class 7math book

cEof; 22.4 1. ;q\" ko| fu] u//] / gul/sg bj' } tl/sfn] ju{ kQf nufpm . HofldtLo lrq klg agfpm M -s_ (a+1) -v_ (b + 2) -u_ (c-1) -3_ (c - 5) -ª_ (2p+3q) -r_ (6m-5n) 2. kZ| g g=+ 1 h:t} u/L (a+b)2 / (a -b )2 ?ksf bO' ÷{ bO' { cf6] f ;d:of agfO{ ;dfwfg u/ M ;fyL;u“ cfk;df ;dfwfg u/L pTt/ hfr“ /] x/] . 3. lj:tf/ u/ M -s_ (a2 - 3y)2 -v_ (xy + ab)2 -u_ (p2q + q2r)2 -3_ (-5p4 - 6a)2 -ª_ m2  1 2 -r_  3q3  1 2  m   6q3  4. olb p1 7 eP, dfg lgsfn M p -s_ p2  1 -v_ P  1 2 P2  P 5. olb  x  1   12 eP dfg lgsfn M  x  -s_ x2  1 -v_  x  1 2 x2  x  6. ;/n u/ M -s_ (3c + 2d)2 + (5c - 6d)2 -v_ 17(k-5)2 - 21(k - 5) (k + 6) 7. u0' fgkmn lgsfn M -s_ (g+h) (g2 - gh + h2) -v_ (x+y) (x2 - xy + y2) -u_ (l-m) (l2 + lm + m2) 8. olb e 1  11 eP kd| fl0ft u/ M e -s_ e2  1  119 -v_  e  1 2  117 e2  e  9. olb f  1  15 eP kd| fl0ft u/ M f -s_ f 2  1 = 227 -v_ f  1f 2  229 f2  196 ul0ft, sIff – &

PsfO 23 3ftfªs\\ (Indices) 23.1 3ftfªs\\ sf lgodx¿ (Laws of Indices) 1. 3ft / 3ftfªs\\ tnsf ljm| ofsnfk cWoog u/L 5nkmn u/ M tn Pp6} u0' fgv08nfO{ nuftf/ u0' fg ug{] tl/sf ;DaGwL 9fr“ f lbOPsf] 5, o;nfO{ k/\" f u/ . u0' fg v08 5f6] s/L ¿k k9g\\ ] tl/sf 2 x 2 = 4 -bO' c{ f6] f 2 sf] u0' fgkmn_ 2 sf] 3ftfªs\\ 2 2 x 2 x 2 -tLgcf6] f 2 sf] u0' fgkmn_ 22 = 4 2 sf] 3ftfªs\\ 3 2 x 2 x 2 x 2 -4 cf6] f 2 sf] u0' fgkmn_ 23 = 8 2 sf] 3ftfªs\\ 4 =================- ======================_ 24 = 16 ============ =================- ======================_ ============ 2 x 2 x 2 =====-n cf6] f 2 sf] u0' fg kmn_ === = === 2 sf] 3ftfªs\\ 2 a x a x a .....(n cf6] f a sf] u0' fg kmn_ === = === a sf] 3ftfªs\\ n 2n = 2n an oxf“ 23 df 2 cfwf/ xf] eg] 3 3ftfª\\s xf] . To:t} an df a cfwf/ xf] eg] n 3ftfª\\s xf] . o;nfO{ tn cem :ki6sf ;fy bv] fOPsf] 5 M 23 3ftfª\\s an 3ftfª\\s cfwf/ cfwf/ 1. o;/L Pp6} ;ªV\\ of nuftf/ w/] } k6s u0' fg ugk{' g{] ljm| ofnfO{ hgfpg 3ftfªs\\ (exponents) sf] ko| fu] ul/G5 . 2. an df a nfO{ cfwf/ / n nfO{ 3ftfª\\s elgG5 . To:t} u/L an nfO{ 3ft (power) elgG5 . oxf“ a wgfTds jf leGgfTds h] x'g klg ;S5 . ul0ft, sIff – & 197

2. 3ftfªs\\ sf lgodx¿ lgod 1: Pp6} cfwf/ ePsf 3ftx¿sf] u0' fg M (am x an = am+n) tnsf] ljm| ofsnfksf] 9fr“ f cWoog u/L 5nkmn u/ M -s_ tn Pp6} cfwf/ ePsf 3ftx¿sf] u0' fg ug{] tl/sfsf] 9fr“ f lbOPsf] 5, o;nfO{ k/\" f u/ . 21 x 21 = 4 = 22 = 21+1 31 x 31 = 9 = 32 = 31+1 21 x 22 = 8 = 23 = 21+2 31 x 32 = 27 = 31+2 ................................. ................................. ................................. ................................. 21 x 2n = 21+n = 2n+1 31 x 3n = 31+n = 3n+1 a1 x an = a1+n b1 x bn = b1+n = ........ am x an = ....... bm x bn = ......... -v_ ca dflysf] tflnsfsf cfwf/df Pp6} cfwf/ ePsf 3ftx¿sf] u0' fg ubf{ aGg] 3ftfªs\\ sf] lgod kQf nufpm . cfkm\\ gf] lgodnfO{ ;fyL;u“ 5nkmn u/ / lgisifn{ fO{ tnsf lgod;u“ bfh“ /] x]/ M 3ftfªs\\ sf] lgod 1 : am x an = am+n xG' 5 . hxf“ m / n k\"0f{ ;ª\\Vof x'g\\ . Pp6} cfwf/ ePsf 3ftx¿sf] u0' fg ubf{ cfwf/ pxL /xG5 . t/ 3ftfªs\\ x¿ eg] hfl] 8G5g\\ . lgod 2: Pp6} cfwf/ ePsf 3ftx¿sf] efu M (am ÷ an = am-n) tnsf ljm| ofsnfk cWoog u/L 5nkmn u/ M -s_ tn Pp6} cfwf/ ePsf 3ftx¿sf] efu ug{] tl/sfsf] 9fr“ f lbOPsf] 5 . o;nfO{ k/\" f u/ M 22  21  22  21  2 21 32  31  33  31  321 2 3 23  21  222  22  232 33  31  3 3 3  32  331 2 3 ........................................... ........................................... ........................................... ........................................... 3n ÷ 31 = .................... bn ÷ b1 = .................... 2n ÷ 21 = .................... bm ÷ bn = .................... an ÷ a1= .................... am ÷ an = .................... 198 ul0ft, sIff – &

