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qrqFq rrqq 6q qni t ffi f+, lqqr d ftrqi + fuq Es ei+1 6r trftr l+q1 qp61 g. t eio, t, o, 1, 2, 3, 4, 5,6,7,8,9. ffi tiqr +l ffi h fus 6c qm fr{ t erd olh s.cv; Eq.r$, (6r$, +69r, Ecrrt, E{_EcrR, rtf{r, <TI-FrRt, m+9, qT-6-G orft xc4n frfr 6. Eqrilsr r. ++ A rr$ drftrq,r { A G r+6 {@r q} yrqT { frfuq: aa: frG{'qrit: (a derq+frq5wRsr; Saqr$ 1i4 eraaru<rtreWntrA*. (;;;) fv +ils rn ere ena t-qn +E ti q*'. (,?) q-!ftq s'ts rd ero fre E-qR ena s} lrfrq E<r6{ur 2. ftqfuka {qrstr d r}id { ft{frcS, 14 il *-te ar aru fr EqR sTrd. t;n tf6 o-tre ena ers * reR fr-c S Rtd. (,,,) fr{ersfr{EqR+frq. (;v) tfu o.ts qra ers +s EqR t*s. 56: *util +1 mfe-+i e-{mr {gti}ii +1 ffi qr, { G {qr { td.S ** m wrr*q qr{ (ptace Va ru e) irerr qrfrq qrr Gace Vat ue) I. ffi sio ql qrfi-q qR sq 3i6 srr ercil cH t qrt * .96 ffi cfr rqn c{ fr. 2 qqf{€ s]-drIFK E(f6{r,T : {qtsslzs s E,r qrfrq cr{ f t ; 7 tr, qrftq qrq z t ; s qr qrftq qn s tsnE t il. frfr irt6 6T Tgrrfrqcr{: ffi {'d tiq t, f+r{ nim+rerfi-q"=:15+t$ aiq) x 1; <6T$ 3i6, 6-r Frr+q cH : (ftr$ eis) x la; ffi h ei+ m errfrq cH : (ffi q elq) x 1oo; fqR * iis m rsn+q cr{: (fsR s'r eiq.) x 1000 sTrR-sTriq. r(r{{rrr 3. {qr zolsssz fr fd&q; (D 6?s,rqraiqcFr (r, gt5',r!ilrfrqcFl (,ir, sifi,Tglrfrqqrt (rr) 4tsTrclr+qqF (v) 2*rerrfrawt EA: qqtm, 14 e +r vrfr+ wl : o (,,) 9 6',1 qrfrq cH = 9 (rr,) 5t5rlrlrftqcE=(5 x 100):500 (;v) 46I€{rfr{crl=(4 x 10000):40000 (v) 2 6l rrlrfta Hn = (2 x 1):2. qqlit{ri (Even Numbers) iTelrtdqcIffi (Odd Numbers): (O d qr*a {qni z t $aur f<rr* d srA 3-A vl {@rd *-dt t. *i: 2,4,6, 8, 10, 12, 14 eTrR. v&+ qq-(qr an wr{ t nim o, 2, 4, 6, 8 fr qti +fl t. (,0 fr erf-d {qrq z t Wi6q1 6qffi q ?r t-€ t{qc {qr} s-6i t. *t; 1,3, 5,7,s,11, tg, tse{IR. e-&fi fEqq rt@r 4I E+-r$ ni-fi t, 3, 5,'1, 9 tt q,t$ Eldr t. g${q {@ri tPrime Numbers): ts {qr d aiq-d erqi t nqr r t gf6q1 gq* dfr d nqr eqYr ffi ffit vrSn {Iqr t ft.r*l rd, em{rq{8fl6-6flfrt. T<rfiurd: trqkffra fr t r*a qfi eiqrq {@r t: 2, t, 5,',l , lt, 13, 17, 19,23,29,31,37 , 4l, 43,47 , 53, 59, 61, 67 ,71,73,79,83' 89, 97. em{fq(@r?5,rqra: qnr p (+ { ,r$ crf-d {er t aqr r \rs dE t di'A tS tt'sr t t*' n2 >p. q-q + G risr si n aqr vs$ dfi v*+ els{Fq {qr t qFI q,-G- ts d. qR w f+i t qq tisr t m Wkqr fr.r< d qrt d erqrq q-fr ttll, 3q-qqr qqrq ffi. Bqr6rrT 4: stq qarfds ffi FrqFdfird { t *{-qt{ fr slqrq {@rS t: (il 173 (iD 341 (iii) 437 (iu) 81r ra: (D Eq q1t t t+ 1t+12 > tzl. l4 t dA qr6q {6qH- {; 2, 1, 5, 7, I I neil 13. se t t+ 173 t{i- t tsfr fi {qr t {otdql frq-m tfi d-fi eltl: lT395erqWd'urt. (,,) EcqrTi t t+'(ts)2 > 341. 19 t frA qqrq rieqrd t: 2, 3, s, 7 , tr, t3, r7 . se fr t+ 341 E{i t 1l t Tf-f,cr tq.r< d-fr t st-rr: 341 qq. orurw {wr rd t. (,,0 Eq qr{t t ts' QD2 > $7. 2r t +S errrrq +ireqr{j t: 2. 3. 5, 7, 11. 13, 17, 19. {qtd c{dffi 3 gfi Q a37 sq6q1 19 t tclrft tff t. ord:437{ourrq{qrTfit (rv) 6q qni t f*' 1zl;z > rr r. 29 t +A oqrq {eqr{ t: 2, j, s, 7, n, 13, 17, t9, zt. qm tt t am frn tu 81 1 Ed t ffi g dqr t frrrn rd Etfr srd:8llqfie[qrq{qrt. fufta*guft<r: I. 2 + frqfa trT f{qq; *i$ fl ,rg r+qr z t t+rft ilfi E}ft vqt$ {sqr Eq,r$ sifi. 0, 2, 4, 6, 8 r+$d. Tqltr{qr: (, sqircrz t frq*&fr, edm6{s6rFfir{ iffi 0t s2790 (r) qqim z * ierrqil Etfr, qdiF+ Es+r f+r{ rfm o t 64596 II. 3 + frqk ql frerr: +t$ { rr$ rtsr I t frr6 61 .r'On vqfu {qr Es * st6T $r +r : t fclrftd. E<rf,rur! (, {sr 674502 + dd il q}rr z+ t til : t $rqr fr'rfi dffi t. era, q6 iqr 3 t Iot'dcrfqrrfi Ehft. 1ii1 {'w em:o t. sidi 6r +q :z td rt Uut-oa tqll-qf, Td €tfr. sflir: ?16 tsT 3 tfotaqAwrAa+. III. 9 t frqFff qr ftqq: ot$ { rr$ {qr s i f+rft rfr E}fr qetu {sr * {s rf+T qr dq s t fqirfid. vqrf,{ur: 14 {'er eso+zr * d+lm trr zzt, S et T1-6qrfflm tfr t. qe: {rr{{sr rtryf6q194*51. (i, {*, m +r 39 t si s t lPiilo, f+rft rd Etfi. qir: T6 ri@il 764589 * i{+T etEl6q161*TfiE)'fr. rv. I t frqk m frqq: qti { Tg riqt + t fer6 611 .a}r1 Eqfu Es.S qtr€ sft{ f+r,$ et+T t qftdematfrrcad. s<rwur: (, dsr 67e5 2 t' <rT { inn qmr{ sffii * Tfr {qr r z t sil a t tqsrff tifr t. qo: 1 {rrgtqetnrrrd,t (,, dgt ss so + * r {sr 4 t, d 4 t ffl-ft Tfi €tfi. <6r{ dqr E6r{ st+1' t q-fr I t fq1r* rfi *fr. orfi: z16 Ti@[ + v. t t Errfra str ftqc: 6ti {.ri {qr e t frrr* ilfr E}fr q-qtn Fsh ffi., qa{ g+{ F{r{ d+1tT4{qr 8tfstrffdt, fnrftAfrt. qrr zrt riqr 8 t EEtfrqr fflr4a drfr t. (,, tet *4et62+SG, rcr{ dR5nr$ si+trfr{.er roztil stgtrqr frrrm rd *fi. srfi: zli! rierT s t frrq-ff i€T +fr. vt. s t f+tk qr ftqq: +t$ fl ,r{ r{qr s t fflrfi dm drft veFs Eq6r {6ri i{o o qqqr s d. E(tf,r8rt: 67985 irqr Urtr0q q s*+ s t fsi'cqr tqr< arn t. 4 q<F€ 3i6,llfu( vtr l t frr{Fft an t+qq: oti A r{ {qr r r t nrfr frrm dnl q-qfo' {+,d t sr6'*t qet qt l {q-Er'it + i}is} + tq dqt tqqt rqr'if + si+] * q}'r +.t q<t o d s{q"il I I t tesrffi d' EEr6{rT: (, d@I 1361052d: (srcIFif + iridi ql qlr) - (fqqq rPlr'ii h eidlql