31li f - agaram
TRANSCRIPT
31LI f '.t {
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1. g{ogoced drSoC 1000rs gqed 8%rs OcUBD Eo o.oc@ ggec6aozil csood a(ozgoro arzderdad8. ergp O6ecs gOeecznoc$ @O $qe eoqoc OgO 86 Oar ooc$cs oaco@d q?
2. ddod o1o:o SogiObo SO2s dzsczocd o@ui ad8. @OO ddoo SogCGDad 1202o gddoOnJ 66'@0 oro ozn tocecs eloO@zd elescordrs.
3. e6cor6ls qcrocdocszrl qz$Onlan: 3a = 8L
rl4. gd rodoJa:, ti-zii
5. dloocl Q qB oocd4dl qlgod?r} OEC A 8ocgdoco eescrcaJur.
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- zryr,c 4f oal o6cc gaDccsar oqoro8 zgoc o oe,cg e{6cr$rdc: ooccoEJur.
E. caeorl Q q16 qocszrl qe@6?r, .,tfr Aegg rsnlEa6edo otrCdnlat.
52, 5.3, 5:7, 5.g
9. dle:oc{ Q gz8 ormdtBdl qlgednl cos 0 E qocs oesccsa&r:.
10. AcsoBoA n(A)=5,2(B)=7eoo n(AUB) = 10 oa o6Q I z1ea oqrod zrr@ n(AflB) I qocs
eoccsaJur.
11. rosors ocsccsrja: * -lO
ogcrod.Sed 10H es@od EzBd rsg, ogcod,Acs8?rJ o6cod.8ed 35d rsczrJnoorJ EBrd 69 Q oozl:q18 qrad 986co 86O2rJ 88o166 Q ooa qlo.EeO qlEo0 Q Od dcsgceoros?EQ e@6zd orlCdc opgoaloal ur@ dc.:gcozocsc 86@coe A@O csOoc8oco 4od q?
AB oA O ezdalgcs B Oadrsocl Eda@ocs8. C gdo:oo Oadao Ors
8808. AB = lO cm q CB = 6 cm Q 2tro AC I Qo oozrlB0odoezrJoescozrJa-
14. Eeeqlrlzo: (x + 2\ (,r - l) = 0
dtcrsoJ Q qr8 $eaCo qee.dzt| gocD€o@ 6.d5egoec!@gd0oO@ go6cs aogzltc orE@o oc8o rog qoddco ercro Q fi6 O, @ac @ qod& qeod2fJ ooidc oc:o cs0rrl gdd qQalo.
(D sc. oroC. e:c. @ oroC. oaC. oc. @ e:t. err. erc.
19. Arp B a))3c€o
^=(1)
1. :a'!- [i@ i],?.,-.ri:s:-r.M ;:-,. r
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XY=2Y2
xdy = zxoz
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Q ezA dleocS, KLMN Oadro O4dgcs8. (N oUOcO Pqdoc Qd od g1ro. Q qrA or*r64d1 qplgodrl x I qoco
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(iv) Ol"EocC Oc6ocO eOdOeuJ oasccctJa.
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ABDEoatOed OUod6c,, BCD orocOod ObodgooOuJ orad q6l:d eO.
(ii) AB I Qo otscoaJnr.
(iii) DCOcercqJ Qo oocoaJu:.
(iv) Odod oBBEcs oesccsrJn:.
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4{hd eacOcszil d'r8c:C 210 arBerl 8ag.6e0 co.
(i) A 66coo@ -@rota-Ci -tr EB666t J "bdro -CrQ giC-,?1rlccadn,. -
A ee@coo0 orococs zrc A8'&@oa, erg€ 90 9qe @ oocqc oozrr d@ pq@ oUeo qcd@oocj Q @
Odt6, oacOcezt d't8od ?fr a&ulozlr B a0coo@ oasod o@ g@coiod @e Q odod cc.
(ii) 046, B ee@co@al @e Q od orocOe3 o6ro ocscouJur.