ca dflysf] tflnsfsf] cfwf/df Pp6} cfwf/ ePsf 3ftx¿sf] efu ubf{ aGg] 3ftfªs\\ sf] lgod kQf nufpm . 3ftfªs\\ sf] lgod 2 : am ÷ an = am-n xG' 5 . hxf“ a = 0, m >n tyf m / n b'j} wgfTds ;ª\\Vof x'g\\ . Pp6} cfwf/ ePsf 3ftx¿sf] efu ubf{ cfwf/ pxL /xG5 t/ cz+ sf] 3ftfªs\\ af6 x/sf] 3ftfªs\\ 36fOG5g\\ . lgod 3: zG\" o 3ftfªs\\ M (a0 = 1) tnsf ljm| ofsnfk cWoog u/L 5nkmn u/ M -s_ tn Pp6} cfwf/ / zG\" o 3ftfªs\\ sf] 9fr“ f lbOPsf] 5 . o;nfO{ k/' f u/ M 2 2  2  1 211  20 3  3  3  1  311  30 2 3 22  22  22 1 222  20 32  32  33 1 322  30 22 33 23  23  ........................................... ........................................... ........................................... ........................................... 33  33  2m ÷ 2m = 3n ÷ 3n = am ÷ am = bn ÷ bn = -v_ ca dflysf] tflnsfsf] cfwf/df 3ftfª\\s z\"Go ePsf 3ftsf] 3ftfª\\ssf] lgod kQf nufpm . 3ftfªs\\ sf] lgod 3 : a0 = 1 xG' 5 . hxf“ a = 0 5 . zG\" oafxs] sg' } klg ;ªV\\ ofsf] 3ftfªs\\ zG\" o 5 eg] To;sf] dfg 1 x'G5 . tnsf pbfx/0fx¿ cWoog u/L cfkm\" n] klg ;dfwfg ug{] ko| f; u/ M pbfx/0f 1 tnsf nuftf/ u0' fg ljm| ofnfO{ 3ftfªs\\ df JoSt u/ M -s_ (-4) x (-4) x (-4) x (-4) -v_ (-5y) x (-5y)x (-5y) x (-5y) x (-5y) x (-5y) x (-5y) x (-5y) x (-5y) ;dfwfg -s_ (-4) x (-4) x (-4) x (-4) = (-4)4 = (4)4 [  - nfO{ rf/ k6s u0' fg ug{' egs] f] ‘±’ xf] . ] -v_ (-5y) x (-5y)x (-5y) x (-5y) x (-5y) x (-5y) x (-5y) x (-5y) x (-5y) = (-5y)9 = -(5y)3 [ - nfO{ tLg k6s u0' fg ubf{ ‘–’ g} xG' 5 . ] ul0ft, sIff – & 199

pbfx/0f 2 u0' fgkmn lgsfn M -s_ 35 x 52 -v_ (5a)2 x (2b)3 ;dfwfg -s_ 35 x 52 = (3 x 3 x 3 x 3 x 3) x (5 x 5) = 243 x 25 = 6075 -v_ (5a)2 x (2b)3 = (5a x 5a ) x (2b x 2b x 2b) = 25a2 x 8b3 = 200a2b3 pbfx/0f 3 9000 nfO{ 10 sf] 3ftsf] ¿kdf JoSt u/ M ;dfwfg oxf“ 9000 = 9 x 1000 = 9 x (10)3 = 9 x 103 pbfx/0f 4 864 nfO{ ¿9 v08Ls/0f u/L 3ftsf] ¿kdf JoSt u/ M ;dfwfg oxf,“ 864 sf] ?9 u0' fgv08 lgsfNbf M 2 864 oxf,“ 864 = 2 x 2 x 2 x 2 x 2 x 3 x 3 x 3 2 432 2 216 = 25 x 33 2 108 2 54 3 27 39 3 pbfx/0f 5 3ftfªs\\ sf] lgod ko| fu] u/L ;/n u/ M -s_ 5q2 x 15q9 -v_ -u_ 15b2  20b10 55b12 ;dfwfg [ am x an = am+n] -s_ 5q2 x 15q9 = 75q2+9 = 75q11 200 ul0ft, sIff – &

-v_ [ am x an = am+n] = y6 -u_ 15b2  20b10  am  an  amn 150b12 = 2b12 - 12 [ am ÷am = am-n] = 2b0 [ a0 = 1] =2x1 =2 pbfx/0f 6 dfg kQf nufpm M -s_ olb z = 5 eP z5 = < ay92ayy1884ybb52 y1y49y-8v85_ o[lb aam=4an/ b a=m3 ePamn ] an -u_ olb x = 15 / y = 20 eP x2  2xy  y2 xy ;dfwfg -s_ oxf“ z5 = (5)5 = 3125 -v_ oxf“ a2  b2  42  32  16  9  25  3 4 ab 43 7 7 7 -u_ oxf,“ x2  2xy  y2  (x  y)2 xy (x  y) = (x-y)2-1 [ am ÷ an = am - n] =x-y = 15 - 20 = -5 ul0ft, sIff – & 201