qlr) : (5 + I + 3)-(2+ 0 + 6 + 1) = 0' erc, fl .r{ {sr r t t Wtaq frqm Ettft. (,, {sr toso4tgsd, (qc rcTFil t *. iHqii +r t) - (fdqq Fn'ii + eidi ql.ah) : (s + 4+ 8 + t)-(s + 1 + 6 + 0) = 10,i tt frqmr€f t *fi. erc: {rr{dqr 1l ttqrrffTfrEtfi. E-t-Errnq {qr{ (Co-Primes): <} xrgd {@r{ a ilcll D (fr q6-errnq q''rertfi, qqt* ts-++t q5sq-qqq-ad-+ t dt. $t: (2, 3), (3,4), (5,e),(2r,65) eTrR. qdr ffiqf{qc, qR et{ riqr vrya dqreil- a iTer b +if i $-*+t f+sr< delr 4 F(, v6- qqrq €i, fr qe dqr aa t lfl Tf-6qr 6rm rtfr. TEr6{ur s : 6t$ {@r qFq + aqr o { t rdq, t t{crff d qrn d at rt qrEw4 t t* re {qI 24 t rfr furn Et f{tfir dfqS. 6€r: rfi, s<mqtg lod. se tt+ qe r{sr o u* u g q e-&+ t fr ,rm *fr t, w< z+ t fr.rft Td e}fr . a6 Q, 4 u* u *-er{rq {qr{ Td t. ffieqr: sq{qradH sqr6€r: le ftl s t ti c{: qrq e{rq = 38, qrqfi = 5, qFFn€: 7, ts$-(,I = 3 38=(5x7+3). qFTEqTIItEBqftqTq: (, (l - 41Et-q ft - a) t .ftaqr fqqm ct'n, z h nql cril*' fds- (,, (x'r - a") il{fi , t qq qrif *. feq @ + a) t far+fiT d{I. (iii) (xn +4*-+on +tdqccdi+fuq, 1r+altf<r*iln. iF6ffiq(d' (i) (a+D2:A+b2+zob (ii) (a-q2:A+b2-2db (ii) (a+ b)2 +(a-b)2:2(d +b\ (iv\ (a+ b)2 -(a-b1z= 4o6 (r) (a2 - b2): 1a + b) (a - b) (vi) (a+b+cf:1d+ b2 +c21+2(ab + bc + ca) : (vii) (a+ b)3 a1 + b3 +3ab(a+ b) (viii) (a-D3 = d -b3 -3ab(a-b) (rx) (a3 + b31:1a+ b)(a2 + b2 - ab) (r) (r3 - b3)=(a-b)7a2 + b2 + ab1 (ri) (a3 + b3.+ c3 - Sabc): (a + b + c) (a2 + S2 + c2 - ab- bc -ca) (xii) (a + b + c7=0 + (d + b3 + c31= 3o6". g;E aiftrdm*r(qram): (i) (l + 2+3+4*....+z)= !n@+l)- (ir) (12 + 22 + 32 + .... r n2\ = !rtrn+l\(2n+l\. dqteli c{{ffii 5 (,,,) (lr + 23 + 33 +.... * F\: In2 V*t)2 . TqrmFffi{urt{qq: (i) a(b + c)= ab + ac (ii) a(b-c)=ab-ac tfqq frfu t Wr q,,r{r ( Soqrftrd Eqr6{ur ) rqTfltr 6, Fraftlua rgrrua 6*t&q: 99 (if) 6S7t x 999 (iii) (i) 7968 x B24g x ggggg f,n: (i) 7968 99 x : 7968 x (100 - 1) 796800 : i968 x 100 _ 7968 x 1 -7968 = 796800 - ,188832. .1968 788832 (ii) 6571 x 999 = 6571 x (1000 1) : 6571 x 1000 - 657t x I 6571000 = 6571000 _ 657 t : 6564429. - 6571 6564429 (iii) 8249 x 99999 = 8249 x (100000 - l) = 8249 x 100000 8249 x l 824900000 = 824900000 - 8249 :824891751. - 8249 8248917s1 f*,lfrAG{wtat s"t1q1q61 6cfnst*,r,= [T)"-# Eqr({',T7. ErTqifqq: (, 9584 x 125 = ? (ii) 5369 x 625 = ? E€Tr (r) 9584 x 125 - 9584 x 53 l0 :9585 x t= 95 84 03 56 2 ) 23 48 89 - 9584ooo : u98ooo 80 8 90 (rD 5369 x 625 - 5369 x54 80 t ro) 4 x l_t 53 69 X 0 4 t00 = 5369 l't) 24 96 40 536egooo 32 - 16 =:r,55625 80 80 Tqr6{ur 8. rrcralfsq: (r) 578 x 63 + 578 x 37:? (ii) 694 x 489 - 694 x 389 = ? (a: f+fiqfrqqERr; (i) 578 x 63 + 578 \ 17 = 578 x (63 +37) = 578 x 100 = 57800 (ii) 694 x 489 - 694 x 389 = 694x(489_389) = 694x 100:69400 qqBEd siilrFR 6 sqr6{ure. E{Tral&q: (, 1203 x 1208 :? (A $94 x 1594: ? EfT: (i) 1208 x 1208 : (1208)2 = (1200 + 8)2 1440000 =(1200)2+82+2x1200x8 +64 + 19200 = 1440000 + 64 + 19200 145926/ - 1459264. (ii) t5g4 x l5s4 : (ts9q2= (1600- 6)2 256m36 = (1600)2 + 62 x6 - 19200 -2,1600 2540836 = 2560000 + 36 - 19200 :2540816. 3q6pr10. mI;Itfrl&(: (r) 684 x 684 - 116 x 116: ? (ri) 68 x 6E+32 x 32 + 2 x ($ x l! = ! (urt 95 x 95 + 15 x 75 -2 x 95 x 75 : ? ErI: (,) R4rrqraiqs : (68q2 -(116)2 - (684 + 116) (684 - llo (l - t2) = 1a + b) (a - b)l = (800 x 568) :454400. (,,) Rqtrrqraisfi : +2 x 68 x 32 (68)2 + (32)2 : (68 + 32\2 l(& + F + Zab): (a + b)zl : (100)2 = 10000. (iii) &qr rrqr aiqfi = (95)2 + (75)r 2 x 95 x 75 : (g5-7r2 l'.' (& +tz -2ab)=(o-b)21 : Qqz = 400. Edrf{ur 11. Eatfrlfcqt 694x 694x 694 +306x 306x 306 694 x694-694x 306+306 x 306 .c---:- (rt:_b') EA: I+[rr{[qsfi : -,qtta=694dql6=306 - 1; _ot+t,) : (a + b) : (694 + 306) : 1000. sql-6{ur 12. Efrift1&(: 547 x 547 x 547 - 231 x 237 x 237 541 x547 +547 x231+237 x237 G4T3 -Q37)3 !H. Gqrriqtaisfr = (547)2 + (5 47 x 237) + (237 )2 qeio= b=237 -C-L-, (a'+ab+b") 547irqt : (a - b) = (s47 - 237) = 310 {qtsr} qt tffi 7 Tqrtr{sr 13. f,FrihtH\: (76s+576t2 -,Q6g-, 576)2 (769x576\ Eet: fcqrrqaiqo = @#!,1atl o = 769,b = s76 4ab = =0. [... (a+ D2 _@_bf =4abl lr(I6{ur 14. (7U x S49 - x 603 x S46)*.Tur*m{gAr$atoanUtrn? f,Fl: 5+r{ ei+T 61 gupav-a -- (4 x 9 x 3 x f) = 648. .'. oilfi€ qfo= s. TErE{ur 1s. (631D7s. { rqilt eia wr EtrIIa @: q$ests' = Tzsr{55(q,5 : {(74)rrE * 721 dq+r{ eio = (l x 49){ E6r{ d6 = 9. (6317)754 : s. EI Es,r$ dT, Bi(rf,rtrr15. (357 x 6{1 ,13)mlqrf efq.Rrtqr? f,Fl: 357 = [(34)14 , 3] = (8l)la x l. 3sz 6156r{ dm = (t x 3) = 3. 6+rfi{+dqtq,=f 763=117+1tsx7t1. .'. 70r61ffi dc'=(l x7x7 x7)6rE6r{d6=3. smfrE si*, = (3 x 6 x 3) +,r Filr{ oiq, = 4. 12401*tfr*tqrt qrrrticrqFrwT6i{rVlq 13 qstt irqarFnt? s(tf,{st 17. <glrs4-r}q5€) (l24ol-13) zoFzlts (ror - r{rq6 - etFrs.f, - 76 BE: 76 478 12388 = 76 :163 456 228 3i-d: qFrff= 163. 228 X Tqrf,(ur 1 8. s000 { t *A t *A dh fr *sr * or1 6; qhrE il te t Wtncl fuIm t qri? f,€: 5000 t irl re qrq ti c{ iss-fl = r. l9lJ000 ' (263 .'. qsri qri srd snfr'E {qr = 3. 