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Page 1: I r, tragaram.lk/sinhala/downloads/gce_al/past/2016/16Aug... · (b) A, B at C o;a6 poauJ qQ r::dOC dd axodcrzoo oaoC ococcd E@ @Eg?rJ 40 oqar4 tsooc6 rsdcor:J ts@ededcazD Q OAgzrf

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= 4abc OO oe:ajoaJar.

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d o6d, z5 -I = Q ar@rodooci gEalo 9e ero @o:c qdoalo.

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e{OEcs r = ),(ai+bj+ ck) $oc oSOoo o8o: oE ce@ggdor O6oroO Cs2t?tc3 Oo OO oeaJouJa;o@E ,t e#c@Eo:E. ar@ggaJo O6oc3 EocgnlOco oeoccoaJnr.

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AL/20t6mlS-rl 3- Ooo eooo

3. ABC$ozoCoo einczscd $ozoCoczocd $cd@cszo csOca}::d qcd qaO 6@0 cgdlnlO oadaSgo odeoc p eodcdzoO

oO. Aq@zr} Q qcdcs Eqoa$ saddo @o q BAgnJ I qcdc: Eqeoad sedc)cso eopal q Ce€:rJ p qcdo EqodeaddcsO e?tgr:J q gi6o cs@dcEcs gOcezo $d@cs Eqood 98og8. dE OodE Q eQzOdr gO oodgo@E q

$oc oSOcOzrJ ce1g6o@43 $edgocsE BC gcad 996o1 8ftd o 88Oar OO osuJOzr}n:.

4. ednu'JOcr m Q gocqOn, / zoc6od Q, qOe ge.sd gpO{Oocoal rBEQO ooq8zoc:,

r = al(sin 2at)i + (1 - cos 2arr)j] 06zr] oqg ero6; o@E a 6x a e6l gcr.r oo.(i) oE oor:, aj SEpO ooq8zoc: :c,$a C odalgce oc gdo a Q oanJoc^:d aot:j(ii) C OOc dE ozoC&zo o@rncO 2mazrttk aOr,j

(iii) n + 4a2(r - aj) = 0 aoriJ

oerujorJrr:.

lonool6 800 Oedeo.

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ALt20t6/rr/s-tl A

5. gOO Edoi octF@zd @z:: einctocd u = u(icos6r+ jsinc) goOroc:Eai O6zlc: Oo cizoalOo m g

ocoCgcrz$ gcd@ooC Q Stego 916 O@ qdo @ eoc eirozr}Oo MQ ololgcad ce@o {o1oO8. o@E 0 . a < frac u 6A oa'r EosbcaeS o8. colgo@rd og m 66 M E goDo- B@oo@'zrJ vj ac wi oo8 ar@,

(i) e9ocoC qozr.r>Cz::u qcoOcooC OocgnlOce mucosd AO6J

(ii) gorco8 ero(€€b?ocs ffi aorJ

oeaJOrrJn.

6. aizoaJOcs M ac q6a a p e9zoczocd OarJrlczocd OgCed dO Edd oco6Od @tl @cdEOEnJ oocd€)cs8. dB ogo Sded O EoOn: qrld odzrlgod v oOcoc,s Sorl o8. oeCoC Orezo cl:d8cr oceccsuJar.

[odol6 8q0 Ood?D

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AL/2016nus-rl -5-

7. R esce@oc8 6Ogrod, r = 1,2,3,...,n Edg gocszr} rozrJz::c gnrd Ozo Ozozo es@eoc8orcO

R E goe$z$8?r qcocs I E(R) oeeccoala.

l^(̂9'CJ.

n

n\T2>r1/r=l

= t@ + l) (2n + l) ggo 6,erzsCo?Dca zod@rrJ R I Sogocoo3 oesco:u}o:.

8. XOOdn coes@ocE Eoglcod -2,0,2gcocan'J ozr}ac qCI:d dOcocd es@toc8rs,rco:rJ B@ogc"* I I I ^n2' 4 ""'Y = Xr+X, eoar@oc8 EocrooE es@eoc8orc orcCEq: e0c conJu:; ooE Xt ac Xr cga XE docooJoESde<r oezoE. 18 es@@or eero@?rc,3 2 Oo oszrJOajr::.

[060r,5 @O Oedo.

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AL/20t6trt/s-fi -6-

9. XcezsJnEzo eoes@oc8 DOglon/(x) ce@oc8nc coo:r:}O @nc.:(lftx(l-,r) , 0<xsleeqocrlx)= <

| 0 , gozod orlzrJS Q

oEzr] oqi 6a8.(i) &=6 OO oe:rrJOrrJn:.

(ii) E'(& ac E(Xz) oeecorrJz:'r.

