%PDF-1.4 3 0 obj <>] /Group <> /Contents 4 0 R>> endobj 4 0 obj <> stream x-K 0sԃlIQ|`?PZDMjwfYe$)p%uj$ zƔ'na7_bJgTN5_ ę打 2tQ`l:k9j'[ۮs5US?na. endstream endobj 5 0 obj <>] /Group <> /Contents 6 0 R>> endobj 6 0 obj <> stream xmK 0sԃlIQ|`?PZDMK , $e>:X3}d$ 0|>`2ϺdTaz#"Sb %^y!\RyFFش΍{!Ԍrm7}rhʺnsG2 endstream endobj 7 0 obj <>] /Group <> /Contents 8 0 R>> endobj 8 0 obj <> stream xm 0}9M6m֣ŃB^XXkMk , PDR,đLR>p>xt 1fYeqY׋[(ъb=&bc$e> endobj 9 0 obj <> stream x]Rn0>L%DI8~%E*rﻻvҪHXgvVk?/Ῑ`][x5 3\zP}POjJݍ^x6/f|4}z}@,ۖ-˺Eu^,< Z_K IQYdCK_%q8>!J"V!2&bGģ%r"HD\}2EL1nhje"a*H:d9c[X1~"3gÑ;O> endobj 11 0 obj <> /SMask 12 0 R /Length 21626>> stream x}@CB<+&č5ƽ6!޸B 88= ~O)vgggKJJ 322ϮAAA>>>zzz +*+++66۷qqqQQQ_U? ^zR=ѣƍ[[3fܻwRT3:uj?1I"05kHYtU/^L8QGGǷϟ7Gjj """,Yr 2>| мVG[_ QۺuׯΝ[ti>} B2@Ɂ D Do422***l;wAfY# S Pw[h5kր 5ӼyslA1c":(--Srr2Ζh )+SLǣ?! ݘ1c(x`#?@e ?T 7> &8l0%.h ݺuɪ΄"0ooo0Ν{~UK_Fx߾}"X˗/W-C >3QD#4\lÀ%< `O:%o?(NC_5A&1ba ,Ç|Ԃu/'/Sa脇|jW^3dVq1>AM1H}aeh;v,\5H\|Y摗/_=ZF!i@;*ʃc`>w5k&-\o:ڹ45UU>|p;sL?~M<z衚Ҹ? @PXvڮ]; g^yhTA]  ebf^Ag}1^ ĢjR/̢W +mk۳Osss+̙ "N`4!z!4սkIIg'0lŋ BYǎOY#s难ЩS'1޿Ad0A)C A)WИ(\C, k`O>+hfˉ`2 g2Y..n-Z Ng0߀_''-ٴ)Uks[{gQF,CfGM_|k^_R > n$..:r颭LMo߾|I }Hu.+hʅ|-V]R[[.|rιsRG'N i/{-޼I,|e(@ `*E:'!ؚ._"W[(啗mؽViرv͠ H-hV`w)1h064Ǐ7R)W2_zEYYY2J8.۶K[n/L(  sV`Y!!!undAW5jNN@:|͐8a 1y$hh 2VO j Ac`x54zԝ(>3qHSG@>y3k,1f.\}O>ʊEzW}< HF |>K۶mo߾ŋ` ;B4iҹ4n:}v}ZŢbSxUDNܦV6斖4*bAkE pTZuuG[;clcl١s硃:|yǶP IBVݻwŞ={B= yB6m(BwTTϟ!dȀ B|-+냯ĩ(\N>>VvzJM1p`QiS/ya%_[#Q5TL|NbT^mL=>~n;tH7N&\-ݴ¢f:˽5549<41v4hŋ>|혘̌/_Ad\vmϞ=gs\Fk2ױS/n\09sVTRҚvX,J] k*Bx!66I&۷oWF޽{Pao޼quu:-\yߧi<|[7%9Ʀnnz ޽temT']-d!5>aiMW`kd}… p y.h|%MaݠMLL~r2\+aXP'@aV7 *JH*OC&OfjȮ%GWus4aDm5z ]333^~&&eg7{xx@ '/T`fm.%’(r?e 9+BO&2QÄUГєW~hk`dѴ{pwVZFAqi .viA#F& zF&^$?]CJ1/<233ׯ_ƌ]cݻw߿ %{O9r\ (Nh|K9%şs~σtfa$bnnz^^ZN6Y.f|TR^U=)T:Ye˛O/?&>mDc[vʗ|xEVa!_.(??snNFA^vA o-!9S\=<ΥʭzX_}h@Qj/^43b'NTH`bO7PQ`EGG#Yf&Z5B02436=}5tB4oy㖭M̜:u[&fN~^fįYpǎYY/ؼalFr ijn{##Q-6501 eKxU#O6m m ,wVZF^vm;L 5"BLs6$ IG/'2"Ogw/_޿?srrfX~6M޶mc`` #&۳Z(~+T1c^KhæNPi;w0XZuentYk`X>u;vL[\鮟\W %u7[tjbo+sl Q˶mx!`/ܰ~¼пK9T/Zۿh/ڲĩHw]ڦoU'q< msE;t~˗+$0Qvjmڷo-C' AwiU|~/Ssl҇ؼxЄ"Qa>ZW^\KEBᗔ#WV\R;B LM`,;KVnnugn.]~A[ac؀D(•DߖG[[m۶aa <_B{b&LP؃`Sh.@-زS,`lط_=[j[r,XLͮ?{a/vⳲAmۀԶ-V`BVv >M=a11&O}cdbRWda1QpEB*4Z<^nipm]ZIUY4 d۶ɿH3scG[­SSK؈ځ^ojBgLں:Z阚l!0*̡>c[X틌Ã?uٲˏh 954bY::Ãff:V^`is l-8PkC+++ q0歞eQ묈{ѯ;j'n=|hqC16jOF=uպ&@qx| uȤU_Y;ΫW/YM-0@PNbo޼UP--kM _~x`dL@HL_xʕ2[YYvFnqIZCCEi4&JRbK#+ADBnlȑqڵү;9Zs{kG۬/_XvرÇvæs6ؙ#FQD BPXt:Ӫj-#<@WK ڭ[aLS> YP<=͟߾f3r8 vqq?m4JK.>|E }233,g$^i C'l?vQm)ԩSu22Uc!2k%a z…n83:uNuB+ɫ7ehWң yq.MP!K3D'8p 1BYl֭-en!O /]><àA^۷߰1ǏOŗՇ@$TD9LLL Ƙ3U455ldkAL.޽{Ȑ믿ܹSዐu=J߿?C'O,W@:#<^϶j b.70 ~B# C}!W,.ۘ`z={21Il?TXg;)lsϝ+UxH,ܼ"‰ZPgyٲe|zŋs7(իW%ѷF@ڨv䰅+ƤI.Ta)xʺF=b> %Y 61k0d:@p?#^P`f]#͉ ~ +)Vj)g@94ReЯ_?_|v .nU/"z=SPT^>]6w8 h6 `A0ZR 8b%}8yBDfnnL\}Qٳgȟ͛:t1. HQ6񫣣hwd988d ]l}mѺuPn݊j]B; ]r Ӻ,^iPTMN֦AG, 9sޘZ_.P1BGlZFPsjxXX5Cp7*ʚd^wTʓGTkomצ+]^P.nq$jhI9(2h㎎(m6aQQW:tQ>fQZZZYYb N}ikkם梨[1fQ]jjj |ht@ "QeE?Y,_)3iw=zlC7.^"5QAO2.xΝx]ƍ (d"ȏm 6\'wռ@>B@ƒ3m!!!bѨu%* 8y"/5#bDEEǼ{H|:bJ4,09YQ^tXLd1XRi_K=|]W=޶/U fs8V-*>8;+SbRIa!Lfw/}\8uZfZZ4:Y.7H-Цw3GJw*dɠ :[n %RcccjbԹFY/{{{+%%nAgر#99QSR'Uȡ(G/\*Gk-5R%jXYbL[ "Xb ע(@I%u5u= &{{{m!>@'oNZQ& d¶?k\S 1leUUU<4X^]]^UB!UV~..;Z֕'O}b z}xJȸQ;N~%ڶ14"SɂJehpy={cn\oӷ&G+Y*"XZ9縹s ?OM5zzZ*իWj '>ZAZ(`df۶+b1aSX-RvM.ɻwVT u/Y"\*wD%T޾N JKCu7Zઝ6קyۗ5F~AIc;v4s6庄‹V>WhB~[ { DFTg:^-ߎzٲk7eIJj_3odtʆ䨘dki]~|BeL[b *٥ScR?ޮ>M;xz9{4j&m3YKl>!kBl Wʪ*3$Pr#GDM'''3R2_$33+W;v,66{IfjI412٪U+"QX8}̸WHژX=we3m*ҩOQŘ^uuB9Mv-jK6;w L}Ks3&jsM&X/BVWaө4*S9s>y9e@ԴEHF&{ofI}g"Ktd 6 %巍7jԈL)r q@~QokJ ׳BzU"_߻x+IrtQ"PH"V)4^o(hQ4hw. <8~ wڸgç]zҢe2YTO9NiY)Nc5ҎϟxUUy^ TPO9sHEH_~ܹsʔ)pɮ7+-Xtb`EE 1 |4;W2SO?lϕ,d`mȡ͠m`kbehm`lJSC[ڋb5Qga9~iK~z85A EcPitjo:Y3Xy{pa11wKy H9g'>6l؂ @RǥF?