Qq6f OUocs qOtscarc<3 Q erocoo o6to A o@ro@ eacOeoroO A6.eC 15 OrBuJ ooOzo gq qod B
o@ooO eaoOesaO dl8od 18 OrBzrJ eoOzl gQ. i
(iii) A oc B cc@co@OeztJ OgA e€€ $€ gcocoo qcqco@ eoccsaJnr.
(iv) A aOcoo@ Scsg @ erocOd aOc go raOc ozncoozn, E@ es@cos€ otocOd 4.H EQSo Brsocoo@ oacod 06 Q o1E@ Ecsc pq6f oUocs qOescaod Q OgO e€€ q@od Qctocoo qcqco@
oocouJzo.
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aqoc 68, zt{g@ aoc cso8oc,: ozrr Eocscozrl 4oa:rl OdEoocsz$ o@6d oraddcoo Se 6o. Sgul eOO 8occcsaJ
eroCdcod qcardcs erano g1doO.
2D€O oroCdcod Sgri odro 69 ooCdcod Agzrl co65)o0al 4al qScsd q oo6rlo ooidcod SgzrI oaar EBo#cod Sgul ooar oozr! crd qocoad Q oO.
(i) 5B ooCdcod Agrrl @6111 9d EgnJ o6od ococsdogcs @orrlro.
(ii) Sococozd 4zrrO qpdler ezSu$zo O<dOoe ozSolg
oroCaog Eoc6dO co6zr)co rod, dOc Q qi8 OO
gdracdcs e€ qQc€ 8d e6 @a @or qzSOzdar.
aeA oocfcfrcl 6oood cddood(pe6o Gldooo Oo e6o6o
(iii) Sg oroddcod Egal o6a 30 zo@ o@@ eceso6!6odeod SEar pO ASrJ odzr: oeoccsaJan.
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eolOocsul oc A@c6ooEJ csUOesO aCA 5d ee:O8oa q1a. oO@ AdaOe2d 2d 8$dg6 O6fO Ozn
qod 986 doc oocq a6la e0.l
osOOelcsal qEoE @G€o a6faof gOroO eou: Oco o6zJsc rod anrOa O@ O6fOcs oeOOoO .@geoOd oCOcod qog oecs ec:OEocoal goroo ocoan o6zdsc todg 61eO.
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Edtedca rodzrJrs:. 8€dg€ adA Bl at B,oe€E E oocq O6fO Grczoc G, ogco q qdoc
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o€A gooo q6O
(iii) goa er6zdodceO qgg, q€o0gUd drz$ coOoard ooo Q q1ro. qgd6: o@o€roc qdO0ai d1dtsOaoor [email protected] zodaJa.
8€edg€ OelOcsd B @6rJ Q oeocq OCOcozil G O65J q Edlo6cs ozooU.l
ctg goooqas
(iv) o@o er6zdoood Q gooo ou$u:c o6fo oqorouJ Od agfacsd c:O6d EEdg€ orsd EoO
eo0oc8oco, dlzf eoooar qlgedrl oescouJzo.
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oOO O:rcd8ocj Oco ezd8cs occccszrjzrr_
ggg 6,oto6!8o oo:ran:sozd ocEoooal ood qal goc:8rrl ooC desrsl86lgro 6lo:ral doa3occocscotlJa.
o@O O6ooci desal8@ olroOporo dorol8@ l2&d g0.q oO.(iii) o00(6 od qrooeoro q1B dcoalE@o6 dronJocs Eocarcs rodaJar.(iv) ooo ouoecj doal8@ ddo lq)r$ ddocqa 6oqo egoC 5&d oo. olrooeors q1g dtgrolg@
Edocqaro csqoc Olcs Oar gQe 6(BcsC0eerf EOcarcs rodalar.
(i) .r = -2 orrt Eo y I qocc ococcsatan.
