o)J"rll6 cd6@1@ocatr m)c(l)locc5rDc? e,co6mo oI(roBoc6oJ6.

mjcacri r 3 m6aoo : 5 o'lrr15

GOrdoJfl Rudloco6rnoud : oD4do)loru"o)lajl6qre6rs p. r61olehJ6"19oi

29

.!osl6ogHco (d)lerjOcco m)oDrlit]@.m"C'lojl6rolos

Der^roJglrlo I rr0l d\p r d/lJg')lJo dr6mJ6"rc6.!6o1ocl mlgo 10 o(ru.01. .dDocoi orcdoo.t

ojco,cd : 3 ouoaoro : 5 ol(r)'lq

Q.s.4

Q.s.6

(!r0Ud0D&nUdlUJCo6n6,ud : ou4rro)l6rnr"rolo il6[olos p rdlo)phlo,iJga]i

Q.s.s

18 o(ru.a1 "rc6or€o)o 41 om).o1. "rcdrdor€ololgp 61.0l m)ojlolomi@lojla, odcotocorcolo?Joc(o) ordsmd$sercmioae orogjgoj 6c5mle.

oljcecd : 4 olJo{aro . 5,D1cD15

{sOUa0osB0d/0lro5mord | 0u4d('eGmlDldjl6o)36rs oJcJod

24 oox.ol- drcB(xdolo 20 orD.a1 orcolorJcoo(xlolpp ao] auo,r.oiomjo)Jojl6(o)los o{c"jo)o 6c6mla,.

oricacd : 3 clocoro : S rfl(r)lq

(00UaaJaBUd/o$o6rDod : ouadoAofluiot(il60)los o.Jco.l'o)o

Q.s.7

coco] g6rlBcdo]cor oloir(dJl(oa\i.oloj6erJos DrcRoi€o 10 oauc0lolgol. pcooo 6 offuoala"loolo

.0DE d. coc"rl p6mcd6tlD) mror,r(o)lomj.6J]. il6()los .rcr3or6d 5 oruaS]olgolo gq)oo 24 orua3lolgolo cD6d. @6nd crjo)o-n66glosroJlo orJcojcoo a6rBldilsld o)c(o(lJ)ojo odqlle.

miea,c6 ,3 mrorroro : 4 olrnl$

6Duda)8Dt/d/Oco6loolud : oiJroonu"ot"jlo

Q.s.8

9 oru.orl. "rc6Grooorlo 12 ool)oalolgd plo)o.llo eg€ o{oirml(Dlo n6 .ri{Ao1@oc(r)colciojDc|c|)

orla6loco0oaddilool (610(0clrlo G6Lmc6c6Yrlo ooLo?

aJcacA. 3 fiuoaoo : 5 olmls

igtord()flR{/d/ocrd6motd : olom0u"rDl",l6

Q.s.9

l2 omr.o"l. coro@oJgp .xA.oroca,Joteocco,6l.0l cta,ld,6rco orandolpp 6 orj.drocooo5sBgcoll ol.jlaol(m]. (,rd('iloercol orJ.drocoroo p.rcroccDll4l6rBc€olaD .]llolomjcolo jle,lo)Jos il@lorlcooo, a6rO.oo

mjcacd : 3 mjoaDo : 5 o'l(rts

OOUaoranUd/Ucr?6lI)oud :or.lomnu"ot"jl6, nJoroou"o)Adl€,orlos dLoo)!rnro,fl3oi

Q.s.10

120' c6L03cdr,c6m)gp orloroco0oo gorcoorcote] g6rBcdol(m ortroDmj.dJlojl6colos (6Dc0orlo rlolloll(oroorlo .Daollerlgp cnocro6DmnoDooi? .sD(o)loaA orLeorerorodgd 108 r do)lotcoofiDqlolgd asrgoccS

crooooLo)? jroll. loo(o6)0l.6) ?