~r`ԗ/_ի ** ݅dd] ś(O+D_Εechh`STo;v\I9hDoኆs窪ܽy ^?S+Ji 2> yա-Z[Pq]fNdj ^y*U j$VBTvϳD6קN 3L|F04>XK,a),ŰI& صkرc6|KWɅitf}Gb2>kGM H1U10[U l蜑}ѫ'O#<'[i+*aj>ͧaBlJ@N~:U q؎:X1q O7* s 5ںJ%ř8/(.:++)1Z ̟?n;<~GP,A"l6 .Qׯpq4&ӣi)|uj,"*,~5yw2֖uPmC1);'G__ũӗ4X@cl$:>WojAW_:99b@T=, <6]5&/m\W_ $&~NHTU"DB1nkUVdjr-,vةS' 䈞=u(+"3P#661Y"@6k ߾}) Œ 'FډTSv` {>bn(10v_P KA`*EKG߽{}vF^̔ʒ:f/IeT&K:wa,9Zl&X< HJJBF!Ɔ XZZJ}6m&FGgbFUpHU7Ҫ*+7JX^O޶_fq5oS/8HbAKD-jVȲa"6D p͜0 -))" @}=Jk7+ 6@6CBa FY F.\0###!!͊cˁ~KSñ)73?G[PT ޠtO[Xڛ)̽ 3ӱu 0_+*eLF|쇌,ml4tBWʱcb* Oȁ">.Z V6HޭTK`M%˥0A9rXdFGJ,L(=4h صS'tq qgLRRP"q@E?|L1T&Ibo'XmY=siP$"dIDUp+070Ǐ˼WX&5``7 2k)"b9D `tXta WWnݎ)bB LF NKOAQޥ`*!k=| mfxh ԯ6';=#ط&Sz 'iHѤgvih9+W+%T6H*?ӧOOO \BᒘzKo P@dLN- -G.߾/+ӿ\Dl]{!e%CQN3,M_+|oP M *.-#E S4̹r:QK$ûvx˗R~BTM9DN24o,0?#r aJ+-EEYJ@/""1dF748rNE[R~Ӧ6M\|؄"NU$RZX\T^ZSvvn-V,۲ʆfgqR"n1(L WHYV[۞ z뭧Y4ʰ55( *,?yxgyy95hדx=RN;w"e4'::ZfXqk*ԩ?[=EOG']m>h[ ڭbSzFVfVI^.Viij[xԌi6mx[Sb T [1Z7G5hMލ[z{ TǤm,,,LL3B#>7(t#3Zuq>>>dAƍ'N al-5۶u[^Q'&~?dP2Q%2^c5)>t}o{ݳKJ|L֍G7EvM1N$z&:ϗ)~``ڹ/[U~Nl FU2loiq0 @>Sk-#XԺeCBdz2^h;O?/]"I޾VaAA/fFpeemlm|pLQSݺæ0̝2YGѡO)Z:Ч(,|y~(K[o ݻw˟GA3VJo& @.|ǮB՘wř;y"B s4[G|%ӫO8v 5GE*Oy/U^RSKqsħ};{+Ob[A?~ݺoU1֭tt~X'NҮ:}[Epe _ Y" tX(yZ6USą_L'Y5O[''CS>vHPS#@ p [ã1Qq-!nғSJʆfmcW%?Da308y0@T@ION*(.ї;/!pN7 ݴm[#My1R0V&-Q|3&L6ztJbE<8Du A:o<07n(QA&N-M;oQN^N.9 a^y 78.+-/7vlm`|.IcFZ X ;7hbq~ԪO; 6~E'&vvMM yჱ SCsFҖߠ` )Y?N<. D)45SQ!q J#mO\ EI)u%BBDThhgdx:}.o޼6bÆA_zB2hǖ-7n0գ*/% (cbZΤ3$eLljg) f3EZ 54)V/ F SHҋTX+Qp|M\u]#}{Ww;Vݿ׺Ug=uGj:\akbܧ:A( XYc xjf|"w[{s飓ʫ/^lei٣K禁~t&OMi%J{1;)ٵkWܑ 4:Y')R]-lnffbjɳO$saƦijMhP3222!!XnQX{]G]ʠˊӬM+2/@N5KJbɦY"*t~mXr֭[߿}ݍJØ7*811QKW''DpɬةPk+,62C}..>ߡo_]y4m6 ǚPç(>cnܶv>~b>r2~U~eEfU2K|fuCMmxe𲪚b/^XűWܹy1b#HݻcUذa nսO nx{po aoWP.]4u]||{Q%6AıQ4q7wriڭk^Zݾ ݿ}{sGgsGGLq‚={YY](T S٨ _$ |C$z)U5JȄ!嗔( iK,xq>}>}jݻѧ"V +* gh6mj@J)*U?w͛^|P!9W"\\s{иp SS-!;Z'5G*PZ~iMzz)>ZPPŋ+WȜ.7"@nh0i(= UWި]nFST\%Pi~_*{kjX[2lʕ.]z&0[SQv='NϞݤys 9yW Rg]4Z*b*t`+_+ {͗f׫S娅7o_\3'3|Sɯo?Ocu~yE[3/k164uLL\}x,olJhӵtEFl?t]j4XG:cұ,=}%9CF{&Lp-PKJ6u~TYÇu6\||<. ĔS+4.]߾>͚e6Xq㊝Yb 2 ]:FW< {>Δi.… ܾRpU!O}_`/zmi9ԽGZDVisc_'ha ؽ$6|$T:bv:t-<,wV]Ç 9J[?-e@@9cll,2xJ!a!q]%ƍچ^\56I̊y~8 YVL@޽*ۑcMPuUYYٱcG}W^~0I7:.xdKNd >H+6$x\=3XjX#B %dyxvϞ^#\c 3P3>&P{Ŋ ՇTai(;yCHH9Cyk!?ωsN 3ׯyI% u\Hj*D&䐐Ѐv|͟'Np"Cn*ݰtsͶ\GSGJtI8<޺}{w=ڀZ|7]?xGbF}ۗ)5[~)'0c ό3{IG'hGJHoL bIxzըY;vTT+jN3XgYEu,;c"ft#/˗/ϡn$Y)ɛ+K&@ѭu.^6~x{{{1_Fq!]P4hA`40U+[sԩ_dèVD{ϝk۳-9d„Z۸^{W!g/};_wb5]f3iW֞aaWׁ0NE!]tVc2MW뉻2[u˗'Qh oUZ,<~|MU[=|Avm_Q,.v.]a.<ǭPyvݻkج:zgnR2t:C#+yyǓ,r5XɭG1w6?m|?D ;6߭[7=}qX7[Qm]]JJf݀$Ԭg9-t_߯?&Vޤ7wNnݭ4iL6KK7[w}+kKG7_ߞ#FҒƐrAtrII8x*]\WPpj=qhmܳgא!CO@@0h:q %sX 5°H]UUwlM&83"whhŒe݇4ުחܗʎݼy3ʰ|4Gn###E4C,K˫7v 쳸Kʾm!(L;wT(tмAP\\ K([jt㍆jENYE-zf{O((p 7eb.>iӳ I%KrNJnA7ܫ}׮'LMЗC"$B,^;LfȖ*إߒ9SHږ Wt!D3`"yP ehl~x6Yqŵl3jNT_t I{:y%P˖sߘ1B{P*9H4BC"Rd FN>&GW^HLMD LSƅG~Lw -(m2ynioCJp|V>fnjC> N\֤Y dKѝos?9F)??drDSqoCc.rrC_rŢohn) @[d2Bi?䗩+^jd@F O)%jA Ǯ]kߣ&dB)~pQf)YՕ e wW廃Lh5ݻ7tFHXM"]z ^*٫.?zSKt+*gjvsGmڤKer,^X j*Fbb+XEӧO?0555A*s!GxUUJ`ir/22>#  )[N/5!$Vÿ@cЪ JruFn6lݫ01] r= E+PV][Z]\.5y,gΜQ`OBv)gC۠Q\y@:?{o> 0@.:RpSNM***"##'L~0ለrefhhPV|Յ300P C@@W૾|@!ݻGcuXMCFo@!!TUEwP‹BCCnjjժ .(S ţ166OxmC^Bt{aR֭[W2~:̪wލ wFT4H8s}yAAqpg*%KP6b1N2uCñc7"پ}'NO9r\7@>8 }!( }K60A1 ݻ#r̙aÆSټy3K(p5!; x22۴ifaz$Bf?w@O|]v>p|iGb7EC,OfΜ)Qh8do>Ќ?~tzCBB : BG PQԣ́2 H2uh@E BW<<<an=[vBq HUJ. 6 i0 HV0Q_"(3Pe^r%E9E^gSG%CA%QQ.M'Nly&:9JLLD;g\DA@Ol$CL \ ,{0Q a,\TMJ%1fШ(iPyܼy@j0Ɩ/_NL{mذE!lٲ%?%%Z~Hqwޡ<ѣ?2@saEQ:QCUV(СCa8FFNxx8rC Rp_~qO: 7 J.X@ԓ'O_ݹsg͑􅁻zjx@cP7:C˗pe۶mDpթߺuk$o? j@iu@ 4axbǎA a@:::> i4 FCڵk#Gwx ? :rHt/ej %=73(0@+QF7vss:T#V (۠6ልeMI!0 h_օB!G}KaN' ,7C#U,bI!BcS# endstream endobj 12 0 obj <> /Length 1165>> stream xݜKTQϔ:Nb0 J+B!h"-{@O]V^JXm,Xc8霹sǹ_}@us_Ηy9YL{9 N&GG}- f\W]O'-m}nQNފYǏ7[M=&dIj?