38 120 l14 60 57 3 8 q<f{B si6.IrF,rd :{qrflur 1 e. 23 04 + {ftqdc *{-m {qr t * z t t ryf rnr F*um di En: 2304 4i 21 t f{lrfi 4-ti c{ tss-d = 15. zrfzu\rce .'. 31fr8{lqr =2304+ (21- 15):2310 2t 204 189 15 sair6{uT 20. ffi {rqr E} s+z t "{r.r t+ q{ a7 p1t aat t. vfr {@r d rt t qrl t+ qr *qqaattm? (rr: *l :+z t .{r,l ti w qFIwf, = r ffiI tqE6-d : +Z rHT Ts riEIT a-q,qt{sr : 142K+4'l =(t8x l9K;+(18x2)+11 18 x (191<+ 2) + 11. erd: s{T{srifi tat qrqtiqttss-6 = tt. E;offietrfiRql slfrrqi((d)' (,) (l + 2+3 '.... t nl= ln(n+11' I (iD (12 - 22+32+.... - n2l: -n\n+l)(2n+l). (,ii) (13.'23+3l ,-.... t,r3) : !n2\ntl)2. (iv) {rlf<fi *6 a, a'r d, a + 2d, a+ 3cl, ...1 gqrl qE = a,€dol<R = d qH1 2{qq = 7.6q r. rdqs =a+(n-l)d. n tt. n qdi m t]q = + (n't)d). 1l2a III. rv<Jqrqtq - f ta+l1,q6it 3Tldq n dTqt. tvt Tuirm *fra.arri,rs -'.1 ye1r1 rl-E:4 ffd ergqrd:.. l. ndq<= afl-l Il. n rrd m qtq : * TEr6ar 2 1. 1 1 + 90 frq 7 {utilqr t fclrffi fri srd crs,d {@A ffi t ? t Em: q {qdi 14,2t,28,35, ..., 84. q6 g* {Iil<il Ad t nq+ a : 14, d = (2t - r4)= 7 aeil / = 84. qnrf{E{rq-r{. t,it, nd.tl = a+(n l)d:14+(n'!)xl=(7n+7). .. 7n+7:84= 7n=7'/ = n= ll. er-fr:t{@rEttt. {qqlc{r{ffi o EErtrur 22. r.5. q1 qS r oo f{ccry d@13fr i5r*It am qrqq. f,€I: e{fie?t{= 1 + 3 + 5 +'7 + ... + gg. T6gf qril<R *qt t ffi+ri = 1, d = (3 - t) = 2, I = gg. " cHr $d gm r< n t. ro t,=99 = a+(n l)d=99 => l+(n 7)"2:99=2n-2:98 + 2n:1O0 = z:50 n50 i* @+tl = Z " 0 + 99) - (25 100) = 2500. Sn- x rr(r6tul 2 3. t sia'r at : t tflim frt ard rrfr vrga {rqreii m +'r 6 *1frq. 5a; fr oieil +1 : t frsr* rli ar$ urga derotr ol qh t 12 .15 t l8 ..... I 99. T6 gs.qql<R ffi t fqsq a - 12, d =(15 - l2) = 3 dqr /= 99. qra Se IIdl 41 {qr : n. n-s, qi TE: 99. 12 .'. a+(n-l)d:99= 12+ (n-1)x3:99 = (n - 1) x 3 = 37 + (n - 1) :29 = n - 30. .'. 3{+e +q - 1, ,,(atl\=- 10 x(12+99) : 15 x lll = 1665. g(16{111 24. wrdr +.e 2, 4,8, 16,..., 1024 { Eia P{3+ v( t ? .4 f,€t: {6ta:2, r:1:2. cr{I gffi trdl B1 {qr : n. eq, n qi q( : 1024. .. ax lt t-fi24-+2x2n 7 - 1024+Zn:210 =n= 19. erdr gf, Td[ +1 riqi : to. ^2 wr: <1,r{ Mwc'ril{ MBfrsc- a-2. r- +=;=2, n:8. orgfrE*rr a(rn -t) 2x(28 -t) (2x2s5):510 (, 1) (2-l) uFrrTrdr I Frqfrka urn { t r+€ + *n qi tuqifiq-a ({) Eltuq: "*crc aen qrfrq cH mr er<* f*d-fl t ? 1. {qr 896743 t siE 6 + €n+q (a) 743 (b) 6743 (c) see4 (4 Ffrt+tir-d 2. rtqr 9l375tl761spfrqq-aq1 ftr (")'t (b) 7s1 (c) 7a4 (A 7o0 3. {qr 72g451ti g+Arsrr+qffi61 s6qfu6a}: (a) 0 (r) 84s00 (c) 79920 (d) F{it6t€Td a. {qtq-o (694 x 538 x 7S7 x 523) t Es'r$ eio qr t Z (a) 2 (b) 3 (,) 4 (d) s t. Ttos d g+( ni-+ wr t Z ( qsoq€o*o qfrqn, 2005 ) (r) s (b) 1 (c) e (d) 1 10 qqF{E 3is?Ifi'ld 6. (365 x 65e x domt? 77r)dyfir{ (frrlrfrcrtflrccftqfi, 2oo3 ) (a)l (b)2 @)a (d) 6 1. 0e5 - 35t) fr E6ri ei-+ ;pr t ? (a) 0 (b) 4 (c) 6 (47 8. (4137)7s4 6r fqri ifm m t Z (a) I (D) 3 (c) 7 (d) e g. (6374)t7e3 )< (625)317 x (341)4el at Wr$ ifm HI t ? (a) 0 (b) 2 (c) 3 (45 10.7589-?:3434 ( {q tosfro qftqn, zoor ) (a) 424s (r) 4ls5 (c) lt23 (d) no23 (e) E{dtqt$Ttt ll. 9548 +7314=8362+? (a) 8230 (D) 8410 (c) 8500 (d) 8600 (r) r+frtqtirfi 12. 8597 -? :7429 -4358 (a) s426 (b) 5s26 (c) 5706 (d) 5476 (") rtfrt+tird 13. 49t 109 - 62835 = 5014 + ? (a) 423250 (b) 424250 (c) 423260 (O 424260 (r) F{qts}$rfi 14. 11992 - 7823 - 456 =''! (a\ 37at (b) 3713 (c) 3813 (A 3823 (r) rqdtol$q-fr 15. 3251 + 5E7+ 369-? = 3007 ({aQo*o ct{r, 2oo7 ) (a) 1250 (r) 1300 (c) 1375 (d) t2oo (r) r+{t+t$rfr 16. (?) - 19657 - T99a = 9999 (a) 636s0 (b) 53760 (c) 59640 (d) 61s60 (e) {{{tstiTfi r7. (?) + 3699 + 1985 - 2047 = 311ll (a) 34748 (b) 27474 (c) 30154 (d) 27s74 (e) flqtqtiTfr r8. (4300731) - (?) = 25356ts (a) 1865113 (b) 1775123 (c) l76sll3 (A n6st23 (r) E+dtot$rfr 19. -84 x29+365='l ({q'fr"efro qft$, 2J07 ) (a) 2416 (b) 2801 (c) - 2801 (A -2071 (e) rtdtct{d 20. (800 + 64) x (1296 - 36) = ? (a) 420 (b) 460 (c) 500 (d) s4o Ytqtqtirfr (e) 21.4500x?=3375 *6 *o*o vftqt, zooz ) 1 231 3 -.- - (")s (b)i @i @; (,) rtfriqtirfi 22. (35421 +7164+41720)-(317 x 89)=? ( tq'frosfro ctqr, 2007 ) (a) 28213 (r) 84307 (c) s0694 (O s4oe6 (e) r+dtct$rfr B- s1*tL-sl 417 15 =r (tq'froerlo qfrqn, zoo0 ) 'n9 817 (o) 7 ton (6) 9lo2o (") 9rolo 719 @ lffi 817 (e) Erqt+$Tfi 24. (1000)e + lO24 ='l (tmftosfro qftqn, 2006 ) (a) 100000 (D) 1000 (c) l0 (d) 100 (e) E{dt+$Tfi dgteTc{{BqrE 11 25.8988:8+4:? ( {a Qo*o qfrq11, 26n7 ; (a) 4491 (b) %1.75 (c\ D47 (d) 2wws (e) E{qtdHTfr 26. 666+6=3:? ({qfro*oqfrm, zooo) (a) 37 (b) 333 (c) 111 (d) 84 (r) Wdt*t$'rd 21. l40o xx= 1050 ( *m tosil" qfrqr, 2006 ) ..1 (b)i3 ., @)i (")s3 @i (r) r+{tqtirtt 28.35+15x1.5=? ( *oqlo*o rtfts[t, 2006 ) (a) 7s (b) s.25 (c) s7.5 (d) 5l.s (r) edtct{rrt 29. 1+33+333+3.33=? ( ttq'*"*o cfrm, 2oof ) (a) 362.3 (b) 372.3J (c) 702.33 (d) 702 C) fl{t6t$Tfr 30. (12)3 x 6a+432=? (&otoefro qftqr, zooz ) (a) 5184 (r) 5060 (c) slas (A s084 (") E{frt+$r-fi 31. 