10. Xeecs@eocO EOgrcsd [1,4] gczr]ndo @n rJzscrocdO OnceSrlO q1r:.

(i) P(2 = X. 3) oc P(X < 2) oeercszt}zr.

(ii) P(X > a) = 0.6 Oor e1$q g a E qa5.a ocscc,raJor.

[odOd @o Osdo.

Page 17: I r, tragaram.lk/sinhala/downloads/gce_al/past/2016/16Aug... · (b) A, B at C o;a6 poauJ qQ r::dOC dd axodcrzoo oaoC ococcd E@ @Eg?rJ 40 oqar4 tsooc6 rsdcor:J ts@ededcazD Q OAgzrf

A^1-1

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*- gcda CIooo e5o6zd B€edr erso:rJz::. B oanOco

11. ag o{OEcsd e:ozr qdOc giE oSOc Qocd $c,rc rsdzr Og ocsEzr} ee@rr}Eo: oO.

o6000 Aeco

OA- j+k P(j + k)

OB=k+i P(t + i)

OC=i+j P(i T j)

rZ=j-k Q$ k)

CA=k-i 0(k - i)

AB = i- j QG j)

o@8 Poc QEcro oO. o{OBo OSgooo I E RrsrE Ogc,rnO eoc 96o ooq6zoc^:Gg gdOoroO qlunrocozsdzrJa. o{O5o,(i) orE es@ggdo Ogcszso,

(ii) gcl@cozoo,

46r S@ eeqeoc gOottoc aOc coaJan.

P ac Q oqzo I Ecrt-cgzn: ao Q 916 8o o{oEc,:, qrdordcgce # U gzgooono t2gn oo osrriorlJzr.

gzqoOoC odaJQzo gdeocs8 ooq8zo e.r@zod6o o€occ3c, 8a OABC oqedogoo8 ozszdgzoo @edoei oarOO eeorscsocs rod?tlor.

AB = a Q ar@O4dgcozD etrocs g3E ABCD qca$ndod, arodcEo gocszo, 8dc$ ogto gdoa?rJ @ Eqtocq1r:looJ AB escqa gOocC Eqod e:addcs @o 88Oa: o6Q o. CD estqa @o: E 6Cea>cs (DA eOzrJotrJ CE = xac ABCE gEBcsO @o orldg@, ADE $ozoC<ec: @ol or::dg@o rs@car oa: eBQ c3. x = * aa oc:erJOnJa.

g2zDe?Dca encOo,ocsal 4

(i) ABCDee@OqdgooE,

(ii) ADE $ozoC<boc.r8,

8ca oz*aJgc,O AB 8o 916 gd orsccsuJzl.

AB oot 6bo colEoonJ, AB 8o ABCE p88c:o@8 8on: odulEoo gd oceccs:rJra.

t2.

leOOr6 8Q0 oeOo

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AL/2016truS-tl

13. SdesO qca:Ecs a Q gOO t:lecszo 6,o6@ O1Q@ oSOcOd Qocd e6eo z gc6@ozo oOcocl8al e,izoa'JOcg

B g"cgOd gdoedo zodg 91o6. dE O@r:roO Oczs'r gEodCOo mkv ol1, o@8 ft Oo Ec:nod q v

q oo. r::socs gto€o qoqo co@al a6.,*> L6,o6@ E6 L = 4 * llnf , Itinl ) rax oqg 60rr, oo- k Lz \Ru+$srnrlloezdOc Z gd csc@o g"cgO @6zrl od zocgo oesccsala. A

6,o6@ OqQ@ obOcO QocJ oogO O€oocJ q tiJ OO gEodCOo @ 6.m zoda: OO Q qiA EO, g"cgoO u earlr,)gcd@eozo oOcoorl, dcs gcd@eoro gder:o zodc gcog e1@odor V oOcoornJ ce@OzdO rodzsl

6Oc co:da.

g@o 6dd o@escsd @or 06r:lo Oo: Ag@o ocoCAod, o@eecs @r: EaJo6o EoOzl Bee@co g@O

es@o ffiOO?rc,: oO8. o1Q@ 8g Oa oOcoocooi Q A I goOcoocd QocO ocoCgOg odrr3g oSOcO

eG*sozoicrod eecq8. ooCg oqn gnd gnrco8 cooe6zoc3 e(0<ecl)oO. ooC6 oqzo

goarrCou groOcoocoE ,/ SocgdOo , I = |*u(1+ e) cosd OEoS oqg gOr:: OO osnJO:rJ:r:. o98 m ceg

OzJ Od ooCgoce8 dzorrJOo q. u 6A co(3@O oed A I oOocs q oO.

o@@ gcoOcocs ocDtrro63?i'J oeoC, oOnoJ pOoBzrJ ooC, ro4]O Etec Eg O- gC Oc6zo alz$EocJ eocE

ioccoo d csztjzr d = |O - "'1"or' p oEnJ oqg gOzr Oo oszrJoaJz::.