إUSNWlNyToqzY W6`gv ]q6٪jW`ߑ~I!CïRu&~޴3,׏ѵV89GY~-QbS~5~Xf/Ǽt"͠Og(m=kCoKjsK[r~?o?2mi -pǘO<3*H5%p8Gimۡ8*ft'/A-Ш+J#h(/lYԊެ9f_n vC+-C6hXރ%'b䯭1)OSϸگFRh-]4 wے57({EUh܍wqiݗ3&:8AH {"#cMYXZC1`%dC $"-5BB[۞B %D`b6s%D1"N1_* %'@_6xZ;t+f_[ID ; BX%N&ZBcş%̆Os(g(yZCe-=̰B&?"X-`) ChlꪠUQbBh2:)cw5 >H-N> /Resources <> /XObject <> /Subtype 16 0 R /ProcSet [/PDF /Text /ImageB /ImageC /ImageI ] >> /Length 2983 /Filter /FlateDecode >> stream xZK% ޟ_q6ٞ%!tO.U d10/"*[U{a۲l=>}/Ƿ?~~K(LǛsyo?\. ^?w~u x|Mu͟B߮~\-5t>.g`G@vOC=rXt tq[FPd:2ʐ+U*C$h A ى \SHPJ@*ԌNK`n@htbH_7KL=k " TD,R:0ht'HDlGΓ|o0GQpK,)+"ρ3 E"h 2 ( XWR!eI{ۘe8P3ہo\73 oRTUCym94yż'T N V`&t,ysbr^։ q8$ `Sťspjkd܋4ùVQl"[@^-fj>prcdthuGHv˩5E|f|4}06,XMoŎ/vM{xZB#2=j&hQ 5=MNlI}D/aگ % Eް% ؄%TC&4 Mk4p8QR5סZ8NXx}~!qu{0Ԯ q7NWJN2˹qDkmW6Z/WFAFBjN~>xpe0du.82?&rqNw:r 3LQ~5#^E88e562BÑ }B$TgwQB$WynQ{ 8A0whփL}~x%4T(BÃ7" \:&>d c><;JqL+`)NY#e -1gQ0IjgAADpګ3m&nwD4QAǜEh˗IH̛ёF!~Fd0G"_$wG2t@q?ay&ІYHkڼ1t>R"[IaJy A{ ig7b S^}?%j5cCLϮ3+mc$HtvahO¼Ψޓ.hL)AG!7bF@D n L_ q0.[֌ >`Bd_b, vTHe6赻+M턦íh1$ߖ;mzh9텄Oщ7dȜԞW tD|ǎT 'Y(џU\C3̈}WsTO! g$Lf;fK)+5!:t)ayaX@k>{F6@R"t:;SqE ˘L,ąQ__4JC$2-ʚv--PϭI_ 2N NREzQƭR?Rg#ͫONn#UON,<;m]Y …S݉'DGM$rYg7j2$"JwRN2n+̳fASJ0GVj#4hE4ȼO /hty,oF5,NHDfr4HuD-!xwnd$LTu-r*ui;l 7bUCIV؛5ڷ,A.R 3 YHN1!V߶~ M@qw/knaƢubGb+$?ܮ16k҈,əz8w a0g  .!\J{ E/Sr p>Cק@c^ |g4 joowKHQ1v4\7"2 _H- ]6p}Zh 0` 'vkuS6؅rXխRN!~7/|qo0۠M  |s+MFLM/a1:Dluah :\&;S`й-1.}GTyhO<$}łoᔓdNQpXht2уa:19fΨ `q}vO0_t5?g*:,\r`.,|?uG4Sã2Zk8ht8Z9z'M6 +Q8 ¹FF4ŕyh^mAz/kBYxYoM2pYS]ak:a|Y1 3|لwP FX> /Resources <> /XObject <> /Subtype 19 0 R /ProcSet [/PDF /Text /ImageB /ImageC /ImageI ] >> /Length 3433 /Filter /FlateDecode >> stream x[K- ޟ_ћlز>z2$U\s̝VI?~_?.\|W> $@S?.?߭>{}+_+_Τ?;r֚C+G"aozf'JuL\F"wA!Fw."|t{1чhm@嶁CUW@` vdsqR&9]3OaA 6<1d0Jf蓡^I6k ñ@깅[m3~ ^X>D-y IX 0@D6P4|4`tYm 9"<k2=<֣VhGHCT8HKs7DrCzJD\XRI#D#!6E@ (b96O/Wn$ǫm,-K I)Lt(Yq,BaV;=s`p`Ys }Yo. )f[@bZQg&$lS#-s7sɛ,|)!vGesxt>7(B昦Ӣ?9wњXզw 9I WODq+IeT0KO$EU֯9حUSȄU8:ϼ{̪ȱCOvᴔ[wylT"s*0h[y;Hdq+#~6,D˗.#IFF·!8]IiN3B`8q! r] #i0B04TUwt*,v(DBDsPg kq[y SڧgCO_3Y}@_9*pS5P\V*+JR+nK@@GAT:c<;]tSڊd)ܕ2zը0ȱ&ɟBsm# 9 ]p|<; Рj,gm"~cɷ|+mAM[M<~?9^U2җvǥ$C$hŧz±nCTJ(T4~#,. ]fˢw/ m$'%$k8葟/݆.hjCI,Mo:%R+mHOr#sǐuI}wxNs+|F5d.;3iE(iw%Ggj:]{VJ+N dO@q &-X2US(OP^tx =dz?h۹Hh̐͏vy֞ik}W lwF߳ᲥKK`~t%Ha'O3#~GG K݁,J .7_i6ƊW0+%UZw9/v1"bQ@$/54b ՚Ӻ50a._-@p#}1"QrL>Zwg\?R격Rq/u[#KL&yrLw4Y;r|{_,ݑq1IJ;9Ogj+hgmNmGm2-1|*#.[l_Hv. #ZF 5FE93#ҥ7F#n!aF /vK 4=U I%i(s?pꀨ]8ʱ8z)sU#=8]]hkf)x]I)LaNIllYԋ@~P/‘E}E72YaMo[eV6OuN 2V\-]^z U_3j8)U&E8Z**MK#h~Rsi!&E_v*cyPXJ\B;N,-|R2#jZ=l ^~H{Gm\9QOwE?UxqGy DT 툎"E FuMzg_6U.{Br_4]8\6 yѷOmsV@ $wYU~+Prdd]Fb |G{z[f;y-@Wi7ھ'{5[`' id-xMw?28 endstream endobj 20 0 obj <> /Resources <> /XObject <> /Subtype 22 0 R /ProcSet [/PDF /Text /ImageB /ImageC /ImageI ] >> /Length 2117 /Filter /FlateDecode >> stream xZ9ޟ8Vۖ,0 $I,WnEC3̼b$U_+! gݯt}˷_Gzr%YZ l=ٛ ƢAl5ξa6=a?Da )a!% ˖|KԦYxiV9N-5VO>LL,b8\G_A>Ű}#߼{5͢GeI+i:uސ=k6Ӽw:`r:ϐdѷʨ`"Je4!U ; ʤ˒~mFך\ [͜G#ofb e#ae\S Ó>N+!KwJcĝKAoVudHY[`.:/6Z{> /*#U;,zn哯m.#`@'0%hgc X2}7I)xvc)VOOoV48e %cMk cߥL(OxWlyY7MQԤF5d7hq s`Y ;X17jŒk VҞfP!]6PAӡL2SA̮qNR[KgSW]M]3)l@A3,HS8l[n~5Ʃ4'ٓ :JV)*(AlrܝLԙ,K<[/Digi0 *t|> !%Jlzrt%r.PWUa ^Iy"(ɀńTB~;u|volf%-~ʙ;WӧC7~=]Eb'G Ta#h\i٨ƶ{x\ F{ӼInm'wY9-@[s:r<' W|,m=v$r:U$MC,OaOg9E:M*5uɊT3!62IK <rdle ھBqGznd %X](!G eTR\2Hn2Ղ>9aT? AN݃{;!~u'\ΙȓA w]/00%żYFkZ ֣5Kݵ:Z6鏍t記#;\lYseI> stream 3Marks[]Nrr - IVIX (a) Find the equations to the tangent and normal to the curvey = 3x2 + x + 2 at ( l, 2). 5(b) The radius of a circular plate is increasing in length at 0.1 cm/sec when heated.What is the rate at which the area is increasing when the radius is 12 cm ? 