cEof; 23.1 1. tnsf lx;fanfO{ 3ftfªs\\ sf ¿kdf JoSt u/ M -s_ 5 x 5 x 5 x 5 x 5 x 5 x 5 -v_ (-15) x (-15) x (-15) x (-15) -u_ (3x) x (3x) x (3x) (3x) -3_ (-64) x (-64) x (-64) x (-64) x (-64) x (-64) 2. tnsf kT| os] 3ftnfO{ nuftf/ u0' fg ljm| ofdf JoSt u/ M -s_ 63 -v_ 315 -u_ (-6)8 -3_ (2x)7 -ª_ (-2b)9 3. tnsf kT| os] ;ªV\\ ofnfO{ 10 sf] 3ftdf JoSt u/ M -s_ 100 -v_ 200 -u_ 5000 -3_ 3,50000 -ª_ 6,90,00,000 4. dfg kQf nufpm M -s_ 2 x 102 -v_ 5 x 105 -u_ 15 x (-10)3 -3_ 18 x (26) -ª_ 5 x (-5)3 -r_ 23 x 42 5. ;fgf] / 7n' f] 56' o\\ fpm M -s_ 32 jf 23 -v_ 53 jf 35 -u_ 34 jf 43 -3_ 210 jf 102 -ª_ 0100 jf 1001 -r_ 28 jf 103 6. ¿9 v08Ls/0f u/L 3ftsf] ¿kdf JoSt u/ M -s_ 64 -v_ 500 -u_ 1256 -3_ 1728 -ª_ 864000 7. 3ftfªs\\ sf] lgodx¿ ko| fu] u/L ;/n u/ / 3ftfªs\\ d} pQ/ nv] M -s_ 35 x 32 -v 58 x 54 -u_ x3 x x5 -3_ a2 x a(-3) -ª_ (x)3 x (x)6 -r_ (-b)3 x (-b)5 -5_ -h_ (5x)6  (5x)7 (5x)11 8. tnsf kT| os] cj:yfdf dfg kQf nufpm M -s_ 20 -v_ 2 x 1000 -u_ (-5)0 -3_ x0 -ª_ 105y0 -r_ 2m17  m3 m20 9. dfg kQf nufpm M -v_ olb x = 5 eP 17x2 = ? -s_ olb y = 3 eP y3 = ? -u_ olb a = 10, b = 2 eP a2  2ab  b2 =? ab -3_ olb x=5/y=3 x2  2xy  y2 -ª_ olb l = 5 eP l 2  l10  l 7 xy = ? l19 = ? 202 ul0ft, sIff – &

PsfO 24 ;dLs/0f, c;dfgtf / nv] flrq (Equation, Inequality and Line Graph) 24.1 Ps rnoS' t /v] Lo ;dLs/0fsf ;d:of (Problems of linear Equation on in One Variables) 1. Ps rnoS' t /v] Lo ;dLs/0fsf] kl/ro tnsf ljm| ofsnfk cWoog u/L 5nkmn u/ M -s_ y + 5 = 7 df sltcf6] f rn /flz 5g\\ < sltcf6] f crn /flz 5g\\ < -v_ s] y + 5 = 7 ul0ftLo vn' f jfSo xf] < s;/L < -u_ y sf] dfg slt xb“' f vn' f jfSo y + 5 = 7 ;fr“ f] jfSo xG' 5 < oxf,“ y + 5 = 7 df Pp6f dfq rn /flz y 5 . (+5) / (+7) crn /flz x'g\\ . y + 5 = 7 ul0ftLo v'nf jfSo xf] . o;df y sf] 3ftfªs\\ 1 5 . y + 5 = 7 Pp6f ;dLs/0f klg xf] . o:tf] ;dLs/0fnfO{ Ps rnoS' t /v] Lo ;dLs/0f elgG5 . -3_ dflysf] 5nkmnsf cfwf/df Ps rnoS' t /v] Lo ;dLs/0fsf] kl/efiff nV] g ;S5f} < nv] /] ;fyL;u“ 5nkmn u/ . lgisifn{ fO{ tnsf] kl/efiff;u“ bfh“ /] x/] M a/fa/ lrxg\\ ' =' ;dfjz] ePsf,] 3ftfªs\\ 1 ePsf] tyf Pp6f dfq rn /flz ePsf] ;dLs/0fnfO{ Ps rno'St /]vLo ;dLs/0f elgG5 . -ª_ y + 5 = 7 h:t} cGo 5 cf6] f Ps rnoS' t /v] Lo ;dLs/0f nv] /] bv] fpm . 2. Ps rnoS' t /v] Lo ;dLs/0fsf] ;dfwfg sg' } Pp6f Ps rnoS' t ;dLs/0f y + 5 = 7 n]pm . hfr“ /] xb] f,{ -s_ y sf] dfg slt xb“' f y + 5 = 7 xG' 5 < y sf] dfg 1, 2, 3, 4, 5 /fVb} hfcf“} . -v_ ca y + 5 = 7 af6 y sf] dfg lgsfNg] y+5=7 5f6] f] tl/sf sg' xfn] f < oxf“ y + 5 = 7 5 . 1 + 5 = 7 dfGo ePg . cyjf, ( y + 5 ) - 5 = 7 - 5 [ bj' l} t/ 5 36fpb“ f ] 2 + 5 = 7 dfGo eof] . cyjf, y + 5 - 5 = 2 3 + 5 = 7 dfGo ePg . hfr“ /] xb] f,{ cyjf, y + 0 = 2 cyjf, y = 2 y+5=7 ul0ft, sIff – & cyjf 2 + 5 = 7 cyjf 7 = 7 kd| fl0ft eof] . 203