colQ@ Eesc AE osor::8 6,olp@e6 ozoCsocd Olodacs Taalat l!, = Zt+l-e @6uI oqg 6OarrsrOgdOz:i oe:rrJOrrJzl; o@8 / = tan0 oO. I t

,,

d gfd, -olp@6o 6,o6@ qocod corrJord , = E oa> Eo Q oo oe:aJoc, d8o 6 = L;+ ao

oezrJoaJn:.

gr5)d

edroaJoc: m at Qa 2a Q AB rJzorzocd qcdOzo G OOD gderc,: @aJoed csa': AB O 6@0 qdocszd OOc qOd86

9S6o tr*' oo oc5aJouJ?'.

AB qdoOS A ozsg,OdO 4Oc g@O €oi61Cg gSOd Erqo qr8 gz::d, Ede{ o ar8 zsd q18 g@O eeagi

zo@6c:d Qod ggOO Ogz:ro O@O Eqocs gin. QdC, zo@Fc^: Qocd 60 eo$al q6fOc oOc dO 88Oo@ 80EcJo6rslcoooal pqc eo6g 61o0.

(i) qdoO GOO)56deorsc,: L86E asdg obOcOzo Ogoco O:r OO eoc

(ii) q€doSdcso0ozoc<rcsudEO?rt::g8o08 oozoi&nooocs, o02 = 6ssin9

@6zrJoqg60:raO glel?rJo?rftD 1 + 3cos" d

qdO 8dd Oal 8O G I go8ocl oeecozrJo':.

gaJ, qcdo 8dd oa: o@coocor3 Q ggO zol$ qdO qdloSOcs q:OorsJ e:@6d O6acs 8@O eO:r$ coE8.

eg O 8g O::: qdoo8 O@orcC Q G OOn gdero, dO L Sdai ardg obOcO Qocd O Ec,:n g

Ogarr Oa OO q q€6'O Ecool ozsi&zs oOooEzrJ G OOc g@c6cs ozl Oo q oozrJOrrJn.6ga

[CIOoi6 EQO OsdeD.

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-9-ALt20l6/rus-rr

16. (a) odr:dc $OcOzs Q $Ozoood qc2ra orgc^:d Qod oeogO oOCacsd e€OOd ood@cs gQ grtd Od OdOcdoo8 Q oOCgo 1,2,4,2, I oOal oOrr} O eA€ zod q16 8gd1 eroozrl OzozoO OrO o:rrr3e:rsJ oO.

@ar1 @ Egdn oOCgc o1O nlzrJors} Eo@ ee@ocgtlco * d oO.

X - "oOCgce r;lrriual O:r 8gd1O6O gOc Q erA ea€ oqozoE dzopO" cs18 oEp. X eeqoc

es@oc8rlc orcej8 oqo ooor Q qrrr.

p 6x q E qcocszrJ ocsco:rJzl.

E(X)at E(f) otrlcclc, Var(X) = 2.4 oo osrrJordr::.

(b) f SEzslor cece@eoc8 Oo6r:o:deoqoc eepOEr: Or:cei6 @oc^r F(y) csrrJa F(y) =1q2, )= 1,2,3OErJ

oqg 31oO. kE q:crcni 18 te@alc8nc Ot:ceJ8cst:J oeeccs?tltt.

E(Y) ar E(3Y - 2) I gretc,ol q oeecoulzr:.

['" | *(2-x) , 0sx=2,

t7. (a) Xeerrjo6zo esee@tocD EogrozoO J\x) = I z

l0 , goard8o,ee@arc8nc tamzrJo @nco q1o. t

(i) P(X> r) ac P(X' tlx ' {) "cerool-.\l'zl(ii) E(X) = ? ,u osaJoc, Var(X) oescceaJzrl.

/b\ -8A es'noflg Od, @O>z:lDos 500 g oc ee@@o goco@ano 10 g ee8zl O gOar ogee Oncejr: E Erz'r.\u ,l

(i) 6ocs@toc8 ogee onCdc cozrJrrc Aq elroO dzozo Od 49O g at 505 g gord ESo@ ee@oc8ocO

16\P31.3x{h

(ii) Sceg @ olzoOo@zr} 95Va a ad, (500 - k) g eoc (500 + ft) g gord 6oOar o6Q ft I qcocs

^..^,"*t^

(iii) olnO eod ares@arc8 o6ts oorCdc cog eroA. o@Oc8ui 016 od@rJ oqzszo A6 495 g o OOc

qflo EFo@ ee@eoc8orcO oesccozrJzl.

-.:. -.i. -1i4

x 2 J 4 5 6 8

P(X = x) 4p q 4p 4p 4p p

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