3897 x999=? (a) 3883203 (D) 3893103 (c) 3$9a03 (O 37e1203 (r) rtdtdtrfr 12.72519x9999=? (a) 725117481 (b) 674217481 (c) 685126481 (d) 6e62r7481 (r) r+frQqt$rd 33. 2056 x987 =? (a) 1936372 (b) 202e272 (c) 1896172 (d) te23472 (r) F{St+$Tfr 34. 1397 x 1397 =? (a) 1951609 (b) 2031719 (c) 1981709 (A 83626te (r) r+{tdr{rfr 35. 1904 x 1904=? (a) 3654316 (b) 3625216 (c) 3632646 (A 3623436 (e) rcdtdt$rd 36. l07xl07+93 x93=? (a) 19s78 (D) 19418 (c) 20098 (O 2te0s (r) Erdt+tird 37. 8796 x 223 + 8796 x 77 = ? (a) 2638800 (b) 2736900 (c) 2658560 (d) 2?16740 (e) Ftdtoti=rrt 38. 287 x 287 + 269 x 269 -2 x 287 x 269 ='t (a) 514 (b) 446 (c) 35a (O 324 (e) F{dtet$rfr 39. {(476 + 424)2 - 4 x 476 x 424} ='l (a) 2906 (r) 3116 (c) 2704 (o 2e04 (r) s{ilt+$Tfr ,l0. 106 x 106-94 \94--? (Hqfr{fr,2006) (a) 2400 (r) 2000 (c) 1904 (d) 1eo6 (r) rt{t+t{rfr (756+287)2 +(756-28T2 :? 41. (756x756+287 x287) (a) | (b) 2 (c) a69 (d) tc/,3 (r) F{fit+iiqfr (379+265)2 -(37s-2612 =? 42, (379x265) (a) 2 (r) 114 (c) 644 (d) 4 (e) r+dtqtiq-fr 43. qR (6q2' e6)2 = 26 x .rfr, fr .r = I (a) 70 (D) 120 (c) 180 (A no (e) Erfr**T$:rfr 12 qqf{E oifirrFK 957 x957 x957 +143 x l43x 143 44 ' 957x957 -957x143+143x143 =,| (a) 1000 (r) 814 (c) 1lm (4 q.{qtfiTrl 7 34 x734 x7 34 -1 27 xl27 xl2'7 45 ' 734x734+714x12'l +127x127 60'7 (a) 607 (b) 861 (") (4 E{dtqtir-fr s6l 649x649+ 35lx35l -649x351 :,1 46. 649 x 649 x 649 + 35 I x 35 I x 35 I ll (D) 149 (4 E{frt+tiTfr (a) (c) zx looo 500 47. sqcerrnq{qldq-frt? (a) 0 (b) 1 (c) 2 (43 4s. verrT dir errnq {qrefr m Ar ffd-{l t ? (a) ll (b) 18 (c) 26 (A 28 4e. sot+a e{!]rqrffiffit? (a) 16 (D) ls (c) 14 (d) 18 56. fsfulqa d t s+r-fr {iq erurq {ren t ? (a) 33 (b) 81 (c) e3 (A e7 51. fiqfufu6 d t +{-$ {qr olr{rq {EqI r-d t ? (a) 3l 6r (b) (c) 7t (d) 9t sz. Fmfufiat d t *r-S {gt srqrq t ? (a) lle (b) 187 (c) 247 (A ssr (e) fl{tut€Td sr. Fmtufisf, fr t qqrq {qr frt-rfr t ? (a) 16l (b) 221 (c) 373 (d) 437 (r) edt*t€rfr s4. fir eisii 61F{i EtA efil{rq {gt qtr-S t ? 103(a) (b) to7 (c) 10e (4 E{q-t6tiTd ss. qR a nqr a t frqq qcfl{ df, il f{q t t dr{-d {sr w qq-{qr &fr ? (a) a+b (b) a+b+l (c) ab (d) ab+z so. fieFofun d U 46-.qi drcar fs'S vr5-d dql el sri o6 fr s*fr ? (a) 10916 (b) 7s62s (c) 28s61 (d) 143642 s7. fTqFdfu( d t dh-{t {'E{t ffiS vrf-d {ql6r sli 6 6l s+-ff ? (a) 8t225 (b) 32761 (c) 42437 (d) 20164 5s. {sr s I 7 * 324 {,{-ffi 3 t fqqffi A fr $ +qrq dt t eta et+' ffi d'r ? fi * q{ (o) o (6) 1 (c) (d) +ti Tfr2 fli't 59. qR {gr 481 6z3Wt-rqr t felrft fr, fr fi r+n w dt t BteI eim m n ? * q * t (") 2 (b) s (c) 6 (d) 7 r0. qRdqr 9721s* 6$ilqr ll ifrtrftA fr *$rqrcREirttfraoi,mer6}n? (a) 3 (b) 2 I (c) (d) s 61. tr {gt 9187 6 * fqrrft d, fr 2t+dct s t * } qs q1 fr4 t etel gt'fiqr 6}'n ? (a) I (b) 2 (c) 3 (A 4 (e) {+C*qliTd t 62. firafrtuq d t frt{-d {wr 45 Wt-rql frrrffi drfr ? (a) l8ls60 (b) 33ll4s (c) 202860 (A 2$3sso (r) Eriit4t{Td r{qEfr qr {Eqrq 13 0r. i+qiafun d tdr-fr {sr ee t gf6a 616 601, 3s72404 (b) 13s792 (c) 913464 (O tt434s (a) (,) Eriit6t{Tfr 64. qR {qI 42573 * Totrqt zz t ferft d, d * qt qrrr rn Rr drn ? (a) 4 (6) 5 (c) 6 (d) 7 (n) 8 6s. 4456 d dA t dE qr {sr dq qri ffi +,rs-d 6 t {da-qr frr< d I (a)4 (b)3 (c)z (A| (r) rci-t+t{rfr 66. e21't d sfiq-dq ftt{-d i 88 t Eiilcr frrrfi E} {er t ? (a) 91s2 (b) 9240 (c) 9064 (d) st}4 (e) r-+H*+tirfr 67. 6as5 fr ffiqdq +{-S {qI t d 75 t Wtn-qr frrr d I (a) 847s (b) 8s00 (c) 8ss0 (A sszs (e) c-{St+t$TS 68. fr of+1 fri ES t ES dqr +r-m t d sr t fofdqr fqrff d u (a) 99918 (b) 99921 (c) ee981 (A ee97l (,) rqdtsliTfr 69. e: deif +1{6d-At*E{qr6tr-dtfr lll t{oin-qrfqrnE}r (a) l1llll (6) ll00l1 (c) 100011 (d) ll0101 C) E{itqt$Td 70. 5 oidf 61 T6 +A t Bla {qT q,t{-fi t d ar t Xof6qr 6clffi d ? (a) 10041 (D) 10004 (c) 1004s (d) too2s (r) {+frt+t$rfr 71. 4 oi6l 61 T6 € t ES {wr +{-d t n 88 t Wia-qr frwm d r (a) 9944 (b) 9768 (c) 9988 (4 8888 72. I 056 d 6-q t q'q eqr frB fs frqqe 23 t Wi-irqr frrr* d Z (a) 2 (D) 3 (c) l8 (A 2t (r) E+it+tirfr 73. 13601 d t qq t q'q qr qer{ i+ tq dqr 87 t t i-rqr iqrrffi d 7 (a) 23 (b) 2e (c) 31 (A 37 (e) 49 74. r{rq + qs' Erc { sTMfi, errFher 6.r I 0 Xil der tss-d s.[ 5 u1r t. qR tqq-d +o d, fr qrq t+a-+ tz <qrqrq*qrqfrqn,2oo7) (a) 4236 (b) 4306 (c) 4336 (q s336 (r) F{iitEir$Td 7s. ffi {qr sl og t qrq ti ct qFrFd 269 deil tcs-d {q vrq +dr t. sq {qr d 67 t qH ti cr tss-f, ? flr Etr[ ( qqoq€ofro qfrqn, 200s ) (")0 (b)r (c)2 (A3 76. i+,fr {qr 61 357 t ti c{ 39 tq e-qi t. ES {@r 4i rz t ti cr tss-d Eqr dqr qFr qrq z (a) 0 (b) 3 (') s (d) tt ( \Foq€olfro qfrqTr, 2oo5 ) 77. s+. \iqr 6l s t qpr ti q{ 3 ts {qfr t. Es {qr + Ert 4i s t qrq ti qr r}qqa Hr drn ? (a) 0 (b) | (c) 2 (d) 4 (geoqe"*oqftqTr,2oo5 ) 78. g+ {q +1 so t qH ti cr r qq {qi B. gs r{qr +1 s t qn ti cr tqs-d Hr dfi ? (a) 4 (r) 5 (") 6 (d) 7 ( gogeofr" qftqn, 2gg7 ; zs. <] rt@Bif fl siir{ I 365 t. eS {iqr d da t qm tt c{ qms-d o ner t$F-d 1 5 vrq drdr t. ot4 {qr er t ? <+qT +cT ftrrc qfrqn, 20q3 ) (a) 24o (b) 270 (c) 2e5 (d) 360 80. qFr t efi d tqsi rlqq-d o t, Cs 6H qfi i qrw+ +1 2l + raTn c{ Zf-crr 12 A fflsr ffqr r{ECif, 35 96 fqq1. sfr qFrq-d Hr t ? (qtoqg"fro qfrqn, 2003 ) (a) 0 (b) t2 (c) 13 (A 20 14 qqf{E si+.rrFm 81. A {qrcil 6r u}rr r z aur y;aq6 35 t. Ea dqrql h Eadf ot ftmo fll E}Il ? t2 35 7 ("):s (r) (d) (D) 35 T n (q{oqso*otrT,2007 ) 1', 82. 