pbfx/0f 1 xn u/ / pQ/ hfr“ /] x/] M 17x - 5 = 15 ;dfwfg xn ubf{ hfr“ /] xb] f{ 17x -5 = 19 17x - 5 = 29 cyjf (17x - 5) + 5 = 19 + 5 [ bj' } lt/ 5 hf8] b\\ f] cyjf, 17 x 2 - 5 = 29 cyjf, 34 - 5 = 29 cyjf, 17x -5 + 5 = 34 cyjf, 29 = 29 k|dfl0ft eof] . cyjf 17x = 34 cyjf 17x  34 [ bj' l} t/ 17 n] efu ubf]{ 17 17 cyjf x = 2 pbfx/0f 2 tnsf] ;d:of xn u/ / pQ/ hfr“ /] x/] M 17k  3  5 5 3 ;dfwfg xn ubf{ hfr“ /] xb] f{ 17k  3  5 17k - 3  5 5 3 5 3 cyjf, 17  3  3  5  3 [bj' l} t/ 3 hf8] b\\ f] cyjf, 17  2  3  5 5 5 3 5 5 15 5 3 cyjf, 17k  25  9 15 cyjf, 34  9  5 cyjf, cyjf, 17k 34 [bj' l} t/ 17 n] efu ubf]{ 15 3 17  15x17 5 5 k  2 cyjf, 3  3 k|dfl0ft eof] . 15 204 ul0ft, sIff – &

pbfx/0f 3 xn u/ / hf“r]/ x]/ M 10n  1  1 n  2 4 2 3 xn ubf{ hfr“ /] xb] f{ ;dfwfg M 10n  1  1 n  2 4 2 3 10n  1  1 n  1 1 1 1 2 1 1 42 3 4 4 2 3 4 4 cyjf, 10n    n   [ bj' l} t/ hf8] b\\ f ] cyjf, 10n n 83 cyjf, 10 11  1  1  11  2 2 12 114 4 2 114 3   cyjf, 10n n ( n 1121) n bj' l} t/ n 36fpb“ f cyjf, 220  57  11  152 1 2 2 2 2 228 228     [ ] cyjf, 20n  n  11 cyjf, 163  163 2 12 228 228 cyjf, 19n  2  11  2 k|dfl0ft eof] . 2 19 12 19 cyjf, n  11  11 6x19 114 pbfx/0f 4 Pp6f ljBfnosf] sIff 7 df hDdf 27 ljBfyL{ /x5] g\\ . olb 5fqfsf] ;ªV\\ of 5fqsf] eGbf 3 n] a9L /x5] eg,] -s_ ljBfyL{ ;ªV\\ of hgfpg] Pp6f ;dLs/0f nv] . -v_ 5fq / 5fqfsf] jf:tljs ;ªV\\ of kQf nufpm . ;dfwfg oxf,“ dfgf“} 5fqsf] ;ªV\\ of = x 5 . To;n} ] 5fqfsf] ;ªV\\ of = x + 3 -s_ ca, 5fq ± 5fqf = hDdf ljBfyL{ ;ªV\\ of cyjf x + (x+3) = 27 cyjf x + x + 3 = 27 cyjf, 2x + 3 = 27 lbOPsf] ;dLs/0f xf] . ul0ft, sIff – & 205

-v_ 2x + 3 = 27 nfO{ xn ubf,{ [bj' l} t/ 3 36fpb“ f] cyjf, 2x + 3 - 3 = 27 - 3 cyjf, 2x = 24 cyjf, 2x 24 [bj' l} t/ 2 n] efu ubf]{ 22 cyjf, x = 12 To;n} ] 5fq ;ªV\\ of = 12 hgf 5fqfsf] ;ªV\\ of = x + 3 = 12 + 3 = 15 hgf pbfx/0f 5 Pp6f cfotsf] rf8} fO nDafOeGbf 5 cm n] sd 5 . olb kl/ldlt 30cm eP, -s_ ;f] cfotsf] nDafO / rf8} fO hgfpg] ;dLs/0f nv] . -v_ ;f] cfotsf] nDafO / rf8} fO kQf nufpm . -u_ ;f] cfotsf] Ifq] kmn slt xfn] f < ;dfwfg -s_ oxf“ cfotsf] nDjfO (l) =x cm -dfgf_“} To;n} ] rf8} fO (b) = x - 5 x'G5 . kl/ldlt ( p ) = 30 cm 5 . ca ;q\" p = 2(l+ b) cg;' f/ cyjf 2{x + (x - 5)} = 30 cyjf 2(x +x - 5) = 30 cyjf, 2(2x - 5) = 30 cyjf, 4x - 10 = 30 cyjf, 2x - 5 = 30 rflxPsf] ;dLs/0f xf] . -v_ 4x - 10 = 30 nfO{ xn ubf,{ cyjf 4x -10 = 30 cyjf, 4x-10+10 = 30+10 [ bj' l} t/ 10 hf8] b\\ f ] cyjf, 4x = 40 cyjf 4x  40 [ bj' l} t/ 4 n] efu ubf{ ] 4 4 cyjf, x = 10cm To;n} ] nDafO (l) = x = 10 cm ca rf8} fO (b) = (x - 5) = (10 - 5 ) cm = 5 cm 206 ul0ft, sIff – &