(ii) 'r-qz$ocs Qodd y-gzdoo E@dd zBoc oogo 1046J droro drsd Ed1.6o oar od o6oc6o<acoc? oEOzrJ, gdrocd ro0ggoro Ooo 6oe.J gdoc&s qq6Jrr.
gd@Oo o0omd. eroo Q q1B gdrrOeA ggrDdl oooerJur.(iii) y a6o gg 0o, .,Q qra x B gocs gcnrodcs ocscoaJrr.(iv) Q qra 6os: y = (x + a)2 -D qczscdooal gzoco rodalar; o@8 a oc D csg egoorc oqrog.$ {^. ! - '= ?o@roddocs8
oa geo ocg qo@ddcznoo oescoc 0o861 .6. oqo, qoesrlzrrqocozS ecsccsaJzrr.
ozdodc otJocsro dcsrsro€ l(xhs, oro ororo cslalao dd,ooe5j @1a: oal2'rc eE oo orocd4dl cr€odzrJeocOurou: GQ ooO:rcro O:scd&szd ooro qzJ0r q1ro. i -'
(i)(ii)
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! = x- + 4x- 2 6'od gdaodo qlQo coqoc orod rodur gq g..oguo qoo oqod eroo Q g1o.
loqot8 8po o6alar.
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q6pc6csd 6'00B ooor g66' -lr
gqg, ocrc@es cs@o Oad Oe6rocsd AqEC-1100 a(SnJ Oa tc@rrs: Oc8zo Oc6a 2A BaJ oo0r 80 ae
"b "@-q O6 froo o18 cs. oOO +AO pOcs aqoc ooc@o osalco rsdp g0aloal Ear Oar odo
6c;cl oocogoozo A, B oc Tcsa: d&r6Oe 8g@Og2tj qo ocod, oaod ocsd oi oec6f ood 88oc cpla-
Ao. 6,q6al B qL Ao zr{ocDa86iri Tq 88oc q1o. rao q AT= lfi) m ao I8o f A Qo"ocs L62" @O-
(i) A, B oc T8 88OOog qg cooourzd cp1q Q g15 OgO coooal roduJzo.
(ii) nfn A 6ec6doo oescoaJzn.
(iii) $oaC.o08zo oq ocEioocaal AB A6 OodoeztJ oocc.suiur.
Ao 6,464|, Arrc B grod, CdOralocJ Eqd 88oc qldod TC = 175 m OzD o6Q o.
(iv) $srodo0Sro oq ocDrooou} eef a Oocgdoo oocouiar.
(a) OB gqUcoarozd esqoc ae0o erpOe Og osrri ooo qdoc q1o.
or6S8coeo - dficsC ?25
g,Ocs4o - dr8ccC 150
or68&saJeoal eso eo8uJeouJ oOzrJEo ardOcood OdO oOO gqUoroo aqdilOO 6doorod q1ro. o@@ rodOccso0 SEar gO8al co62D, O(AAAcctr, cDdzt o@zll oqqooO OOc ood016 cs. eOO rodOcoO aqoc grbOo eBO6O Oto Dur 90 9qe dt8oC 6 525 A.
(i) rodOccsoO 88a O1EEEoJ or6ur ro.ees oc gO8ul @{6u) yoe6 ooan coOocO ccozod.c6
gcoecszil oocozooa}o.(ii) csOoc0 cs0zodd g@ecc Eaqc rodOccsoO 80u: O16BEccuJ o6ur oc g,O8nl oSa oO5)
oOa @ ocscoajur.
(b) 225 p+3750s5500oro gco0crrocO E qrpo oro or8 Co6O 65eOo gocs otocorlur.
etora gdoon: rag drc, oquo EgooerrJ gdo droro x B oodraccSnl qUOcozS oc q6cs droro (x + 2) IOadocs8rJ ooodal uoeod oO.
o6 d1o oqoa8 O6oOe eoOcur lrq, r qlgoduJ OUod a0roddcszd oosOanoc Oo BcoQeOzrJ
x8 qocs eg,Q qoOdocanoo Sardq { ocsroalar. ,E A qcoco coqtoo l.4l ocscqc ordro.
(qdce r our oudrxsro o6od6cs or' "b.)
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o EdEod ergg od@ce oo6c6f ato l068rd oorddro o8.o o€9 ode,crO eeogrJ 886 o1@ od@cso O 916 ooOc6! zolO o6a: dO qceeaJrnecsal @
oo@rrl 884 @dgod q18 oeoc6f a1O o6arO OOc 4a8reJ qg co.
o qOteczr: @dg@d cpldod Od ooOc6! rorOcszJ o@&.