cnjca,cra' 4 mtoooro : 6 o1cn1$

6DudaJ6BUd/UCo6r[6t/d : ru.Jolonu"oSoj6[ol6rs rxL6lo)elo JG,ngr]i

Q.s.11

t5 oru.o'1. (6ro(oolgp 6l@l .riA(oo)o o6aB) .lAadroco0?6lBgcoil orl.taol.ml. @d edcoccrt"] p5nec

ao](m ora(d]d)mj(d)lLildldlFJos orcBdlogorl6glos .Dl6o0oLo)? clrL6(oerolodE.rJarglos (d))6o(oJL('?

ojcecd ' 3 "-oaoro:5 iD1(r)15

Q.s.12

lsro0?argBud/UcofmoUd : qJolo)flrriorldjl60)15)s 9(r6lo)phjodJgoi

oo.6io)sleil.oA atdol:J aol orJ.drooj.Dl. n6olos drcB(i3ro(oo 30 oruoel0186, p,o)oo 40 ocruoelol96-(l]n('ilool lrolorl(ooooLo)? poro(oo L0 ortroto)arjo)l" n66glos olor6BBC.4 orccoo c.Daolfi)(')10jdcD)oloool g.jloj 50 @J"r dlodolloi GrOoa .{Dl(') o)or(orcalo?

mica,cd : 5 oDo,roo : 8 olmls

Q.s.13

cD0?(l,gBud/ulcoono){td I oj@lo0uioa"I6,Qreos axjcJoo

nrcB,llgpol 16,r oruaelolgolo !.r.ol.}llaoroo 17 offDcrAlolgolo (i'Iol!) ortroa)mi('l" ndlrolos elo)o

ooL.D? (srdojloal orjcdjl'o 6c6rrl.a.

n$cacrd, 3 auoooro : 5 o'loli

oord(0)flBud/oco6ma,ud : rxJoro0lj"otdjl6o?6s olcJo)o

Q.s.14

9 oru.o"l. Grq@algp crtroa)aJo)ldidcalojlcorcco 6l(0l orcL(oo g"rcon.ri]3] 12 ocu.ol.(grooor,lo 15

oc!.01. gco).o.xlDl99 orA.dro)o\j.6loeca,l.6J'l(())clo oo] orcloadrdil(oi orcdE (i]rdgocmcal4l.4 L"rc.!{rbjo

6el4cdc06 "rcL.oJo

crilo6roroloor@,1@i orlolo)mi(d):dlacajo')la)cco orcLoordioog p.o)05)oLftD?

a$ca,cA | 4 oDoo)o j 7 o1(l)'15

{soud@gB0d/ulJo6m6,g6 r arJoru}01J"otojl6@los oucol"oo

Q.s.1s

10 oruoelo'lgd or"lo)o {sro(oolgj! orA(drococoo g"rconUi}:] .ol.r}oo)lo fuildlcolo 6rccoo orlorDmjol

"na,lo)l6rlec66il. m'l(I) g"rclrDcut:g .xlorDcouo.dldilocA cd,l(Bc6c6ni 216'co)l0 m,icrn porcccDcolg

orsolocor0ontoce cal(Bc6)c5ni 2884 (o)loc5n;. o5rBl orJonDmi1o)l" jla,6glosco)o orlcdj.oo dc6mla,. orjci.oJ5sBod .d)oojlerlgP (oDo(o6r)lc'lr)o

"OlId;?cnjea,cd : 5 olroaoo: l0 o1o15

oDrda)sBud/uro6no,ud I 6ocgolol6r(B oJcnl"oo

Q.s.16

6l.dl aruodo)lodos(o)los .l@o1oo3 mlgo 24 oatu.o"l. crodil(m]. claoil.di dlorlo ojrolojlol!)sldoc1].m )69xJo.pllco Gnrgolo)loT.r3r joo arem;a.

nJcacrd, 2 cruocoro : 4 o1rnli

rsD('doJgnud/Ocosmd,ud : Eocgol0)l6rqd 9dcllo)phjc,fl goi

Q.s.17

l44rir(6)]oL(o orDc$]o"lgd porol(d)erorlodg.,rlgg cLnrgoa)lorrA lrr0oooLo), crd(')looe oraJo)l cDoolgg c(])cgoroloaa 2r ol or er n r oggcri ooLort

crJcacrS, 3 rnrocoro : 4 o'lrn'li

Q.s.18

{sOU?oJgBud/0jco6nocd : drardo€oJglooiaqd olc.l"odmgeos nrctaloqJo

o6rd (sod(Dc(J]cpdrBglos croo6dBcd .Daoilollgp GLo(n6D.ruro 1:3 crO6rd (6D6Jc.6nD(6.jlo.q ol.\c.jo)o50 "smorDqlol gd Groeo)coS (o6rl3cocoro(oiloq orjcoj('Jo