-u_ Ifq] kmn ( A ) = ? ;q\" cg;' f/, cfotgsf] Ifq] kmn (A) = l x b = (10 cm) x (5 cm) = 50 cm2 pbfx/0f 6 bO' { cf6] f jm| d;} u“ cfpg] k0\" f{ ;ªV\\ ofx¿sf] ofu] kmn 21 5 eg] tL b'O{ ;ª\\Vofx¿ s'g s'g /x]5g\\ < kQf nufpm . ;dfwfg dfgf,“} Pp6f ;ªV\\ of = x eP csf{] ;ªV\\ of = x + 1 x'G5 . lbPcg;' f/ x + (x+1) = 21 cyjf 2x + 1 = 21 cyjf 2x = 21 - 1 cyjf x  20 2 cyjf x = 10 ca, Pp6f ;ªV\\ of, x = 10 csf{] ;ªV\\ of = x+1 = 10+1 = 11 t;y{ tL bO' { ;ªV\\ ofx¿ 10 / 11 x'g\\ . pbfx/0f 7 cfOtdfg tfdfª p;sf] afae' Gbf 22 jif{n] sfG5f] 5 . 5 jif{ klxn] afas' f] pd/] p;sf] pd/] eGbf bfA] a/ lyof] . ca p;sf] xfnsf] pd/] kQf nufpm . ;dfwfg dfgf,“} cfOtdfgsf] xfnsf] pd/] = x jif{ 5 . To;n} ] afas' f] pd/] = x + 22 jif{ xG' 5 . 5 jif{ klxn] cfOtdfgsf] pd/] = (x - 5) jif{ 5 jif{ klxn] afas' f] pd/] = x +22- 5= x + 17 jif{ ctM 2 (x-5) = 1(x+17) cyjf, 2x - 10 = x + 17 cyjf, x = 27 jif{ t;y,{ cfOtdfgsf] xfnsf] pd/] = 27 jif{ afas' f] pd/] = x + 22 = 27+22 = 49 jif{ 207 ul0ft, sIff – &

cEof; 24.1 1. tnsf ;dLs/0fx¿ a/fa/L tYo k|of]u u/L xn u/ . pQ/ klg hf“r]/ b]vfpm M -s_ a + 3 = 15 -v_ x - 7 = 78 -u_ 7m = 8m + 6 -3_ - 8x = 2x - 4 -ª_ 3 y  6  7y -r_1.2 + 6l = -2.1l - 1.2 5 -5_ 5.4x 1 x  7.5 3 2. xn u/ / pQ/ klg hfr“ /] bv] fpm M -s_ 5 ( p - 10 ) = 10 + 7p -v_ ( 10 - k ) 6 = -8k - 10 -u_ 4 . 3 - 3 ( 4 r - 3) = 0 . 7 ( 6 r - 10 ) -3_ 2 (3  5t)  6 (2  t) 3 2 3. tnsf egfOx¿ ;To jf c;To s] xg' ,\\ 56' o\\ fpm M -s_ x + 5 = 4 df x rn /flz xf] . -v_ x - 2 = 5 df 5 / 2 rn /flzx¿ x'g\\ . -u_ y + 10 = 0 b'O{ rno'St ;dLs/0f xf] . -3_ - 2 + p = 3 Ps rno'St v'nf jfSo xf] . 4. tnsf kZ| gx¿sf] hjfkm nv] M -s_ a/fa/ lrxg\\ ko| fu] ePsf] / Pp6f dfq rn /flz ePsf] ;dLs/0fnfO{ s] elgG5 < -v_ Ps rnoS' t ;dLs/0fsf] cy{ pbfx/0f;lxt nv] . -u_ a + 2 = 10 df a sf] 3ftfªs\\ slt xG' 5 < -3_ b + 5 = 9 ;fr“ f] jfSo xg' sf nflu b a/fa/ slt xg' k' nf{ < 5. Pp6f sIffdf 28 hgf ljBfyL{ /x5] g\\ . 5fqfsf] ;ªV\\ of 5fqsf] eGbf 4 n] a9L /x5] eg,] -s_ ;a} ljBfyLn{ fO{ hgfpg] Pp6f ;dLs/0f nv] . -v_ ;dLs/0f xn u/L 5fq 5fqfsf] ;ªV\\ of kQf nufpm . 6. Pp6f ljBfnodf hDdf ljBfyL{ ;ªV\\ of 555 hgf 5g\\ . olb 5fqsf] ;ªV\\ of 5fqfsf] eGbf 55 n] a9L eP 5fq / 5fqfsf] jf:tljs ;ªV\\ of kQf nufpm . 208 ul0ft, sIff – &

7. Pp6f 3/sf] cfotfsf/ cfu“ gsf] nDafO, rf8} fOeGbf 2m n] a9L 5 . olb k\"/f kl/ldlt 132m eP, -s_ ;f] cfu“ gsf] rn /flz ko| fu] u/L gdg' f lrq agfpm . -v_ kl/ldlt hgfpg] ;dLs/0f n]v . -u_ ;f] cfu“ gsf] nDafO / rf8} fO kQf nufpm . -3_ ;fx] L cf“ugsf] Ifq] kmn klg kQf nufpm . 8. Pp6f Ifq] kmn 200m2 ePsf] kf6L{ Kofn;] sf] nDafO rf8} fOsf] bfA] a/ /x5] eg,] -s_ nDafO / rf}8fO kQf nufpm . -v_ kl/ldlt hgfpg] rn /flz ko| fu] ePsf] gdg\" f lrq agfpm . -u_ kl/ldlt hgfpg] ;dLs/0f n]v . -3_ kl/ldlt lgsfn . 9. Pp6f ljBfnodf cg';Gwfgsf] j|mddf Ps lbgsf] xflh/L clen]v x]l/P5, hDdf ljBfyL{ ;ªV\\ ofsf] bO' { ltxfO{ ljBfyL{ dfq pkl:yt xb“' f 6 hgf dfq uon ePsf /x5] g\\ eg,] -s_ hDdf ljBfyL{ ;ªV\\ of hgfpg] ;dLs/0f nv] . -v_ pkl:yt ePsf ljBfyLs{ f] ;ªV\\ of kQf nufpm . 10. bO' { cf6] f jm| d;} u“ cfpg] k0\" f{ ;ªV\\ ofx?sf] ofu] kmn 51 5 eg,] -s_ tL ;ª\\Vof hgfpg] ;dLs/0f n]v . -v_ tL ;ªV\\ ofx¿ slt slt xfn] fg\\ < 11. kD] afn] cfkm\\ gf] hGd lbgdf ;fyLnfO{ af8“ g\\ bO' { Kofs6] rsn6] lsg5] g\\ . Pp6f Kofs6] df hlt rsn6] 5g,\\ To;sf] tA] a/ csf{] Kofs6] df 5g\\ . bj' } Kofs6] sf rsn6] Ps} 7fpdf hDdf kfbf{ 120 rsn6] eP5g\\ eg,] -s_ hDdf rsn]6 hgfpg] ;dLs/0f agfpm . -v_ kT| os] Kofs6] df slt slt rsn6] /x5] g\\ . 12. Pp6f ;ªV\\ of csf{] ;ªV\\ ofsf] tA] a/ 5 . olb bj' s} f] ofu] kmn 48 eP, -s_ bj' } ;ªV\\ ofsf] ofu] kmn hgfpg] ;dLs/0f nv] . -v_ tL b'O{ ;ª\\Vof slt slt xf]nfg\\ < 13. Pp6f cfotsf/ ?dfnsf] rf8} fO, nDafOeGbf 10cm sd /x]5 . olb kl/ldlt 110cm eP, -s_ kl/ldlt hgfpg] ;dLs/0f n]v . -v_ nDafO / rf}8fO kQf nufpm . 14. dfly kZ| g g=+ 1 bl] v 7 ;Dd lbOP h:t} Pp6f÷Pp6f ;d:of agfpm . ;fyLx¿;u“ 5nkmn u/L ;dfwfg u/ . ul0ft, sIff – & 209