52{1 € r*a:nqqtZ 0,994 ; (a) 27 (D) 33 (c) 3e (A 66 <el efrt*€rd u. qRffi dqr t ooxa I,nq 5 loa, d qt {qrt: (a) 80 (r) 100 (c\ 7s (o e0 ge. mqrrtrfiproperftactionFrinqlsq+qJ#col et<R fi t. *n=*,t, 4 5 b\= ') 3 (b) 3 lo G)l @i ( gtogsofro qftq6, 2g06; 8s. {qKff 1,3,s,7, , 2s +1IW 6ti vt sIR Xq{sE + qrfi ott er< t Wii 61{et ffi tt'fr z (lalqftqn,2006) (a) o (6) I (c) 2 (d) 3 m. ffi {qr 7 t Xun 5qi HE q} q{ gulrsa }' s$ nia r t. t5S n-+i otE {ut wt t ? (a) 47619 (b) 47719 (c) 4861e (d) 4'1649 lgeoqeofroutqn, m06 ) 37. 1igapif227ZaqSZS61qsfl-{oidld{611,lrtqrqttqtq<rqtl'fqqdcrqE}tt.N+ifqii mqlqf+-irtrt? (geogeofrofrI,2w7) (a) 10 (r) 1l (c) t2 (d) t3 ss. { rqFIf, qq$ftst * eril qr er<n Frqfufut d t f*.q riqt t {.t-dql fr.rff d'II ? (a) 3 (b) 4 (c) 6 (d) 7 (qco*oqotrr, 2003 ) 89. t *qrrra fqqq-Wfsii * qril 6t qm fiqtoEa d t fus {qr t Tt-ilql frtrft drn ? (") 1 (b) 6 (c\ 7 (d) 8 ((tro*oqovftry, 2963; qo. qf< r {+ vrga {wr El, fr (6n2 + 6,4) f{qfrk( d t ffi {Elf,ql fq'rffi tT r ? (a) *46168 (D) 6wl12+if t (c) *'q612Q (4 t-*a tst (grofroqoqftqn,2005 1 91. fi6frfu6 d t at{-d {@I, 1461 + 462 + 463 a 4o+; aJ gl6q1 tqsrffi 6irfr ? (") 3 (r) 10 (c) ll (d) t3 cz. FrE{tdfud d t +ti-d {'qI, 132s + 326 a 3zz',u 3zt1 fr $6+1 616 atfr ? (a) 1l (D) 16 (c) 2s (d) 30 ( gqoqqofro qftq11, 2go4; 93. 17200 fr1 rS t fs$rffi 6{t cr *ss-€ f,r drn ? ( (qoqqofro q+qn, 2006 ) (a) t7 (D) 16 (c) I (A 2 94. ({ - d),(.r - a) t rytrut frtr* ilfi dIrTI, ii-df*- (a) n*{rftur7ar{urd (6)nqt$rfrwrrSaderd (c) z+t$ rftftqqsrfd{slt} (4 nst{fccc{'qrd {qtsi c{ tffi 15 95. (49r 5 - I) fTq tt G6sS tf-*qr ferrfi E}rr z (a) 8 (b\ 14 (c) 50 (d) st 96. 6767 + 67) 61 oa t qrq tt c{ tqs-d ilr E}n ? (a) 1 (b) 63 (c) 6 (d) 67 97. zq+-qqrTlt+tffi +t erTrrt+cr 3 tse-stt. zn +]4t qmtic{tcsRHrfrrn? (")3 (b)2 (c)t (Oo ce. fflr rrqr t ts (232 + r) q+ { rr{ f{*q {qr t Tiilqr fq,rft E}fr t. ffitun d t dn-s {qt{s {qr t frrrff d,fr? (\cowo*o cfrqTr, Z00Z ) (a) (2r6+t1 (r) (2'6-t) (c) 7x233 (O es6+D g. @743 + $4\ aqr (4742 1 43nz; 6 ssstre Uqrcrs firqtefua C t +t_er drn ? @)@7-a! (b) (47+43) (c) (47a3+43c2) @) F{tt*t$Td 100. A Ra rrt Trrf# a rer 6 * {rrd q6i 6>o t, t {qfo, q irerr r g{r FFR e-*lq fi tfi: a:6q+aq€Y0<r<b (a) (b) b=aq+r,qEt0<.<, (c) D=rq+a,v6Yo<r<b (4 E{4tfrtiT6t r r. gq' sr* i 98 7 6l Fdrfr {qr t gqr q,-G cr Zfr lf,ul qr. Vsi st+ s h o XoHq-f, 99 yltd f6q1 d 5 5 g1 if* lre-ctnqrts st*'sdt. sfisrrt: (a) 553681 (D) 5s5181 (c) 55s681 (d) ss6s81 r02. Ffis {'sr o1 : t qH ?i cr l ts {qi t $s {gt d l 7 t snq t+ Tr 9 ts {qt t. T6 {sI r 1 flrt? (a) 339 (b) 349 (c) 369 1a; uim.B err<f< ror. g+ dq +1rs'qFrd 4 ircrT s t ti s'qvt: r flr 4 r}s qqil t. qs {qr +l xqrrn s aqr + rnq q{ t qH ti q{ +q.Fd ficfl: flr dt ? ( \Foqeo*o qfrq6, 2ng3 ; (a) r,2 (b) 2,3 (c) 3,2 (O 4,r rol. qo {q ifi'rrtir 4, 5 ilt 6 t ti fiqfl: 2, 3, 4 ts qqil t. T6 {qr t: q1 rnq rR (a) 214 (b) 476 (c) 9s4 (4 l90s 10s. tdfr dqr +l s t ,n'r ti * feq qr r€rfr i qrq qiri +1 {flerw ft fu qr y*rr aqr. ssi s ss s e +gumqd 5,9, 13trqrrnfrrrmf+'qrffirfiq{r, ltqqer+, g, 12ytqH. qRwsqdqr +1 sas t qFr irkil, A fuq.d f{-il{ dar ? @) 2a (D A4 (c') 2e2 (O sB4 165. f1ffifuq {@oif d t f$Tfi {safi 132 fr $6q1 frrrm dFfr ? 264, 396, 462, 7.92, 968,2178,5184, 6336 ( d@t+ilte qfrEr, zooz ) @)a (r)5 (c)6 (O7 r07. +{ oifrI d ffi {qrd o t qoi-rqr fqqffi tfr 6, (a) 14e (r) 150 (c) lsl (A rc6 108. rerr 45 cr$-d rtqd or ftr f+-a* t-? (a) l03s (6) 1280 (c) 2o?o (d) 2t4o 109. l t 3r + +s sfr qrfr sq{qpt +r +'r ffif,{r t ? (a) 16 (D) 128 (c) 240 (O slz 110. (51 + 52+ 53 + ... + 100): ? (a) 2s2s (b) 2975 (c) 3225 (A 377s 16 qqF{B 3i6Trfrrc r11. *ofr ( 1). [, n) ( 2 *(, t I n + Er llqtfnq-qlq fufilt ? (a) I n (b) I -( n@) f,n@-t) (4 E{f t6}iTfr , 2' t trz. z: t oo <-+ qi o t ltro frrr< eli ard vrpn {wr+ t? ffi (a) 8 (D) 11 (c) 13 (d) 12 (e) ls 113. too a-o +1 vq qq rr5< {ur:rif *.r ft t+-fl t ? (a) 2ss0 (b) 2s1o (c) 2s80 (4 2480 (e) fiit*t$Ttt 114. A iridi +1 s t frrrm di srd s"fr vrf-d {@ret m t{ ts-fir t ? (a) 1035 (b) t24s (c) t23o (4 94s 1,1 sttt+t{rd 115. 6 + 72 + t8 + 24 +ro + ... * GnaiTs] mtq tgoot ? (a) t6 (b) 24 (c) 20 (d) 18 (e) 22 116. *d l, o, 12,24,48,..., 384 Effi Tqt a1 {€qr ffi ii t ? (a) 7 (b) e (") 8 (d) 10 (e) 11 111, 3 +32 + 33 + ... + 39 = ? (a) 9840 (D) 19680 (c) 29523 14; sr-t+t$rd 118. 112 + 22 + 32 + 42+ ... + 10) = 2 (a) 330 (b) 34s (c) 365 (d) 38s 119. 122+42+62+...+20\='l (a) 770 (b) 115j (c) ls40 (d) 385 x 385 120. 6P + 122 + 132 ... + 2or =') + (a) 385 (b) 2485 (c) 2870 (d) 32ss Fr{qItIT 1.