5(c) An open box is to be made out of a square sheet of side l8 cm by cutting offequal squares at each comer and tuming up the sides. What size of the squaresshould be cut in order that the volume of the box may be maximum ? 5Or.X (a) Find the velocity and acceleration of a particle at t = 4 seconds whosedisplacement is given by S -j t2 + 1rt. 5(b) A circular patch of oil spreads out on water, the area growing at the rate of6cm2 per minute. How fast is the radius increasing when the radius is 2 cms ? 5(c) Find the maximum value of 2x3 - 9x2 + l2x + 5. 5 endstream endobj 23 0 obj 830 endobj 21 0 obj <> /Length 12342 >> stream (^?h,Ԋi( (Z1?is j-*1uZ{{]KIPGX`[EHх}P<(E}"; rA _X_[ >=Ⰲ^w`ܳRo'wtبi!GD4! ˆbόPB4, AUw[F6 'uVh~߯׺c_[K~kl%+PIi,$"""1+G,뒖{98s_mF_^^GO_}7~_koIu__z_f)5_sS_&>}~__NMmuBAޛ 0Ӵ(v]vS*}f+U_Wwidئ*wTNi6FŰJ;aC*; 'wl\m4ħjb AMbm4= uba!4 nmtɺ !A 4iLSH4M5 DlG09C""3݈DR{i{J]A[!0ˆɸGNw-Rɲ),#D5M6Ѥ6XA$[$K:KӪOOw@#|^[tftG>fAs3#ӡץ"ޝ] [I6WCB|DZD:mCb:zeqM.o`øA ;Uw~?}H-~*PK֪ޓ_e/?r W*b(plz"ͦJnc'.Ga_ab4?ԷZ&JY "?X|;yI Eo$`<%xL(,5AHhS 4ӵXzBcxz{C VυpB;ۤJ zvGȄ"UdzׯqWJZ",SLԊ0o%qʏ43Qfffz.yfGƁkfdSق'yo# f%r/3l^:fPM5h6m[#{aI.=&H 3 cGM%CJVmVnK`I˰ۭ鴯7O^?kɺo;L?-_mZߧiW}.o]׮Mkմ5~5] ?_ޢTֻ֩^{W^{^>>>1[ΏSמ2?V/ _U/ѕ?_m5/_~_^PE"A?_گߠ/#BF~~k_U{mi/K!~CxE3LqgfNfj6k5~m3[)/4ں_m+0~0^ׯ_Hw=_na/~ Vkvbtkw}0o_~ }V"]^n/1LVWئNla7w-wF~ǬIXtM;Jh4ӦMӵWM6`v0dsa&iCbP8a$!S *iIɹn)0AXA4ASd4*6N*(0Dth})ӆ 3`«AM\V1 ViL&IA` h4¦"8d)؈ !˗(GЈz$?~~hoyCj/ҿlq[q鄟OAa^z_/^?K}/a_kgoW"M(kϯ06#5i~W>lo<{{_]}BFH0Uͧk׻iw . u_pdyᄻzva;K)bd8A5D n=ڈ᮫{IUۧG6-bSNIi+j&ġ44m h0$:V7AiL4kL&AM6 6 b8.\SH4W k-/a0M4yCA""0#崞{i;'bUWe(I7FlJ Ən%F-m: ٹ7&'TUi A$l:Nma [N:Nҷ[{I[Um;VOJmjV M=kukz _z޶nmzzzxպuN~Ʃ-C5hw j=vt?ƿIXk}˰SrzR xa?wFw ?Coޯ-p#?owѣ5nw^yz_7_fkK4%KK~ïwWou}6fGwngj:ۿU:uE^ӥ޿}'Iۯpn_+JZozJIq]_֒~}zwim o^8ctxޒKȣ  @t?~zC8Q׏kޤ=o0Oά?#bjj_L?{ׂjOGDNKp'^PlSz3]w}]]pm+vMxkMI_վ߆1)u~uGa6{]׆a{ vD"v:ObN;8dt0WmCIؔ)6iX㰅A1lRmzlCUa؇bPLzŵa+dMEЍA4ڊd.6BDZ(rn%bPw4>I&AM4H9'l29& EL"94#eA)"M4S 0q[L&a0ˆL& &A"A!DDDg#DDDqKIN0H1-U,Db?奢22G`y8h97;,G|+9#"--aN U]*۴ !=c_k;9*M_֕}W!$1.fn==s6gl3aa3 &lP ̎3˳C%83{0Ȃ?xf$g40gtlyq a4:Aa4uxL ¦<7E WK*; 3& *hT; hG#CZd#[ [zhoQhbSOWzvN GvN 8koG<3 &aC.0P4A78fٽoywIv鷦NӽKa?O0H?xM7Nt=jNӺMU:^Uzmt_ӴT +bnx&>_?A_ s(+_x?t/xVϿ{ \cO?XmPO_u)R8Vwz[K\_{fk߯7>V][޽euϯ%]5&ݤdK6M m޷|N_S]tnS+VO/UX]ALlSa84h6*MXokq(wwnI8݃IӃMG"9Ed$h7 )4بe66)M;bc A$M $ڠM6I A[MT0yC4@죔4C v3@ a43X C hDZjahV(H,'F7Izf:Xպ]]im؅I`D+Љ&wFK$v)HetxjD\0L&w`iUH&PªkWxiCýzKsZ3^AĻIi}w}W~׵T"2̢Stjf盍Џ';ΙN@FSyfCqu٩5;4#2ϑlfC32\83Qs>3p#2̌! ax320C@]GzxAB0@  h#8jFxFv";M: 0L „;G4{hjGӪZ=l#@aN6RvN6 ۵z)N({m0fŤ)Ahtcbw mNe:&kVҺ}Wީ{nt6NR}&]װ/ut&_]+7owoWKI׾'KQ_{}Ubե{_݇:tӤ=i5U+t⻏#?nwaޮ-~l;|A7-/.A~Az{z׆V_׿wOi~ILñLwwٚ3^U]f>hԞE?|oPz~[uc׿*"VUK m[WI{ktkٿڴ am{ ߭zw0["]}QWUm[IAm쎽b+5ӆ6)bbp{i]lR8>iKM]- L*h7CNcM6i6)ӧallJ4ӦrCؤb u$ A$鯊i ڴ; &}Aara4a5A2 AM )ǴS4!!!4aETDDDDDDDDEDDDDDDDDDDDDDGu_턊r]V"a[ԙ X8M(gɴG"'D&q*(k]֏ ;)B==$WZ%8j?z0ks;9ݙL::j@Q#vb>P}!!: fA31h8Dq3 BxA -zjth=лICG  %GAin.-oayQlnwݓi6aaM%^t˶R@=ۥOM7[_>_mڔG봼N/+oߘMϯAKi_kk~)?oerԃ[i "RT: EekiZSLRէl58ka' O)0Y7 D$8M4AIAbM0rR Qi,GF́KZi+e K[_04QJjG#嬭xY)4vRHȳ;1dv^ ;=j$B OIôv >}ܙ#TT'cvkm<}Vu߭~O[UZo'dB1ԟ!8瑴gl͐ѩ Σq2?qǤ 3<5qf yhdA|r? ^93<( 4 S  tPA`a 0Aa&0Ta4aav'MPFpv}0BaFh*iiƍl0 hXѡB$hp˴{aGBFt|nGON$m 4= 6 ۵NهWa5fvMI:.eIn.ONV2˅M֗%exն_']y} mҺ?CO]=^7__׽?WU0^J~^V7_o?xnO5x?_/~g)ЅKj?UwC_B k0,hף[[;|#G#GG ߠ_~O]LuN$4]3_XcZ_]~^jOg=.k?____mU_z޽_]zKõˬO0E<NBT׿T|V_J‚)#^]늆kadt@ح8?cثA\m֪Cv; $0mvC(i5`MPM)`҉&(t !Q)Aġ0irN 4AI1 ATVMA2ni4 &L4˄ɹPM01L wgaa4s #> &B"B""#qZfGDDE'Dzn.^6J_[IS &E7ɲGYB;̊d_;A# #2Y6wځO ; U4:L${{[piS[>".VSX@mʐR !".%^TOR꿭cWtqBM`< yDhgvi#H5ٚ7 vb423/"qfQg V:5:˲mg㙆l͘@ #@ "7tga5EA)60P0P 0PǂaMpAM QTx,*4j\ќ4-=B #;P0Pa#m;HTh֨ѭkwB{uBP'iq=,0Skq'|$%T:z2sh'dJ*(&%@ fn&tIzig$d6u켤eIm'OPO&ۨO[/.4ƷPozi޿W{~I}kRomizzZioNU^rCNc=<0Z6C]>V?usfwn'n=2<{6E;=mffD " 918˚ߘ#A$(P@0  x aBaBiL FwgKM/]|#[[CQhДqڶħJ{Tvl#c jz2 vuw=oNO.