24.2 c;dfgtfnfO{ ;ªV\\ of /v] fdf bv] fpg] (Representation of Inequality in Number) tnsf] ljm| ofsnfk x/] / 5nkmn u/ M -s_ olb a / b bO' { cf6] f k0\" ffª{ s\\ xg' \\ eg] a / b lardf s] s] ul0ftLo ;DaGw xg' ;S5 < ls t a / b a/fa/ xG' 5 ls t a / b a/fa/ x'“b}g . a / b a/fa/ xb“' g} eg] ls t a > b xG' 5 ls a < b x'G5 . s'g} k\"0ff{ª\\s 3 lncf,“} ca eg t 3 eGbf 7n' f slt ;ªV\\ of xg' ;S5g\\ < 4 > 3, 5> 3 6> 3, 10 > 3 x>3 -v_ x > 3 nfO{ ;ªV\\ of /v] fdf bv] fpm M x>3 -3 -2 -1 0 1 2 3 4 5 6 7 3 eGbf 7n' f ;ªV\\ ofnfO{ x n] lsg hgfOP xfn] f < x rn /flz ePsf] / 3 eGbf 7n' f w/] } ;ªV\\ of ePsfn] x > 3 n]lvPsf] xf] . oxf“ x > 3 df 3 eGbf 7n' f ;ªV\\ ofx¿ dfq kg{] ePsfn] 3 df yfK] nf] (O) dfq nufOPsf] 5 . -u_ x > 3 / x < 3 nfO{ ;ªV\\ of /v] fdf bv] fpm . oxf“ x > 3 egs] f] x rn /flz 3 jf 3 eGbf 7'nf] 5 eGg] a'emfp“5 . To:t}, x < 3 egs] f] x rn /fzL 3 jf 3 eGbf ;fgf] eGg] a'emfp“5 . tnsf] ;ª\\Vof /]vfdf x]/f}“ . x>3 -3 -2 -1 0 1 2 3 4 5 6 7 x > 3 df 3 klg kg{] ePsfn] ;ªV\\ of /v] fsf] 3 nfO{ ufn] f] yfK] nf nufO{ /ªu\\ fOPsf] xf] . x<3 -4 -3 -2 -1 0 1 2 3 4 5 6 x < 3 df 3 klg kg{] ePsfn] ;ªV\\ of /v] fdf 3 nfO{ ufn] f] yf]Knf nufO{ /ª\\ufOPsf] xf] . 210 ul0ft, sIff – &

dxTTjk0\" f{ tYox¿ -s_ olb a / b bO' { cf6] f k0\" ffª{ s\\ xg' \\ / h;df a > b / c csf{] k0\" ffª{ s\\ xf] eg] – hf8] tYo M ( a + c) > (b + c) 36fp tYo M (a - c) > (b- c) u0' fg tYo M ac > bc hxf“ c wgfTds 5 . efu tYo M a  b , c0 hxf“ c wgfTds 5 . c c hxf“ c C0ffTds 5 . ac < bc a  b c0 hxf“ c C0ffTds 5 . c c -l6s« f6] fd] L (trichotomy)sf] < jf > lrxg\\ ;dfjz] ePsf] ul0ftLo jfSosf] bj' l} t/ C0ffTds k0\" ffª{ s\\ n] u0' fg jf efu ubf{ jfSodf ePsf lrxg\\ x¿ (< jf >) ablnG5g\\ ._ -v_ olb bO' c{ f6] f k0\" ffª{ s\\ a / b df a = b 5 / csf{] sg' } k0\" ffª{ s\\ c 5 eg] – (a + c) = (b + c) -a/fa/L ofu] tYo_ (a - c) = (b - c) -a/fa/L 36fp tYo_ ac = bc -a/fa/L u0' fg tYo_ a  b hxf“ c  0 -a/fa/L efu tYo_ c c pbfx/0f 1 x>2 x+ 1 > 3 nfO{ xn u/L ;ª\\Vof /]vfdf b]vfpm M ;dfwfg oxf“ x + 1 > 3 5 . ca bj' l} t/ 1 nfO{ 36fpb“ f, x+1 -1>3 - 1 or, x > 2 ;ªV\\ of /v] fdf bv] fpb“ f pbfx/0f 2 211 2x - 3 < - 7 nfO{ xn u/ / ;ªV\\ of /v] fdf bv] fpm M ;dfwfg oxf,“ 2x - 3 < - 7 5 . -bj' l} t/ +3 hf8] b\\ f_ ul0ft, sIff – &