(c) 7 @ 3. (c) 4. (") 5. (b) 6. (c) (b) L @e. (r) 10. (b) 11. (c) 12. (b) 13. (c) 14. (b) 15. (a rc. (") 17. (b) 18. (c) 19. @) 20. (e) 21. (b) .,, (e) 23. (d) 24. (r) 25. (d) 26. (a) (r) 28. (c) 29. (6) 30. (:e) 31. (b) 32. (a) 33. (b) 34. (a) 35. (b) 36. (c) 37. (a) 38. (a 3e. (.) 40. (") 41. (b) 42. (d) 43. @ 44. (c) 45. (a) 46. (D) 47, (c) 48. (o 4e. (6) 50. @ sr.(d) 52. (e) 53. (c) s4. @ 55. (a) s6. (d) 57. (c) 58. (c) se. (d) 60. (") 61. (c) 62. (") 63; (d) 64. (c) 65. (c) 66. (b) 67. (a) 68. (a) 6e. (c) 70. (b) 71. (a) 72. (") 73. (b) 74. (d) 75. (b) 76. (.) 77. (4 78. (b) 7e. (b) 80. (d) 81. (a) 82. (") 83. (b) 84. (c) 85. (a) 86. (a) 87. (d) 88. (b) 8e. (d) 90. (b) e1. (b) 92. (d) 93. (c) e4. (a) 95. (a) 96. (c) 97. (b) 98. (il ee. (D) 100. (a) 0r. (c) t02. (6) 103. (b) 104. (") 105. (a to6. (") to7. (b) 108. (a\ 109. (c) 110. @) 111. (r) rtz. (c) 113. (a) 114. ( d rls. (b) 116. (c) tt7. (c) 118. (d) tle. (c) 120. (b) H.rlvw) *. ea r. e{fie or<t = (6000 - 6) = 5994. ?. g437s1g 7 q;1rqrfrq qH = 7oo. r. oilfre sr<R: (8oooo- 8o):i992u l. f<t rd XoTis-d t {+ri 3is = (4 x 8 x 7 * 31 i 5+( ei+ : z {qBii {ffii cr 17 5. Ttos { f+r{ 3i6' : le\26, 7l qr f+r$ ei+. vrg 17+;ze or {+ri 3to = r. slo. 7ro5 { r+r$ =O x 7):7. "tm 6. si6 = I :+ (3a)I6 or f-ori t'+ = r. 34 +,t E-+'d .. 365 ET E$ri ili6 = [(34)16 * 31 6r g+.( ,{+ = (r x 3) = 3. 6sr 61 ffi 3i6 = 6. 74 ol {frr$ eiq. = t + ?ayt * f+rg ;f+. = r. 7rt 61 5+,r$ eis = 117a1u, 731 6r g+( .i.-o : (r x 3) = 3. .'. srfr€ d'-o = (: x 6 x 3) 6r {+'rg i}ifi = 4. 7. les qt Efir$ oi+. = K7\23 ,. z3l q.t E+.r$ eiq. = (r * :) = r. ,se 61 ffi ef6 = 113r1t+ * 321 o.r E+rg oi6. = (l , 9) = 9. . . ges - 3sty 61 Strrf 3i+. = ( 13 - g) = 4. 8. (4l3T754 s.r EsT$ ilis = [{(4137)4}1s8 x @137)2ls.r f+rg irim = (l x 9) = 9. 9. (637qt7et +'t f+ri etfr = (4)r7e3 sr Fsd sifi : [(42)8e6 * +] 6,r E+r{ ei6- : (o x a; 61 96( .rio : c (6zsft't * 5+'d fs : (s)3rz qT F6ri st6 = 5. (3+11+et o, E-frli 3i6 = (t)4e1 $T g+ri ifq; : r. si$€ sis. = (4 x 5 x t) E.r {mr$ si6. = 0. 7589 10. q[{t 7589 - "r: 3434. iI,;{, x = (7589 _ 3434) = 4155 - 3434 4155 ll. Cl-fl 9548 + 7314:8362 + x. 9548 + 73t4 .. x= 8500. 16862 - 8362 8500 12. rIFII = 7429 - 4358 7429 8597 -x + 8597 -x = 3071 .+ x = 8597 _3071 - 4358 =+ x -- 5526. 8597 30'11 -3071 491109 5526 13. 5014 + x= 428274 + x.= 42827 4 - 5014 - 62835 428274 - 4232.60. - 5014 423260 l4 11992 15. 3251 4207 -x=3007 4207 - 7E23 + 587 x: 4207 - 3007 3007 4169 + 369 : t200. 1200 - 456 4207 371 3 18 q<f{€ 3i6fir( 16. x- 19657 -33994=9999 9999 + x:9999 + 19657 + 33994 + 19657 :63650. + 33994 53650 3699 31111 17. x + 3699 + - 2047 = 311l I 1985 + 1985 + 204',1 x+ 5684 =3tt1l + 2047 = 5684 33158 x = 33158 -5684:27474 = - 5684 27474 18. 4300731 -x:2535618 4300731 + r= 4300731- 2535618 - 2535618 + .x = 1765 I 13. 17651l3 19. 84 x 29 + 365 = -84x(30-1)+365 -2520 = - 2520 + 84 + 365 + 449 = -2520+449=-2071 -2071 .-tB 30e5e"x_-___- l+96+0$* 2O. | #4+t _ +6+ - =450. 331+ 22+l J - 2t 4500 x .r =3375 =+ ,= 45ee.** =; 'l', 35423 317 x 89 = lll x (100 - 11) 31700 + 7164 = 31700 - 3487 - 3487 + 41720 = 28213 78213 84307 - 28211 56094 2r f<qrrrqraiqo = s * 1 *, - ; -(r- +) 765 + 1,20 121 = (9+7-9)+ 4 t7 15 885 -68 765+120-68 817 817 ro20 lo20' 24. f(qr rrqr ajqfi : (lfl:;e + 1924 = 1921 ' 1g2a:1nQ1 -2\ = 103 = 1000 aiqfi =8988"8*1= I 1 I 2247 25. f6ql{ql = 280.875 l1 26. Rcr rrql aiq6 = 666 r 7x 1 = 37 1050 3 27,. 1400xx=1050=r= l4O0 - 4. 45 (70+45) ll5 2s. Rqrrqlds+ =35+15, ]=,, 2 22 32 +Z-xl2xl2Y6x+x6 2s. 33 333 30. -- 4+;- =864 3.33 372.31 r{qt$qr {ffi 19 31. 3897 x 999 = 3g!l x (1000 _ l) 3897000 = 3897 x 1000 _ 3897 x I -3897 = (3897000 _ 3E97) : 3893103 3893103 32, 7251q x 9999 = 72519 x (10000_ l) 725190000 : 72s19O000 _ 72519 - 72519 = 725t t748t. 725lt74El 33. 2056 x 987 = 2056 x (1000- 13) 2056000 2056 x 1000-2056 x 13 -26728 20 5 6000 - 267 28 = 2O2927 2. 2029272 34. 1397 x 1397 = (13e7)2=(1400-3F 1960009 (1400)2 +32 -2 x 1400 x 3 8400 - 1960000+9-E400 195 t 609 1951609. 35. 1904 x 1904= (1904)2: (1900 + 4)2 = (t9OO)2+42+2x t9}0x4 3610016 = 3610000 + 16 + 15200 + 15200 = 36t0016+ L5200=3625216. i625216 36. 107 107 + 93 x 93 = (107)2 + (93P x : (100 + 7f + Qoo _7)2 = 2><l(too)2+721 l':(a+bf+@-b)2=2(A+b2\l = ! x (10000 +49)=2 x I0(X9 = 20098. 37. 8796 x 223 + 8796 x 77 = 8796 x (223 +77) | .' i " b + s x c = a x (.b + c)l = 8796 x 300 = 2638800. 3s. fflr ?rqr aiq6 = o] a 6z - yo6 : (a - bF : p87 _ 269F = (l 8f = 324. 39. fflr rrqr Eiqif = (a + b)2 - 4ab : (a - b)2 = (476 - 42q2 = Gl12 = 2794. 40. Eqr rrqr ai{fi = (tO6)2 _ (s4\z = (106 + 94) (106 _ 94): (200 x t2) = 2400. \a+b\1+(.a--b\2 {1. f<qrrqlai,rr - ta- +b-) =!(.ul' (a. +b.) =r. lz. f<qrrrqrajq+ = 9l!t:9:b)' =4ob =o 43. (64 + 36) (64 - xl = zo,!zo,= roo ile=,='*ii" =,*. -. e-- . (ai +b31 44. IerTqraNi?F = 143 A_;;6,vEia=e57iIzII6= = (a+ b): (957 + 143) = 1100. . a5. fql qa ajq+ = .';o--.br).r-. = (a - bl = (734 - tzit = 607. (a. + ab+ bz) .