޶ƭS'K}iiۯ_bV+CVi_h80;*"H JWӴK]Ww J]+wߤ~_3__hIJߤ}vֹtFkm-I?^^IMd^:a)ڑl  I KKJ 4O+MSV% T 0T -]nIi4զ#Na^kja9ODDD&B""""""""""""""""""#m}[JVQ-1aJfx-|,?嶓GY?- ?Q̩̓xQܕGLQB/SB2UQ5j%>[(SE-%G5-GۃU[QZ(I ?;Hkj[F?QQ-uTQZ9fqS%mַsE (rTb  endstream endobj 19 0 obj <> stream 2PART - C(Maximum marks : 60)(Answer ore full question from each unit. Each full question carries 15 marks.) Marks III (a) Prove that cos0l;il6- - Unrr - II + sinO_.__________:_ : I secH.cosu Itf sin A =i and A is acutc. find sin 2A and cos 2A.Show that tan 75o + cot 75o = 4. OnIV (a) Prove trrat ff$1 . #H = 2 sec'A.RI(b) If sinA=;. sin B: J I A. B are acute. find sin (A-B) and cos (A+B).(c) From the top ofa light house 90m high, the angles of depression of two boatson the sea level are 45" and 60". Find the distance between the boats. Uxrr - IIsin2A+sin5A-sinAProve that cos2A + cos5A + cosA = tan2A'Prove that cos 55o + cos 65o + cos l75o = 0.Solve AABC, given a = 5cm, b = 8cm and C = 30".OnProve that sin 50" - sin 70" + sin l0o = 0.Prove that cos 3.A + cos 5A + cos 9A + cos l7A = 4 cos 4A cos 6A cos 7A.Solve AABC, given a = 2cm, b = 3cm and c = 4cm. tlNrr - III (b)(c) v (a)(b)(c) VI (a)(b)(c) 555 555 MI (a) Evaluate (i) lim,J0srn2l.c9lj! (ii)x (b) If x = a cosrO. y = b sinr0. fird *.(c) If y = a sin mx. prove that S * .r, = O.OnVIII (a) Evaluate (i)fi,*-o!#I (ii) limx--yr (b) If y = log (sec x - tan x), show that S = -sec x. 2x2+x+llirn. ___..- ----=-' x'-2x'l I /1 + 1=51 (4+2=6) dzv(c) Ify=AsinxlBcosx(A,Bareconstants), Show that # *r=O 45 55 endstream endobj 24 0 obj 1264 endobj 18 0 obj <> /Length 19008 >> stream &i|Z\审q[WMT׏-$/O>}?I?KKK?^ZI始h\ a>}wc?"8A6fGeo%~?_a<#߰mtZ}KM8q\DDDG-7@4Cf  lk/naנMƲ,[^݄$_ g_cVDT}??~HUՆ44` h57b2dF2;uM֠i 2l+ㄒn _]wouGl3qȹ3l7ffٚ=}4^*iBi 0*x&;UMm"ؕTXq > K'O[Um0\2im[NMC_o}kk C֕g޿߯A~_ߏKO^o_'_ͧoMM^jh?΍Al-4ؔN ƚm6DEeX ڟ-p"b؈VWq+t)E/\ɰL.0Av$TUўa؅L 랎gbYI:w;Tw \0R4Z|wv];uz?}m8Gǔ]_dA#l˲]!D] Gh73Dns0ƬBdZ4iðC5x@aB &A &a@u3l\FPA^K$MCNFTl:46``B؋G<4hhøpa=0͘Ab>3A<3v^>32_0333F,?pw!7JIJ:M.[ W 6h q}{h&9O{ѭtxhpBѝ;B"4ѣpBa08`Gvݷ_K~^zZO7&('d46ħ;a%ׯv??[uT_m+I_}0-$o{i%?]?r׏ևc{}p߆z+KҬ Ѫ߷a+_1WWұmN_Ow 2L?bi.bO'ma[o./]{~m~k4ϤϢK߂(uk3A7 uޫS^I{KKˠWO_a~i5IK`orYK k{{_~../MGJK)8;M66%ڱVkw o؆*#+_aKOua5im}L+a64¶%M{PbM0 !&h6Hqխ642بi14icaa{DDDDDC"!L 2idM>iOdI/;SȮ5?Vh4:I;aV-2IX+HYA(Mi؄i&akMqDXL! h &LBmDE_qIiݴ[2(/0Gfѡ۞wFUt&㪠)ݭj&v kdj.W/FIa&o97{5^Th%kk{ZM6Q_blU7Aa!! Scء5_.:*J,T_)%-xW5$ABAHDTGk8DQBN 9)u θP@ιdMU;nҺmS?5abt*ZeIdOA:|Y0{Z zߤݥr 3Üy7;%8"vqg@q==vA9M8Fv(NH:i¤0i(PA@aB}ifa rȪp1)x`?A6hH:>4hnF%AGʡkh44{{b); zwwޛwep޿v:WMe?=:_Z~Zi=:Vc_u kQFj[tv٨ZMu.8@~cImׯ /B?l5iE|^a=}}%FwKlHe^FMxm)AW֏?5 :]KI+[, ;wuO[_m!o]v7޿}%}{k#[[[Moڷ&rK9@bpA0AlRh6-;iFbPm*iapNS6!h0Mrp 4ՈA 4tM6MŠBI4m41JAQ q2@h0D}KnDDDDDnմmh+i8hTu,R&(Q1QGgU&!bbLxŃ&Pzھw h^r+ jkkT'UER4t_ƫ}FQ!+WOwy#4fNSFt'Wޑ MS@A  tmKA8km4QCa4mBCix. 7I=a.ĨjNM t`rioçKI'޺ZV,7Uݪ+xL#{o cvɀ!-Eџ?R'o_,Sߤ_KOQ["wxii[}_+E?;_I.'YC#j_C#_ A q 1Nid &)-&+U8"! !ia4#L alTDDDDDDDDnm(bU-":7Iޞy_A[%g]Kna.U41i* ֟kS, Fl;A 'Tf31#BGv >QoF4xGwN~izm6iZZWb]+I{iz޺X5!Gxs֘wi~῞oϯ*&i/y}2mE;>]jqMLiZXf7] ҴNZWLWm!E02̍JLM*) "HB"/ 2vYń3i:244$.ۈAFY %~{gz' i:_kVӮZy3D ]2?0_Z3K!0"vG̝wR{ѭHQC 9 G]FѴCD|h椄D &zZoII&ڗoxJE jt{hꝿMX}?dtG^ ꒶?Џe Qu_"5c[cqAkoL9K_w/+dZ #SֿlD"v5W^~k"[ڷv#7H[V+>a]ּSzd.Th0*a46NXkOuM&a-Pa4UvlP"͒$w~""""+ua mWϑ44k{FIvcT0ONMRAAtA:M+{E-']]nCVݿJ_#pcw(^="ȩuo=;<)nI [>a?OVjwbzc i^ a.4Iح/m!E4i1 6M0 a2cQGTMwGImV'a8zM[F"B$Iw졥H+8LH243!qH@4M8I0c Nx0rPhe%Nբ6 (ڱj_5eA5% gg~"gjki+݇JٺKouIvRl4/ww_6Tqߕ0}%Oݵ;jr0s1fB}S1dFyܪhP(OSɎP{, 0 A2 5\ #B4%G8`݉OH?;H6v=it{ Ѡ4-(04Tkomzm&Ʒv^bJܸҶiI:N6rwI }+?xۺW:`Vxi7/K֭~MɎ^|?5 }6;; >G2?7oah]OiP_WgjW}3m'#G۠_/VW })Dz K 7 >yfk?M}nS%}{ik}__yqa~0`N˙g\ȁt3D{.h<3#83ͳo0077d8l!dECF"x:O #@a OFwaPhhx(P@ @o#8kӅ Z[ a h0X0a0 DX` 0ds0F˙`Z|WH6;RqH6$bq `ҤIo}ozdr.F=ZN %;G<4- GhZ40`i4{ 76 z0N zj:M}nl2ti>tdt7'/h5קzJ}~]kozmm~?