cyjf, 2x 3 + 3 < - 7 + 3 cyfj, 2x  4 cyjf, x <  4 2 cyjf, x < - 2 ca, ;ªV\\ of /v] fdf bv] fpb“ f x<-2 -5 -4 -3 -2 -1 0 1 2 3 4 5 pbfx/0f 3 tn lbOPsf] ;ªV\\ of /v] fsf cfwf/df c;dfgtf nv] M -s_ -4 -3 -2 -1 0 1 2 3 4 -v_ -4 -3 -2 -1 0 1 2 3 4 -u_ -4 -3 -2 -1 0 1 2 3 4 ;dfwfg oxf“ -s_ df 0 df dfq ufn] f] nufOPsf] 5 t/ ufn] f] g/ªu\\ fOPsfn] 0 To; c;dfgtfdf kb{}g . ca o; ;ªV\\ of /v] fdf 0 eGbf bfofl“ t/ Arrow lbOPsfn] 0 eGbf 7n' f ;ªV\\ of kb5{ g\\ . To;n} ] o;nfO{ c;dfgtf lrxg\\ ko| fu] ubf{ x>0 n]lvG5 . oxf“ -v_ df 2 df ufn] f] nufO{ /ªu\\ fOsfn] 2 klg c;dfgtfdf k5{ . 2 eGbf afofl“ t/ Arrow nufOPsfn] 2 / 2 eGbf ;fgf ;ªV\\ ofx¿ To; c;dfgtfdf kb5{ g\\ . To;n} ] x< 2 xG' 5 . To:t} -u_ df -3 df ufn] f] nufO{ /ªu\\ fOsfn] -3 / -3 eGbf 7n' f ;ªV\\ ofx¿ To; c;dfgtfdf kb5{ g\\ . To;n} ] x > -3 x'G5 . 212 ul0ft, sIff – &

cEof; 24.2 1. tnsf kT| os] c;dfgtfnfO{ 56' 6\\ f56' 6\\ } ;ªV\\ of /v] f agfO{ ;ªV\\ of /v] fdf /ª nufO{ bv] fpm M -s_ x>1 -v_ x<-2 -u_ x > 5 -3_ x < -4 -ª_ x + 5 > -1 -r_ x - 3 < 6 -5_ 2x + 5 > -1 -h_ 5x + 3 < 18 -em_ 3x + 2 > x + 6 -`_ 2x-5 > - x + 10 2. tn lbOPsf l6s« f6] fd] L (trichotomy) sf lgodcg;' f/ tnsf egfOx¿ l7s jf al] 7s s] xg' ,\\ 56' o\\ fpm M 2, 3 / -4 k0\" ffª{ s\\ x¿ xg' \\ eg,] -s_ 2 + (-4) = 3 + (-4) -v_ 2x (-4) = 3x (-4) -u_ 2 + (-4) > 3 + ( -4) -3_ 2 + (-4) <3 + (-4) -ª_ 2-(-4)>3-(-4) -r_ 2x(-4) > 3x(-4) -5_ 2x(-4) < 3x(-4) -h_ 2÷(-4) > 3÷ (-4) 3. tn lbOPsf ;ªV\\ of /v] fsf cfwf/df c;dfgtf nv] M -s_ -5 -4 -3 -2 -1 0 1 2 3 4 5 -v_ -5 -4 -3 -2 -1 0 1 2 3 4 5 -u_ -5 -4 -3 -2 -1 0 1 2 3 4 5 -3_ -5 -4 -3 -2 -1 0 1 2 3 4 5 ul0ft, sIff – & 213

24.3 kmng oGqaf6 bO' { rnoS' t /v] Lo ;dLs/0fdf rn /flzsf] ;DaGw (Relation of Simultaneous Equaiton in Two Variables from Function Machine) tnsf ljm| ofsnfkx¿ cWoog u/L 5nkmn u/ M -s_ tn lbOPsf] dl] ;gdf 0 /fVbf dl] ;gn] +3 agfP/ lgsfNof] . To:t} 1, 2, 3 /fVbf qmdzM 4, 5, 6 (0,1,2,3) Process +3 (3,4,5,6) lgsfNof] . oxf“ Input = {0.1, 2, 3} / Output = {3, 4, 5, 6} xG' 5 . oxf“ s] kl| jm| ofn] ubf{ dl] ;gn] Inputs (0, 1, 2, 3 ) nfO{ Outputs (3, 4, 5, 6) agfP xfn] f < oxf“, d]l;gn] u/]sf] sfo{ x]/f}“ M 0+3 = 3 1+3 = 4 2+3 = 5 3+3 = 6 ;a} Input df 3 hf8] b\\ f output cfp“5 . oxL hf]8\\g] lj|mofnfO{ d]l;gsf] k|lj|mof elgG5 . d]l;gdf /fvs] f] cªs\\ nfO{ nufgL (input) elgG5 . dl] ;gn] lbOPsf] cªs\\ nfO{ pTkfbg (output) elgG5 . dflysf] ljm| ofsnfkdf (input) nfO{ x n] hgfpg] xf] eg] pTkfbg (output) nfO{ y n] hgfcf}“ . ca bO' { rnoS' t ;dLs/0f ca, y = x + 3 xG' 5, hxf“ x / y b'j} rn /fzL x'g\\ . dflysf] ljm| ofsnfknfO{ tflnsf agfP/ klg bv] fpg ;lsG5 . h:t} M x0 1 2 3 x y = x+3 y y3 4 5 6 0 3 To:t} dflysf] ljm| ofsnfknfO{ Arrow lrxg\\ lbP/ 1 4 bO' { ;dx\" input nfO{ x / output nfO{ y agfP/ 2 5 klg b]vfpg ;lsG5 . h:t} M 3 6 214 ul0ft, sIff – &