- c--- 1o2 +b2-ab) I I I {o- i=Ei :iEi EEiEi = --------=-------- (a'+b') k+bl (649+351) 1000 ' 47. yW qqrqdE{r z t. 4t. offie+r =(2 + 3 + 5 +7 + ll)= 28. 49. s0tEtasrqrqrire{ra$; 2,3,s,7,It,13,t7,ts,23,2s,3t,37,41,43,47.{{+1 {@r Is t 20 qqf{E sio'rtFn so. qe t to qz q+. qqr-q {isr t. st. qe t f+ 91 qr Iwrcro.s z t. era' gt 1m errnw {wr tfr t. 52. l 19 ET TUFrcIo-g z t, t tz er Yr+rqo-g I t t, 247 6I $r{su-s 13 t, 551 6r UUr{G!-g 19 t. .'. { ri ri@'Bii q t eti gfr ri@r 31q5q afr } $. J4v <21. zr tdEerqrqrirc{rit 2,3,s,7, t1, 13, 17, 19. erd: { s} qq urnw rieret t qnr qlh tdi. 'ri {qI t6l 16r Isrq-€!-s z t, zzt fl I"rtqo-e t: t. q A ffi t rri 373 Ec{ {.r$ dq,qi Wta-qr tdqffi rd dil. qd: 373 F srqrq TiEIIT t. sl. fir eie}qflsctEtA€qr 100t, d z tryir+rfarr+datt. .. 100q.E e+{rq{@r{frt. Jrot . rr 32II 1s1 srs{rq{iEald 2,3,s,'7, rr tffitfrtrmrfrt}m. ord: l0 I (:F erqrq rirfi t. ss. <] fsqq vq-d {qrefr oT tq q+ qc-d@T t .' . €'q{iqr t. (a + al q.6, s6. ffi rfirrfa{wrfr.e,i+rr+ri rddsom. et+ z s7. ffi rft yrta {qr } s,t m q+ri sts 7 rd it F+-il. 58. qr;IT * *- +trR qr , d. a-q, 5+l+7 *x+3* 2+4:(22+.r), Tri-irqr: t frrmd'n. .. x: L, 59. qHT * * ern qr , d. n-q, 4+8 + I +x+6 + 7 +3=(2g +x1, ltt-+ s t frtr€dTr. 60. qFII * fip16 q1 1fr. A-O, (6+5+z+9)-(x+ I +7)= 14-x, T]tcar tt t frll-m dtlr' ,., x= 3' 6r. s-qrq s-{+ nrd 6{il t f{, 632 T0tdqr a t frq-fi d-dr t. slf,: 31Se qrl = 3. 62. {rr{{qrsitttyd-+qrr+rieiqoelqqr5t.srd:flitTAfirirqrstWfrqrftq*a}'ilt' 202860t etdqtq: rs, d stfrrrfi6tdrt. .'. 202860 Tri-irqr +s t fs*rfi EIfi t. or. qe t t+ l 14345 Toi-ir{n 9 dql 11 +fr t fs'r-qa 6tfr t. ekT: z16 t Wtdqrfsqffi dfi. {i@T qs ii 64. 72 = 9 '. 8, TrE orqrsq t q54*}'p16q1 ,1{. { T{ tqT dl s t fsrrff di A'ftq ri@I 73r ftl s t fs'{ffi Ehl EGs. 3rfl: r = 6. 3trr, (4+ Z+ 5+7 + 3 + 6)= 27,d tWt-fiIfrqm 9 dfit. . . 425736 {oia-qr zz t fq,rm e}fi t. gftI: x = 6. {ffi dqtsil cr 21 os. qH ti q{' 6Tus6(742 c) ,< 24 er$erireqr =15-4)=2. t6 t2 66. qHtic{: 4 ss) ezrz I rol srifre {qt = sztl + (88 - 65) 88 = 9217 + 23 = 9240 417 352 65 oz. rilrr ti Yr zsfs+ss (r r 75 98 75 qrfre {qr : (848s - lo) :8475 235 225 l0 os. s qsif 61{.6tTS{qr =ssses. srf lrll { rosa 9l ssssq EJ t st qFr ti c{ tqsq = sr. 899 . otfre {er = (99999 - 8l) = e9918 8l? E09 728 81 rr rfrooootil coo rq. o ei+l +1 d6t *A fiqt = looooo. 999 rooooo +1 r t I t rnq ti c( +ss€ = too. 100 t@I = 100000 orgEe + (l I I - 100) = 10001I zo. s ei+}d dA t +A {'qt = toooo. arfioooo I za: loooorhJ ar t qrrtic{*ssa =:2. 82 180 srrfrE {rqt = loooo + (41 - 37) = looo4. t64 160 sefree{ r rr 123 8E 37 119 zr. + q+t^ +1 q€ t s-d {qr = sssg. 88 999e ihi ss t qFr ti c{ tcse = ss. 319 264 e+fre {wr = Osss - 5s) = 99,14. 55 72. z:Iroso l ls 73. az)r:oor ( rse 92 87 136 490 ll5 435 2l 551 522 29 wfre{urr =e3-zt)=z Tcrt qti qrd r{qt = zs 22 E<f{u sifi.rrfim 74. qFII qFIIEET =p. nd, $lsftt'= l0p. s{rqn =r}c*-d x 5 + r}FEfl = Y = Y =, ' 2P= 4$;' P=23' .. " qFFRO:23, r{rdfi = (10 x 23)=230, I}CSfl =(2 x23\=46. qrq = (r{T*6 x rrFFF-ct) + iqs-€ =(230 x l!) + 46 = 5290 + 46 = 5336. 7s. d@r=68x269+0=68x2d9. etfTtm:z\zll qfr€tqsd = l. 269 84 68 489 - 2ln 46s 1614 202 18292 20t 76. qril clFFEf, = k I rq {@II = 357k+39 = (17 xZlk)+(17 xZ)+5 = ll x ()lk+ 2) + 5. erfre tqs-e = s. zz. qm {cqr x 6} s t rnq ?i q< TIFFFGI = r IFII r}rF'el = 3. il6l,x=5t+3. .'. * -- Gk+12 = QsP + 3ok+g)=5(sP+6&+ 1)+4' srd: I t[J s t rnr ti q{ ttsse = +. 7g. qra {6qr, qi so t qn ti c{ TIFFFEI = effiI *q$?I : 29. .. x= 56k+29 = (8 i 7t) + (8 x 3) + 5 = 8 x (7k+ 3) + 5 eril: EH ri@ll +1 s t qFr ?i q{ tcs-d = s. 79. cl1r EIA {qr = r oqr q€il riqr = (r + 1365). .'. r+ 1365=6r+15=5x= 1350+x=270. era: stariqt = zzo. 80. {@I =(tzx35)=420. sd qrtFq = 420 + zl: zo. St. qHrt{EqrtJ atIr{I D t. ?8, a+ b- l2i.q,t ab=35. a+b 12 I112 " ab 35 b a 35' 1] s2. srfreq6 = ( 3/\- lrr* 4/ \. nr^?l = g6 - 3s\ = 27. 83. qHI IiEqT =r.(E xtt ooz"+r J =:o = ,, #,1 = 36 +.x = ("',. ?) = 100 qtfie{cn = 1oo. 34. fl6 =r.6q, q14 lgl-x2g __-x=-:+ x2Ox2O + 20 - 2oP : gx ) 20* + 9x - 20 = 0 + 2o* + 25x - 16x - 2o = 0 + 5.r(4.r+ 5) - 4(4r+ 5) = 0 = (4r+5) (5x-4) = o * *= J. {vt$vt{ffi 2s 5 OIiI: 3P[q ltff = 4 . 35. qq f, fu 9q456 cr Eor$ do s t q(: Xprrffi-d + <rfr ft dn t !H E1 {qr = 0. re. wm qr*' an 6{t t f6 td {qr rqsfir r+d dc, r t aqr s} z t $6q1 6* E{ t 333333 t. 333333-7=47619. ez. etz t fo (z 272 - E7 s) = I 397 Tot'flr x t fflrfi dr[. 1397=llxl27. frl ii+ld ofre {qr rzz t ffi *oT or q}rr ro t. er<: g. q-a qrfrq gq-pfo z, avr 2r + 2 t. T{ 1zr+ zf - 1x12 = (2x + 2 + 2x) (2x + z - Zx) = 2(4x + 2l = 4 x (2x + l), til 4 t f+dcrfflrfi Etdrt gg. T{ qrfre fqqq-grt+ 1zz + l) i1en (2r1 + 3) t. ir6t (2n+3f -(2n+ t)2 : 12n + 3 + 2n + t) (Zn + 3 _ 2n _ l\ = (4n + 4) x 2 = 8(n + l), d s t T{ilqr fflrft E}dr t. 90. (6n2+6n)=6n(n+ r),qlsqfcr 6tdqr 12 tTkcrF.rfiEirn, i(t.r z(n+ l)qsrq{cltt. 91. (46t + 452 +463a 46t1(l +4+42+43)=451 x 85 = 46t x : d wsrqr ro t frr< drfr. n@ x (340), 92. (32s + 326 a 327 q 3281 = 32s x (l + 3 + 32.,,-3r;:325 149 = 324r3 x4x to,QmtWtr4Ernar)rfr. 93. fr r {i[' rrq {e1 S 6 (r - aj sts 1.r + a; t gteo frrr< frrn. .. 