{QVW*OH]cNe|+edc`/,uk}_u/\!oFW8=n5imoW5F~޳5_uKu~iv}owyO {o{i/~ +fӇX_ [MVItp{_:{:ot]߱_i# Z0[_9ﶺ^kWuӯ ^WPmi6N vMqýir1ݱL4N}qZ\U[unu biŦLTSdI 40QTS *ah4jkQI4ڴ $ضS{ Za-6KӤIB4M0 R @(x0B $bP_vLXN E1 6M ( )b ) S&M+"""#˨(/q &ViuH>"""7KzU4JIZW 1B] L&)b 6 DUQ; $(L8&T3NdT0(L3veo-&UEpIpﻺg@N$Cq~{^z]x䟐$v|$y]=}R]iy6WyHO;nnBz.h`>Gʌ3~#Y3A+h")g7dLdHA,:=:#<4{a<F R^K= ,zA(L$GiBa a3A Ӱ@A3t :MVkAշF *4~~ħT  h.TmCj,#;Fѝ񺷺TM- , *m.^'>]Ktܸi7O: . Ndi:NI87^+in?Z_kK-&P-j?lok^z X`0Eź6$m!V` k¯aQ\G}oxGu~3+U>$'ނ{p_F/nNWWKޓA>ApE脪oᾗ۳4PK~9K`kK>^a+#. w}sJH{6Xi?_tZVIwlvL]Uū 1Mn#zM}S6GOv7IҴ1biiԐpղCmqRCALVA4!iD& &ic҆GuJ A ! ! a0h00Mh M627d$ Ia!4­A b5 %DDDDDDDDDDDDDDDDDDDDDDDDDDDDDD0 & bAlL[eXfv.3ڧk_ٞmὩopQ]xov [tNL!pD\QGɢ/;RxA)P) &@wRIjP+A:(hqh33q@*C9:4B}^Bv WnƕؕnJuޝRl]m/u[YO^ݱ{*.WaT,?иo)QKjFCVW}kk n:\]{iiؔ:Wj?qYV8igEMTH0 MSIY[iIږP*"""""[' Pzh7B#;GPEzוdhFbוy;[,p@xھ ޮ6FzN6}&ѭ,+a*һ}[Һ}i}=6E_o[UХK#]+)Ré'۾`4<k-n.<yTW)67'~7W.S:_[<~}턵LںcI+[JSiZWM %Si_b(&a A3 h6)Q8*a[ܚ HȰjJB;ϑ[4;™ZL -{h-e(ߝꏡG@MF<m&UYܗX_~tR_"e^ ^KFV~?{6o]:fKb/]Kު%"O`zFk_]kzom/J^u=%I7. ]PAاcEC lUJ%0ᄾTi4'  [AbLT0iEZYe'qDDDDDDaaab VnDDDDDEtm!2<Ւ.ve|T<YِelMwpѸY5|AIM tpIiNԛh i6muI6!ۭkHBE&f8w D^:D ꎨw>p8w U%"f34 qǍra2 w] FH[I.x4 GjqaPaPCR {PWotm'Iwm2I6Eܘbv%@ 'Nѯ/aP}'WҸ_noCiu A5VOtWQoꁂkݤWof_rQ^9#]AoHE[Cgӂw@aD_#oK1?# ;'GKnXX߷U9K݊_'WݯkV>^{].KׯKK~!}^ja#2wjBjnumzom$hIEE'# ZuV ᄢ[bBOP .T ¶Q +ai8LSI6 0M8`0idm/g89CA"M0A'`a!4.$: !1Z %m!qU`bZm$$AaeTb!ZD  nuՄEf@u}O^ҿa׭ݺ] mn"?s+yvaȒ]!/z +ӥObw~a{fC)~j=oV_נo7Ն+7}uz4F8qCdt/)I nOz1B7}FS0_E>&o~_A?oFI7ڷۥMo}*6{Aޟ{O/zv6e0z %_l/ޒWv{=wiUv aVر Q m+رM֖ 6tc$I]pL5I$h1 *! i *( i %koWkNؤ"",!00C8L $LB Pz 4aIæ% ^DDDDDDDDDDDDDCL&bA|VDDDC+P9ʈ ]½0(MTW+ "ٌ2̅U&qrclAB V;YxѿIj 8Cѡ@յwzxO}W_7c^kTy2pǣ[3F]goR$>3}MDdnr L @Emr@Ͳ B1Ojvi>5THдk~nа &L#@a4K0A /{#&; dJ' 3wJ`5v4lCЎvKWj%E:ZN5av_~?]ҋZWKZN ߴj{n*tG΂ ?U 77^pKз 1ZF{._>o5J_! ڶ/K뼤3ۿ9KI\UZI.G޿}!#|Ue,5-ZWI{ڛ]nFkK󋥵&_\5m%JJ.^+}ԅtmk_kbڈM bNSbl4j 6+cKD\ CL ]A$in1 iCN:M5ɺ֕Q<""""!"! Ca0[I a/ZBЈ]/5mRMRh$eI(eT1j j#s;إŰA _j[sq`˂}kuʳ_ߏoI ?`K1 6DDDLu@Ξ= #^.RZOI}=?]uHc .z{M~^& 6N rаcدF&MwuQIwW u堲.G# gHCIJ Akcz~%;5khj*ka:~ڈ<)"Ցpgiш =t$ݻLBhe}4 Mڥl*+KSva$'*ox?I{V|mſ~*,IH߰{6ERM0 뺼uӫFkzybowtwkBU 0UFy<8 yQ*G}Et3IN𙆃 9ZߺMz6uWh~4}<4սm+P|!_{ݓPᄓM5[Ia)EIީ Jꪭ"/vAl$M2nl a5i Al4}T#M r%VhK]EqqQ) 486ޚY*nHH3 7IB]T"$Q4XAqQL07IzJ j jI'̅6I)[h&+oAziW.It1]DRbj-^J!\fJJ5JE88\m5LWPzYI$}tTi"2[J+&IZM;P+wi8&uGYuo%?XU'n;.}(mo7G`Fd~M6ֲ$8UG!EGVD̏g ڠDx.aVI:i7鄛RW.&ݦqC]MKKW'ᐄqHDӺMzUvշt[oAm#LWan6JMJJ0?mOILTS{  Ac&8FQaa4s2n#?"")~[oI$mFHڇ B*e7¾ZGwoAإ.eyf|%ۮ_]#k0lE.3L*/PKkAd[~*4jD +;tŘM3o;smj@&ZlghAi ,CL&Za`$B)]v 6q!ln*ߚ#8i#I>WA@0L@`f3c.~]A# *Z\͚z:=*;0MhFT-ڥB0pa"nV4|!~vBӆ%(o\v J4$%8kA{tӶ7&WL"Z4~~OUlTVzӶ/a0!X~38]__⩝KX,:Qﵙ_tΠGoi_gi}(,7 7|W~?1}}uþ?[׻k_]/)!DOKtn&i5b"#Wmv^m*uI2n M0MNIG:M6YDU =@ρ2 E ;ɶbAPq1WUI;Sa;HVҡDUF_tF,GiY AޔioCIKW[E;&-D- iP%n :OVuDFmTK}J!;n[v$vdSDE\t/Ajz]e&3O {zk䤍f0nR џu綍njզ_[5*:>z ?a馟ݬ4b#ˠ8 n~I4ڄSiZKg>[Fzf2_9CiXgbu|# T2hDqH z[`aWH%L aBm;DD]|l5c61F<[HʨQPM0&&!m""""-$<ߤFA7tIIsLr$9C|"""ڷ4'сf KphS=s7?7ǪGc_ O{OÇAm„a2xU0 ҫ_h{ R.ۻ]dVoB"zOΠ'޿&;'wIfrvN펕i]OuUe5͢/%!wm/_&/k]T#}bX1C'o|AoqKo/}zoijH/'%_ݴʇDBz4_-T Cq9V~3g0炦M✡7m$4.hnBK%z~־d }k5Zֵ_ގ=/MQ&_h=BA"7tӴ㨮dL-5ӽCꃤӵl"=7ZTA&BM{&Ӥ"kjZ_` q W]Kza""6)7B wJ޼JWQbV-#VtQ[mJ[uznN) YӢcX $wxWCWI&AD}<պWI#WR tk,uZީ=޿kzwK{-cyn*Л?QvHDTP V3%<&TBJ)G7x2Wm&hv,%OkJvtGKI[С{_]R_m8dc3$h3hf4 2js,<4.3m˙ YFGϲֱ<6EжߠѝU;Ċh05h`ѱFw$dJ ia$F<4h ˷{?