(i) @O@ Ad8@ci B8O oooqd rsr,o od@ o<6rrr oesccarfur.
(ii)e@@Ed8cgorod86@o@Cocqceozoq16$6oooc6|b1o@6?'eescco5J2'.
(b) goaCahoO ogl8oro €r€,9 crQci 2 eO. OO.d8*J o€rqg qgcrcocs oan Oar qrod, @qO2fr cso 4olOurerQoe o0rsnc.: ?A or9.
(i) @O@ oglsocJ @crog ggetcoco orscoaJan.
(ii) ooo od8od adoa eqc: 1458ao oe:nJozrizr:.
t. eoro qzJoOro ESOc<6 esqac cm/mm o6OcrrcszS co8o eod6 qcdcsd oc zsOzoQOd [email protected] oc8oadu}1. Et1@c6 oBOc e4a4Q@ o qdoulzo.
(i) AB = 8.0 cm, AC =1.5 cm eoc gAC = 60o oa trQ g ABC SoroCoco EUocdco rodzrJan.
(ii) AiB I ozoCer cooOodqrso [email protected] rodaJzo.
(iii) CD = 5 cm Oar eBQ BC ecqce Oro D gdorcs ee€ rod D edeDor$ Q BC ecqcl de:Uo zodzn
at leBB ezoCo o@OoSqzscs @o O odrdgce 88ozo oodocs EUococs zodaJa.
(iv) goa E6Ocdcs zodzn 6q OadocsO B8O rDOd do6ceacsd Etf@c'c6cs zo6, Oce Oodocs detlo rodur
gdorcs Eo6ce zo@ zo-dia :
(v) P gzJersr,r, Qzd roc BE@o 88oa o6Q oc BAP = ertno^ er6q I ABPaO{Eecq $ozo$ocsEU@c+6o zodafal.
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g. A,Bat C csg d6:oc3 Q q18 oadoco Oo 888 gz$e:s 36. CBcoA E tp18 oadood EdrsOocs8. Qdrsg, CBoUOoO oc Agzdorocd Q OadrooO qrQ deUoroo O I Q o$ o8. loO Q O8O OadooO qrQ
qoad derUcszscs @o E gdexs 88Oc qldod CAQEOada O4dgcsd Ozn e6Q ,a. ae n = ro 5)@
Atn = 3xo ao oerzrJoarfar.
loooQf BQo asuJor.
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dleo @oO Epedr elBcoO EOod todoala.
(i) ABX L,= ABY L,oo oerzdorda.
(ii) BtY = 2rAB oo oealonjar.
(iii) Xf cec zo6zr&o. ABY LOUpOecs =ZxNY A OUoO6cs OO ee*riOzrJnr.
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q662cm Ozt tso: csro6 ooC6cbd 6,d olocO eoCeoc.J cr6OcOO ccOcu: o6@cOd q16 tia agf Oado
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oqozn qe@e$Oczooa 8ftdQ o ococcsaJa
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OgztJ @OO orOg Eoqc 5Q gcacfto SEaq oncd4ft 88ood ooo Q q1o'
o olOg 4oaxrt Od olOgOaOOd 8O1dq 6cog@ ozlcglp 85zd oorn 66'
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(i) erora Q qB qcsOg6{6 oOrJ diecsOour OoA EgeC( ergcoO EOod rsdoour 9oo Q qBoocd461 d eg 8d1e6o rodnJzn.
@ ceqo, 8e(dq coqoc EoldQScog@ 61Q EcsgO erQ SguJ
(ii) dd olOgOroO OOc 016 olOg csoO:rcOroO 8ftdE Oeo6O erQ ABaJ Edlo'6o roda otroqdoOzr3 d1cxsOoouJ g96r rod qz$Orlzo.
(iii) @ ologoo EordQ Etsg@ erQ AguJ odzr oeoccsuJEr.
(iv) O ologoo AoidQ 6esg@ era SgaI CD52r @ olagoo Aa(dQ EogO ete Sgzd cD62r)
oqq6c.r8. orOE oqzoroO 6A1OQ AcsS@ etg 86zd o'our ococcsajar.
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