"OtcD?oJe.o,cd : 2 (ruoacro : 3 o'}(rti

{BOUaC)168td/tucofmo,ud : c{rrgo, rxJoor0!"o}ld116 pola,los oiJcol-(0)tsngl6s 6)too)4Jo

Q.s.r9

6 o.ru.ol- (slqoolgC aaol corco.cocgo poJd6t 8 orD.o"l aoD(DoJgE oljrdomjo)Jojldeo]cdolrDlo.x

D,ic8 cl.(oilool p,o)oo .OL.D o)c(to'ldlolo ?

clj'c6cd : 3 (ruDooJo : 5 olotj

Q.s.20

ru[Ol]?(0,6Budlulco5mo, Ld | GDadococgo, oiJl0to0u"oreoj6, oofin1otdtsrlglos oJrJoo

aco crooorlgp 6Jol Grddococgotlo nol olJotorJo))o_jl6(o)p ! ilt{!)(6lorl.tr3 6cmrt4loldo).m.olcorcoer cjrdoroloor:j oo) .€roolorol6rBcaolml. aordd1-rDcotcg.drdjloo! aoDcoo 9 o(rl).o1. cDo6pl!)@o 21 o.ru.or"l. GrtccDco? oer.r)o:oJoloilo(q (xJcoj(d)o 6c6rDlo,.

mie a,crd : ,l aDrDaoro : 8 il](rtq

rso{td0uanud/ujrc6no,d : (ol?du,eocgolo)l6'.p.UcJo"

Q.s.2r

1:srdd(1)ccr)cpcdljojlirocco] Grcol orcL(fJootooe orjcaruo 60 oru.01. crod],lcm].

nrica,crd,

oD('n('E o0Lo) ejlgd

2moaoro:4o'lrti

Q.s.22.

OD{tdaJ6suud/Cuco6noud:eocgo,drdrduJcocgod00n1o3.l@Bglosg.mlo)eldo.tgoi

oco cro(oolgg (o5rd .srd6(l)cocg6dBeloi occoccrDloap()lo g"raolo)erolodgd 120 lr.oJlol(oomo3lla'l96.r1oo croel.m]. @orc"rd6o;oca{ ao; crncgo;enecdolo)c(l'8 croojloaS ploloetotoggoi

"oL.D?mjcacri : 2 ruoooo : 3 olrrlg

f6fd(l)JC(0)o 6

CfDgo.r0fruoOgerOB

GDoaoolsRod/(xc06Do,sd

. 6nilmlooglos rDljre.ruoo{a,oA ec6rn)cm.d.

Q.6.1

r,l "OCm"l

(slaa,9r6sBc.6 oo2j n6aoo 2 o.ruoelolgd crolorl "Osladlocdc(a l, B docml

GDil(Bldoglos rD],r6m)ooJJ6oA coloctaoo (2,4), (6, 8) .Ocm" a,llt. pci.dr crd6s@BoA

g"rccocsjl:j 08660 6r@l oolJol1olgd n{)mj "Os]('ro)c(ni A, B "A@1 6rtlcRlaoglos

(jr)l,r6crr)oorj60a "o0o)ccotol@olo.

n6]660 6l(0l ol:ruoalolgd "oo.msl.dl0cHcoa c.OCm 6[il(B]ollloo3 ml"r61:rDoorl (3,6)

"OD,lloi "€lad,o o6rd oo1)ol"lo'lpd (sro6lc.nrcra

C oJlos cr)ld6aruoolj oocloc (ojl coll dol o.

fiJcecd, 3 aloaoro : 5 o'ht5

so{n(0r6BUd^rodmaud

. 5rrilcBldoglos axl"r6oxoorJecd 6c6m].m(fr'lfij

Q.6.2

5 offuc4lolgd GroooigE o@: orlooo ( 1,0) oOCm 6DilcBl ce,L(Btzc(ot .ro4coi glic

orjoroo r Grod]!!o(dr1r) eltorlslcm 6Djl(Bldog)os atuldd)(rno6rjaoa "6<ri:iu

or5ororo ya6rd6,9rooro alsilolSl.m Gnil(Bldoglos (n)lir6m)oFlJ6oa o8.oi?