/zҶiKWaZN֓im_Iu[+IINkiwu~۴z0\DA>ȃmCdI޵nI[i6PVT8kn‹EƯ`ǠB"+E8/{kq[ra?'u}/)_.Xa_woƝ%,Voj_;i~uӽ?. >>d_)E[6j*pŶ^Ka;Xo^n {_q?no-oas1_]zi}@ݼ~6/FN]6:Za?mwۥ/_/?R=ގV龯_ϫS m"_H[Uv^۫^m^Kri݆o 1i:ұLU_auMz֗Nҿ[* % K!vdSo҄ni!i $bLa08[ UqJbƪl9NjFK0K0IPA4ł*4!qq0!AЈjqҹ+A:z""""7&7WUz`TI$cm#I?JK$m*(5!!5ŦA^lU__aECva=aPvk!1MGAe) 0gU)G Eɢ@ endstream endobj 16 0 obj <> stream 'i ED (15) - 1002 Reg. No. .................(REVISION - 2015) Signaturc ..................DIPLOMA EXAMINATION IN ENGINEERING/TECHNOLOGY/MANAGEMENT/COMMERCIAL PRACTICE - APRIL, 2019ENGINEERING MATHEMATICS - IlTime : 3 holrs(Maximum marks : 100) PART - A(Maximum marks : 10)MarksI Answer a/1 questions. Each question carries 2 marks.l. Prove that cos2A- sin2 A = I - 2 sin2A.n2. Ifcos A = ; and A is acute, find cos 3A.3. Find the area of the triangle ABC, grven b = 3cm, s = 2cm, A = 30o.4. Ilv: x cos x. Find !I .' dx_ 5. Find the velocity and acceleration at time 't' of a particle moving accordingto s=t3 -2t2+1.(5 x2 - l0) PART - B(Maximum mark : 30)II Ansrver any .five of the following questions. Each question carries 6 marks.l. Express 3 cosx + 4 sinx in the form R sin (x + cr), where Cx, is acute.l. Prove that cos a + ct 1T 5n 7Tg ":-+cosf +cosf =0.3. Prove that (a + b) snr ! =..u. A;B4. Differentiate cos x by the method of fiit princlples.5. Fincl fl ;r l<'+ l = 3axy.6. Fincl tl.re equation to thc tangent antl normal to the cune *2+ I = 25 at (3.-4).7. Prove that sin I20" cos 330" + cos 2.{0" sin l30o = 1.(516:30) t2) endstream endobj 25 0 obj 1135 endobj 15 0 obj <> /Length 17212 >> stream /Y>?BGDm"gXEh&H(A4lO4A #@]jh&+VmmtjkjA?}?tY2w6辯TҦ"BַD߽ uU! HV|n8f9G3<#u;m i8bnK99=Z<؈ b]!z WlV{R!DzD8q|QҴɛfs7o7#q"GHVu(6[nk_U^M;OLb7&oLn73y^DDDCM;TOMo_wT8BM4M4NRFu\!BRA 0avrT0<1  !A ia : 4$xfMN ID@PADDDDDALF"?u"#tGB: 芁Iѫ#%mL7VDSg02@B ml0Hd Ca8h2dqJr6 "FQgd=!mM8@a t$9CcRv6&La $ mI]۪'H7 O!2N#p"P4!h>d$ĵ-9Um]uwNaզ@5aOᓝC 0|u]n_~IM>wll6laQaw[CIqwKnzޒ}#[PMwZM0q߯i?ۯNE+h?~{hm_4WJ<z:W{_K_owwu^$v^꫿h_ޗZ\{oi{i%^oRח.8Wi~ww_o[iz^ߴ'_Jֺ&{u|T.J+}¬+}/;]7|(ou/Gn#"!KtL SM  ; ";O߷6fn|1*lN8q wK]v pX_];[zj^*K/}o O4{a+KZaW/ &l_jk_:]iq~?nI6NTдdi29§ZMW3L¼?;" 1LB]`WմGHu,@4H|Շ/6=^WS-i7%_yao?^X5 {xOj&0`T"Cʥ5duY\ iRmJ^H3&#C uӦ᥶kMqxm3ٛg"mmc">zU~J&v¦ ADv'a5OҦ%@v%8q{u  &NZ[Kk`߯駮I\zV?%SF>uI/?Ktm[÷ߴ{]}MXC_ѪAAnL&M4„Mj[P-ܜ$t6)x 5m+Ss )PQ[IhhOǣ4E9F޿!/OAﶖǰj _ _x}g~+AkG}/8ָaHvJp%U񈈏V\,,-)A(BMTuaFW@&vfݣpB:"qvPKcYvvG';{UIkF#13z"""""#aUidiDDDDDDC   eX?d3M2Ύ4Ԩ\C֩C .CʄL$]zjT(}yKmROZҊVcuJ^ ߦ]*ޭ7<0udP9Ǣ2]/P" &";AAt1F-?h&GEm]* j)z65eڗ[Rf*BzO'IzlRc]Qaw/WlkVpՍ?.$e8.Nkp56qG տT P7ȏX}q_ b"&$R O_NrZWZAM6э"67SmxE=l 1K{ewMN†(|m6:[^KKY-AAM!H(&M4W"""""""" eR:L """"DeE_^^ *;HhVv!=}=vkTm?Tp4_ccU dhwa#"h3s4i_3dAǣ37hOT cAIl*i:0ar r3;L4~ƶ?zNw $ha *hGv WZi:Nuth;f L:l*'VV/vO}?)/kQ[ҺB>eC0K F{ vmnm K"Wh/a_~IV޷O]_nU_ڶ}pa*JYCa5S)뵰-J & 4tai (8ډCjMXi]e[MJ@ a<D&0 Ma46Ih1QH5\Z"""A &q42ȝe"ΝbwyD2 PPfDDd ,amt{oYz930 ̈3ǙSz6:V4kMp3XA;@ ύ.ឌ3BϚ;Q&2о/uP훐N('m&Ѭ0X$-!=h#A3  g3P,z?{r?커A]L.{t&6 x !hIH0a0:93nqbOZ_k^+-YzN8rnQŦ:L!i[>UbcoӠBi;'bUN*=FS/Cߵ]VNa:X_0יGAwpuim? P*4C>I5]a?u/X0w__v>imnZ{kYW!qٚo~(r~WUi'"ҵki}U!#w^ϧ^ Wӏbڑӥ{W" +ڛ׫KI iԃM'IP `MbBnmNKl.zV{+#] !a4a  M6M9'H00JB`{B`JaN""""""""!hE0dA!;pa6*E i+5&iqQ"""&4ݭ;M4 ^""" XnPbvuIR% UH$ʓ)DGП7G3/wۯ_JY̊~XHfIA u +}N{O_ʄmtSju"aIpA A:"=IAϣn(`v44{hk0$_:I6i;µSK[7 'Iڥi1Uv,T~?:.^TЃ vVWO~뿐WЍÕwx"=EF'Ky]owKvnJZ lUꮙ4V< N"8aRxP":PuD8kzh}q堇;tTүu=mS~{jkpˀKq+jWY,`vȦwW&;TUs&;J;;FE9%ZiDFGj:Xn-%Nv__%Фh>?_ԧ^ $#3A2vj#3k |B8P0=0F85@3"#9dhf摚65UK_֏WQ AGaP˴= #/&4 |gSFȝZ7OӤI7[t3rNh&MP1mGa„ m `Fk {4Luۛ=kizMtir.an LNwh `L#8`0uh3ff#gD E"(umiiIuvm6;Z=FM IgaAa0n63C?-cK]stpؕ|; &GPdu޽(~ E u}_JSm7jjeH;Nڰ#?l.%#_&Wu뿿W#$ނF]㨤ۯTKwKA~3 !{gv}UfbO4W_w)jiߟ_~KׯKH%_$m88ۦ *l% aOio޿_ 'qӵb5amAbՆ˥m/׿}ߏ"N&gX`4bI Ěl[Gl&)Xi?⬺o__O^W)!a4"&M0 0A¤brNM6K a})4%~cTDDDDDDDDDC O+ݴ % HiW|5b%_ЈaB&öa h6)a4lJM0\46%QDDDDDD! L&& ܲDֺBuxZRXYp*@Q`Q73a8=OZR,*h5 -PthZ'"Oj_T޴>Ȭ0A@G >:}Z_6[Jd`1UDUkZi )&z_6SvaMSA>"",(U[%RL(KAX6RI$)sԡtPA޻tDm'j?X0NR@/MWClV=]m?