07zw - r2q Tridqrfrrr€&n (rz + l) t qqi( l8 t + (172m- t){ttrqlfql61}rn rs t = 17zooqfr 19 *tctrfiE.{iqtqrd = r. e4. r d{ $ crTd sqt d, g - O,(r - a) t fErrfi Etrr. 95. (t - l ), (-r + l ) t Eqm erfr t n qqfo z gq. qq riuqr t. (49)15- tl = {(72)15 - I } = (730 - l), + (7 + l) qqh I * ferrfi E}r[. 96. (t + l), (x + l) t {ukql fqrrfi ilfr dqr vqF6 ,t Esc d. .. 167s7 + l) FI€iFrr (67 + 1) t f.rllffi dqr. .. (oa + l) + 66 tni oe t qrrr i+ q{ tqsa = or. 97. \til n = 4q + 3. Q, 2n = 8q + $ = 4(2q + l) + 2. st-(: 2r tftl q t qm ti w rlqqe = z. 98. :nfl 232 =:ilrll:rr; e12 * t) = (r+ I) EnfiyEtrirriur -lv{Tf-6qlEqffitmt. rq, (2e6 + t1:112tzyt + ll = (J + l) : (,x + t) (l -: + l), ril i/t TEifii f{.rfiE},rr ffr ft + l), xt E iilqr fqrrfid-drt. 99. Ett n fuco A a (l + a) rrt{ (r + 4) t frqffi E}[. -. (4743 +4343) iqT 14zrz +atrz; {ty*o (+z + lr) tfrirfi E}.rr. 100. Division Algorittm Er{r A Rt TA grto a eer 6 + {rrd A Wrf6 q ncr r qryq ti dt fr a=bq+rqd0<..6. t0t.987=(3x7x47) erd: *s'risr 3, 7, 47 i t r-*fi t f+rqr t r< a'n 24 q<frE Etctfii 553681 -+ teidl 6r +rr = 28, ril 3 t fal]-ft'Tfr EtdT) 555181 -+ 1oi*] +r frn = 25, d 3 t fqsrffi rti ttm) 555681 5] qrrr ii qi nTa d.n t6 q€ 3,7, 4't g I qt+ t fu'rm Etar t. ero, qfr wfl stt t 102 r: l3p+ l1 i9I x:174 + 9 .. t3p + 11 : 17q +9 = l1q- l3P= 7*, : g:jP p or dtt da tn ffi q - lfl .mw* t. Errn p = 26 (13x26+11)=349 103. 4 x u = lJx t+41 -y 5 y-l , = lOrr*l):(4x9+l)=37 t-4 of,6T 37 q1 s-qFrd 5, 4 t qlq ti q{ 5 37 4 5qp6 frqrn'o : z, : 1-3 104. 4 x z: (6x 1++1 = 19, 5 y = (5 x 2+3)= (jx I0+3)=53, 6 ZJ x: (4 x y + 2) = (4 x 53 + 2) : 211 t-4 erfre rieqr = zt+ 105. s x .. z : (13 x 1+ lZ):25, 9 y-4 .y= (q'z-8)-(9\25 I 8) - 2-11. l3 z-8 x = (5x),+4)=(5x233+4) 1169 t12 4] 58s t l169 qFI ti c{ tqse = sa+. 106. 132=4x3x 11 264+11,3,4({; 396+11,3,4({; 462-+11,3(x); 7s2-}11,3,4('b, 968-+ 11,4(x); 2178 -+ ll,3(x); 5184-+3.4(x); 6336-+ 11,3,4(!) srfr€ {@roit st ri@I : 4. r07. fr{ felrfi E\i srfr rirqrij t, 102, 108, t14, -. .,996. 3tftJ e1 o t q6qfiqcI<Ri6ttq€r{ a:102, d=6 nqT /:996. cra E{ {qtS El tqr n t. n-e, a+(n-l)d:996 + 102+ (n-l)x$=996 l):149+'?=150' = 6*(n 1)=894=(n snfre{'@Tiil et+iqt = tso, 108. :IT{r Sn:(l+2+ 3+...+45). qE q6trIIl<R +rfrt fqsC- a=1, d: I EQIn=45. , 45 (45 -\ sn= ; lza-\n-t)d1-;.12x1+(45 l),1)=[ 2,46J ,4.5, 2]t :45 x (20+3)=(45 x 20)+(45 x 3) = (900 + 135) = 1035. 109. Sn= (2+4+6 *...+30) q€ qs tIrIl<R ffi t tqsC- a = 2, d : 2, n: 15 II /: 30 riqtst c{ {f#cri 25 ' s,: arr-r=I x(2+30)=(r5 x 16)=240. lt0 ,S, = (l +2+3 +... + 50+ 5l + 52+...+ 100)_(l +2+3 + + 50) =]!9x(l+100)-T +s0)=(so x r0l)-(25, 5t) ",, = (5050 _ 1275) = 3775 lll. 3lf€ tq (t + I + I + ... n qd ilfi) _ (r 2 i = l-+-+- + ncdEs \n n n = ,-,In( f + t ) Ln-n-t z+ I )='- z = 2 =1tz-t; I nEII If< = I =4 rr2. { {qrA' t: 24, 30, 36, 42, ...., s6. T{ { sq61 +.d q t ftTIt a = 24, d = (30 _ 24) = 6 dcrr ! = 96. ql:Tr $e Ird 61 {.q.r rq, z siTE = 96. = n. a+(n-l)d=95 + 24+(n_ t.y,6=96 = (z- I) \ 6=72+ (n _ t)= 12+ n= t3. erd: e{frq IrA +1 +iqr = r:. I13. qfre tq =2+ 4 + 6 + 8 + .,, + I00. 116 qfi srll<R ffi t ffi' a = 2, d = (4 _ Z)= 2 der / = r00. qTfl E-f, lrd E1 dqr = n.14, n ei q< = t OO. a+ (n- l) d= 100 + 2+ (n- t) x 2 = t00 + (n - l) x 2 = 9E + (n- l):zf!3 2 = 59 .'. 3lfre frq = 31aa .,)=T 50 x (! + x 102)=2550. Z 100) = (25 l 14. srfrE +q = t0+ t5 +20+25+.., + 95. qE qi5- qrnfl ffi t f$ri' a = t0, d =5 tTqr / = 95. cr+ €S yd E1 {sr = n. ird, n ei rq = 95. .. a+(n-l)x4:95=+ t0+(a-t)x5=95 .+ (z_ l) x 5:85 + (a_ t;= t7 = n: 18. . srrfr€ frq = 11r* 18 . t)=,x(10+95)=9, Z 105=945. II5. q6 qfr sqrd{ *,rfr t ffi' a = 6, d : 6detT S, = 1800. qr{rEqffidgnnr<t.n-< n * 2 tzo*(n- t) x fl= tE00+ i - rr, 5+(n_ t), 6l= rs00 - n(6n + 6):3600 + n(n+ I)=600 + n2 + a-69g=0 + n2 + 25n _ 24n _ 600 : 0 a n(n+25)-24(n+ 25)=0 (n+25)(n_24)=O + n:24. = ee-a, gre v* +1 riwr = Z+. 116. 46 qdF'Xuild{ ta t fu{IS a : irql, : qrA 3 ! =, +1 {'qr = z. tr, z eirq = rr,-r. $f, C-d .. 2*t =384+ 2Ft :l2B:27 +(n_l)=/3lr:g Jx ero: 5o rd +1 frgl = S. eqi{€ siflFTd 26 ll7 q-o luryil-or M t filse- a : 3, r = ! =, u^' =' a(rn -t\ -'fgiff 3x(1e683-lr 3tr{Ie qFI = V) ti_l) -- 2 3x19682 - 2- = 1,9841 =29523. + n2) = ,<r+ l) (2n + l) ll8. (12+22+32+ | zrd n= 10. ei-(:.3ifr€+r = *,.'o x ll x 2l = 385' + 42 +62 +'.. + 202) rr:; r19 1z? : ?,'r;:r;'.Or;r? r;|!irr; f'.ir','l',*, 27 ,ll2 + 22 + 32 +.,. + l02l = -, * x l0x ll "2l [" 1,z+22+" *n')=] r(n+r)(2n+l)l = (4x5*?7)=1540' + 22 + 32 + + l02) +2Ozy = g2+22 + 32+...+ I 02 + I l2 +... + 202; - 112 lzo. lllz+ 122+132+ r') : I 2}x21x4l 6 l0x I lx2l 6 Ir 12 +22 + * n(n+l)(2n+l) = (2870 - 38s) = 2a85' New Release !