.nu'ca>rd , 4 .nroarro:8 olml5

{oo{n(ors8Ud/ujccflaud

. srrflcBloilo.S cDl"r6cDo6lj6od ac6mJ(moj.

Q.6.3

oruo6dBod aorddir5sBoidd (ruocooo6BBgcco) aol !r.dJJoomtoae o6r"BJ ,rlpraglos olooljccscslaun (2,4); (8, 12) croani. GDa,ei6dBd o(oddoco('),48C, "Ocm "ror;oo oo9]g"jl.6rorcco m)ncmonj; fiDoo{ceacsil6od l3nsco,cpodsloro)ar. "ro)lo.6rrno.re ogl olel

6glos m)ljr6m)od{d,('a d,c6mld,. ^lo)loaddioo3

m"lgc,rlo orlojloJlo 6c5rDl6. gc

"r(o)looloiooe oi dld6rt.donoc€ a]1g" "0.16;?

.nic&id : 4 .l1)n(\)o : 7 rfl.n]i

(0lovaCorgRUdru)co6rn6trd

. EDnorloiloag crulda(IDootjocd 6c6mlcmotoi

Q.6.4

oxoelsl{6j1c6c6mo lrc 00,1.di l(-4,0), r(6,0). C ojl.di .rnmlo ,48 ,oilcerddd ./o+it

SJgg ero6Dorc6n; CP cndlei56BUi oro3] Lotcdc6mcrotoco "{}e,cB(,b!-jlL(oo olo(oiaol6.

P o)]os o1))d6ruoorj ooad? CP colos mlgo "Oad? C colos .rDldaoDoolJa,uA o{)el

aJcacd. 4 aDrDaoro : 7 olm1d

lgDrd0rsBud/(r)ro6n6ud

. 6njl.Bldoglos rD oo{c c sc s]d},ua 6c6m}fD.ojloj

Q.6.s P(0,4)

c8,0)

",ilLc,tcddjl.di lB orjc.r!oc(o] (srdd€!orAcnoo P

"OaTJ 6nllcBloiloSelsll d},s.mlcolcarl.m)

l( 8, 0); P(0, 4) .sro(orcoi OP (o)lo5 o'lgo "O.rd? B co)los mroo{ccscsi'ldod orUor?

mjca,c6, 3 orJooD. : 5 El(nlq

{0ol]a00renud/u.Do6rD6,r/d

. ofcBlonooi crr)ddrrDoorJdod 6c5mloD1otoi

Q.6.6

" nL(D@rorcdE oacsl(dloilo'ldlolm ,-)a)I@a OABC

( a$ OA = 6 6$).D1 zaAOP : 45", z?OB = 15"

{aD(a]ooi -Po)os cutd6,c-no6!.\6ui "Oad? B

colos (rn],.rdlcnoo.rjd,ua "o.roi? oB crq(bocol" o

cdrl(Bocoo)o or(b,olaol(m orjroa)o r (.Ide$joadr0)

6lS;lD]Si(m 6nUar]6oglos m)i"r6$uoo{od d0)m;?

oric6,cd i 3olJoaoro, 6 o1(n15

lsO{nCo,ABUd^JCOfl@,Ud

. 6Dil.Bloilool o1)]d6o1)o6!Jecd Ac6mlcmcrtnj

Q.6.7

L.ojlc.a,c6mo ABC \',d1 A(2,0); B(8, 0); ,4C : 5 (()l6rDld. Lojlcd,c6rD(oloioa3 "rodgoj12,rcololoicol6rrtd. GraasrdsEoA oro:j L6tc6c6mo IBC olos €d],cr3@!ill(o)o ol(b

coj€ole. C (()los or)]d6m)oorJ6od aJ5rDaoc€o)6.