_Hֻ6D$K:_%\I#5\nC$W ab"+zV}(f&(P$l,Flٰ5f1[tyw}QV>iuTT b厹!鷂ڑa<}v_o}U*jM ! """"?(嘭K94`Τp•Gyڎ)/tѠ6S9jvj{h&=>w)Wu7f̎3{!KZ<6PAؼ&f\͘@2l m%8%8;B„hh^Fz}ovONadJNn^v[UCI}czKO+KuC3j6oZ ۿG<0ZZMk{agz[T5;]AV &a0JZikާWWU *exL&UM6NAKm%""""""""tŊ"#VSqSs )PQIb0BxԈK Ϣ JIv ڧ~äd|ǧS#"|J$ۯZ׹O{HB7ǒ[t- VMV_ڑ'ƪVU~N ]pmSie=Ah` y3z9W4jKu7xa4 Zh #Cv0 Er ЏFs[$/u}VOfvII:ħt = Fhγ4.dFM. /7kNAN ''6هAQzgM# |gD?f34i unIz߭?NtƭA 4h !D'/B4>3{6F/H~ֽ%K;ݾI7OtM&ÜnܬѠ0G"=#Gw\T%M_ RO fK?:. J g:vM$MmKUͨ}qZnZH)V _^4zJ?3]߿VfvoIB8a}1MZ]{W\7w =oX} _a}uguT?^ҫP/k 4\Cm6}y?(~홧m/7UN*7H8m-T0RI꿴B]8aL}Wiy1kytuaP4i4I>a0tVNثJ=Ӻ S _ m[ [}A_ DDDDDCB: U؄N+Cbcm"4"#(qhA0FsAGLMCeͅ &WlTC۷6"""""""z E4NcA0ҿAߧ&duT"""" &x*ʰDt(0 (p 'K֗^"""""""-Dt B+`b!geS*E+(;fBj2 I(•m?£dd}2P%t;S/mTH}ٰ6Gi~ӥڎe=tN۵4p3qb8dd'emkk( Gsp $A *)r9fFgѸ'Fℿ@[LzM#GƏwjH +'L0#v^0͟>hNw7鶅'KuowKH;*SE5& ((A =/w ouwxN /mv q*zBSA30Gό]$hyN$ibbҽǥv?]}:O0OpunpQh 4PDv`9hF nmuU_]ЂX1t|jީѢovl7GZ3m*Z}(>M$ >o_kI:WV6a=mȣki}6Poq _b31 ]6X"}\ԃ_}~- ^vOkMJz'[>o8WXa7 -WJ6Ҵ'׺~t4r'6TT]1KcVWt ⿳kB iI ;NimTsvV|'.%RpPDzMؤ A 5Nӵtk\""""""""VT1 4Pl4ؤئ A⵰pg1""",Bz4 i: dsj  S"Јa!WAmwDDDDDC u$Cn$&Y -SsR6-Fa;f0@MY&"EeV&Wӆ]6kGDp@2s(6_zMJi=6}>9Y ~!$5[%~v#ΡKMύBBizR@O Nݭ{=V ƩoAKZ~@@d (}o#? ?`$ rp9`c!]|I_/a޿֖Gi} lgn WJի>owoHkmL'[Sl]hQվҾIv+ ᾫl0v*iϴ _}ڽgOh Ӷ+jM]"iE6=|ۨ aAI 1ca~@"b*"mi6"!' ŠKA fV~#҄4ޭ}`+CJ^M8tŃI6Һ4>u{'<>M߽wMWit9^J76҆ (v嚝ގ;\Tw ~n -^+p)=śrPjzY0aCDV~l 8Ke m]/~)s?gd,)i/VJmL! FѤfKK4":(Sh8g";R9s3D]f֍_thC%vSx ";6Pgc:.DvD2:"E XpjoŴⅢ0x/$G{u.ݯbNCA:<I[_U7'"L+d'N_ ૾C7mu[#~V_?0{١_/յm`uHyuO@3_epNȉko/0Ml1m/M-`": Bv 'SnI2'4N"""""""; *M4m[b#h1 պ̕ n@+RI=.IiU.R3ҡ$*Tft*ˆu28dT))fW/Oռ()xdXn جPi0Mv`Ŷq]8}猫 GKyދtZ8$"ڭ. !lEٲ=hg.Dk^vO0l4Tx`Ax nl4EyfFz'4y=}A鷦 Om6iha xL R`Bf# gTmњ7fӿ'Joޥ}7 q*h h {lj l& 0glZvҠtNA鴝&A,S 4{ *aFwK_]B}7Mjҷנ˶rXv%;O`/0Nv/}^^+O #[ίz7{Mzo_ڿ~WYA~N@?f_CnSm_֯VJ3]8^_5[KH}_ϯZۯ?߯k׃~%6IE7u_֫o{?zh!& A&tӶݤG[]vuWuV}O XM4a!*a F&U 5VEeֿ0^+MPB!IհA%2CAN aI;Պv*""""""#91 Dwi A0 /B"#QDDe(UcJeT @G0Z;KU_-;W?H0[e.NF.[dm__+KMi2r[KW҈~ .:38 +#Cs6.?\sDWT}w(7ιN "L~R*@0@2LFDatHW$;Pi=(0Nƒw B8|37ӥbz O;ZN'7zzkH~DA?o^?>_5tHG&¿WwU *eYc}1n xׯo[p#;m}'_.VշKT+M`MnJi8elPV|S M"#A4GI=^̆k] ;,HrlmU.І-ֶZG}݆i7aN"#5 t꺥-nUB'HеV- 6+iGaKކW%dLEE~ d 8qwPRgeh/u*'qZZ+hTSŮPA:4HZ뮿]qjy|鞁0HC<Fyg76 \$JR 를rJBO T0V*<4x4¬0#0@vr3ZB"&5 $""RN*!\IYK*%QE L9]H),v&%DuVvEЎ2$2W5T E;*'3BR/!!QCHVm44hMB44 d'|:6AxM[jPG`;Gf&]'۴jӈAmڼivOXZNxn'# ?m]nASvz; v9%KdH'K_l HaP IT>l$ *\ E/C=WJo~o$ ?bVcaQ&ׅ:8'ᄺv߫KV '" +jݳrҡB4֘OئPYj/kQGJ݊~6==GzҺߡ =moǯ^WAxani/H_^c~~G:azWlzNF"1|_z_ԧOfy7һm]jvM1_vT;H⺶~lӥ[-4حi(w¦k]XH :Cjo E _DHhCGTB[H5L1LS & +I;zi#=9?4݊MSBiDDDDDb"&0iKT#Q-d6f$a/2LH$x*KdQn%"tShoWAZVK.d0"Cm$ت }7=韼X"/&WЍJpIުW+U f:؊ޭoJ?-AS#|ZB@ endstream endobj 14 0 obj <> endobj 2 0 obj << /ProcSet [/PDF /Text /ImageB /ImageC /ImageI] /Font << /F1 10 0 R >> /XObject << /TPL0 13 0 R /TPL1 17 0 R /TPL2 20 0 R /I1 11 0 R >> >> endobj 26 0 obj << /Producer (FPDF 1.81) /CreationDate (D:20250311010711) >> endobj 27 0 obj << /Type /Catalog /Pages 1 0 R >> endobj xref 0 28 0000000000 65535 f 0000001578 00000 n 0000087758 00000 n 0000000009 00000 n 0000000300 00000 n 0000000529 00000 n 0000000820 00000 n 0000001053 00000 n 0000001344 00000 n 0000001677 00000 n 0000002111 00000 n 0000002237 00000 n 0000024121 00000 n 0000025530 00000 n 0000087661 00000 n 0000070234 00000 n 0000069024 00000 n 0000028825 00000 n 0000049801 00000 n 0000048462 00000 n 0000032571 00000 n 0000035905 00000 n 0000035001 00000 n 0000035885 00000 n 0000049780 00000 n 0000070213 00000 n 0000087913 00000 n 0000087990 00000 n trailer << /Size 28 /Root 27 0 R /Info 26 0 R >> startxref 88040 %%EOF