.r$cac6' 4 oloooro : 8 o1o15

l8DoAO]fr R0dlOrJiA6rD€,Ud

. 6DjlGionoae .ru)deiruo6rj6d .sc5ml.m(d)loj

Q.6.8

L6)lc6c6mo PQR (di P( 4. 3): 8(6,3); PR = 13- Lconcec6rD(dlolo0A or(o*goj 60 d.dJl.or0o

(ol5rrtgc6rij. lP > 90" a1o crg6ni. crddsj5sBUA . o4j L1ojlcacrm.oll'tooi n$a,cr:oo

inLo)o orod6ol6. R oq rDld6(ruo6){d}qA d6)el(oJla.

micacd : 5 mroooro : 1l o1m1$

sq(rdQJsnrd/uDo6n6rd

. 6rrncBl€6Jglos m)liracruoo{Aoa 6c5mlamftrt0j

Q.6.e

. nl.oordjl(o8 d"cffi)lii ABCDEF 6!@l

o1)r2 osioJjelsocsnj. p(6r'loal610] orcoo /6 col6rDid. l, D pd(o)los ruljrairuo

orla,ua "oelo)]6. -' colos o1)ld6

moerS "{)<rdr @c "erorj'a)€roidt oca

croo] .!@6sBogrolo mj"rdrolaol(m

orlroloorolooe Grocoo ool.o?

v

cnjea,c6 : 4 cuoaoo : 7 01rr'15

lgO0Ao)AD0d/,r!cla5m6,rd

. agrodigr6sBgiloerolo crdarloidol alDcol')ozclc, orodcioelco)lo m)Jjloanjo Jaiui

Q.6.10

,rloios ao(rrtslgE 6nilcRlaoglci ir orodir(o.adtml (Tlaccro(ooc(o) arocotoe] 6lcol cscsll

6rilGJ@togcolo 1,(6'rda.rlol6t(r)l (ruoc(rooocror oocoloer 6r.0) ce?csl 6DjlcB]€oogto)lo

.D O o.oil Oll O! erola'.

A(1,3); B(3, s); C(-6,3)t D(3,-2): 86, a)

o!'ca,cA : 2 aDoaoro i 2 Elmls

so(nc0rsRsd^no6rn6lsd

. J (srd4gr61dtml m)ocoo)(oocoo . ooiloer (o6lr; sDn(Bl€o('3 o)aolellgp cndeto

Q.6.11

jr Gnasroirilo)l cDDc.rD(Docco oradotopr omr; 6l)jlml€opc5m' ( 3,2) go (4,2) po. p.5

.o5n; 6m'lcJaoui (d)or2lerlgp (sn6ero "Ood?

(4.2) "O.rD 6ar,i(BlonG8 mt.rD)o 5 q],)6rrnd

!yd6610r pc('r 'r doo]-il 6.o.rn0o,"gp 6r)J- RJdoglos 1 I , e, n oo{dJd o@l o"dr .

cnjcacd : 2 all)nooro : 3 o'].d5

rsrond0)6Brd/(l)cla6m6rd

. .y Grdaigrordiml ruoccro)(ooc(o) oicoejloer 6rrna3)€out ('oolFllgp cLdpro

Q.6.12

l crda,gro]djlcol rDoc(roooo(o) oroeiloer 6loJ aJlrnlorcerd (5,2) pc oto,r cn6,9jc!l

ocao,il di)dalslam 6rtl.Blonoq ru:ardl(rl)o5ril6ua doel('ls. pc odrEl 5i-florJ€oglo

oorilerJgp ('rdeero "occ;?

pi, (xo y (ard6ei(6lD'l{n3 .ril.mlo ooLco orlerjl{ oaaoer

coc6ni,

mjea,c6' 3 (I!ol@0 : 4 ll1(r)15

rgordo)6nLd/0jco5lnd,0d

. Groa,g,r6sBEiloer 6lxl(Bl6o0a aoJzollellgp @loeero

Q.6.13

(2,5); (a,5) "Oor1 6nllcBlaooi cerc€1dl€oJm ororolo (3,6); (3, -3)

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