pbfx/0f 1 lrqdf bv] fOPsf] kmng oGqdf output s] xG' 5 < (2,3,4) ;dfwfg oxf,“ Input df 2, 3, 4 5g\\ . Process dl] ;gn] 2 u0' ff jf x 2 agfP/ output lbG5 . ×2 2 nfO{ 2 n] u0' ff ubf{ 4 x'G5 . To;}n] 2 sf] output 4 x'G5 . 3 sf] output 3x2 = 6 xG' 5(4.,6,8) 4 sf] output 4x2 = 8 x'G5 . ctM output x¿ 4, 6, 8 x'g\\ . pbfx/0f 2 tn lbOPsf] Arrow lrqaf6 kmng oGqsf] kl| j|mofnfO{ x / y sf] ;DaGwsf] ¿kdf n]v . ;dfwfg M oxf,“ Input 2 lbb“ f output 5 aGof] . x y To:t} Input 3 ubf{ output 8 aGof] 2 5 logLx¿larsf] ;DaGw x/] f,“} 3 8 5 14 5=2x3-1 8 = 3 x 3 -1 14 = 5 x 3 - 1 ;a} Input x¿nfO{ 3 n] u0' fg u//] 1 36fOPsf] 5 . To;n} ,] y =3x - 1 x'G5 . cEof; 24.3 1. tnsf kT| os] kmng oGqdf 1 bl] v 5 ;Ddsf ;ªV\\ ofx¿ /fVbf cfpg] kl| tkmn (output) nfO{ tflnsf agfO{ JoSt u/ M -s_ (x) -v_ (x) -u_ (x) Process Process Process +5 x3 x7 (y) (y) (y) ul0ft, sIff – & 215

-3_ -ª_ (x) -r_ (x) (y) Process (x) x2 Process Process x3+2 x4-1 (y) (y) 2. kZ| g g=+ 1 df Input u/s] f] ;ªV\\ ofnfO{ x / kl| tkmn (output) nfO{ y dfg/] x / y larsf] ;DaGw ul0ftLo efiffdf n]v]/ b]vfpm . 3. kZ| g g=+ 1 sf] ;DaGwnfO{ Arrow lrq lvr]/ b]vfpm . 4. Input / output sf] cfwf/df vfnL 7fpd“ f ldNg] ;ªV\\ of /fv M -s_ Inputs 1 23 4 5 8 10 15 Outputs 3 45 6 ? ? 12 ? -v_ Inputs 2 34 6 9 12 Outputs 0 12 ? ? 10 -u_ Inputs 4 56 1 2 39 10 8 10 12 ? ? Outputs 2 34 6 5 ? 18 ? 7 10 13 ? ? -3_ Inputs 7 Outputs ? -ª_ Inputs 1 23 ? 5 ?7 8 4 8 12 16 20 24 28 ? Outputs 5. lbOPsf] ;DaGwdf 1 bl] v 5 ;Ddsf ;ªV\\ of Input (x) u/L cfpg] output (y) kQf nufpm M -s_ y = x + 1 -v_ y = x + 4 -u_ y = x + 7 -3_ y = 3x -ª_ y = 4x -r_ y = 2x + 3 -5_ y = 4x + 1 -h_ y = 5x - 2 216 ul0ft, sIff – &

24.4 bO' { rnoS' t /v] Lo ;dLs/0fsf] nv] flrq (Graph of Simultaneous Equation in Two Variables.) tnsf ljm| ofsnfk cWoog u/L 5nkmn u/ M O 1. rty' fz+{ x¿ (Qudrants) A (x,y) = (3,4) lbOPsf] lrqdf XOX' / YOY' cfk;df nDa xg' ] u/L O laGb'df sfl6Psf 5g\\ . O XOX' nfO{ X- cIf elgG5 eg] YOY' nfO{ Y- cIf A(-2,4) C(2,5) elgG5 . XOX' / YOY' sfl6Psf] laGb' O nfO{ pbu\\ d laGb' elgG5 . O D(3,-5) XX' / YY' n] cfk;df af8“ b\\ f rf/cf6] f rty' fz+{ x¿ aG5 . B(-3,-3) XOY nfO{ klxnf] rt'yf{+z elgG5 . X'OY nfO{ bf];|f] rt'yf{+z elgG5 . X'OY' nfO{ t];|f] rt'yf{+z elgG5 . Y'OX nfO{ rf}yf] rt'yf{+z elgG5 . 2. jm| dhf8] f (Orderd of Pairs) laGb' (3,4) nfO{ nv] flrqdf bv] fpb“ f, pbu\\ d laGba' f6 X- cIflt/ t;] f| ] b/' L / Y- cIflt/ 7f8f] b/' L hgfpg] sg' } laGb' A sf] hf8] LnfO{ A(x,y) sf] ¿kdf b]lvG5 . A(x,y) nfO{ j|mdhf]8f elgG5 . h:t} M laGb' A pbu\\ d laGba' f6 X- cIfsf] bfof“ (+3) PsfO / Y- cIfsf] 7f8f] /v] fdf (+4) PsfO b/' Ldf k5g{ \\ eg] o;nfO{ A(3,4) n]lvG5 . OX df 3 PsfO pbu\\ d laGba' f6 bfof“ / OX df 4 PsfO 7f8f] nDa xg' ] /v] f OY sf] laGb' g} xfdLnfO{ rflxPsf] laGb' xf] . pbfx/0f 1 laGbx' ¿ (2,5), (-2, 4), (-3,-3) / (3,-5) nfO{ nv] flrqdf bv] fpm M dflysf] nv] flrqdf, -s_ (-2, 4) nfO{ nv] flrqdf bv] fpb“ f OX' -2 PsfO afofd“ f hfpm / ToxLa“ f6 4 ul0ft, sIff – & 217

PsfO 7f8f] OY ;u“ ;dfgfGt/ agfO{ hfpm . To; laGbn' fO{ A gfd b]pm . -v_ (-3, -3) df klg -3 PsfO afof“ OX' df hfpm . To;kl5 -3 PsfO tn hfpm . To; laGb'nfO{ B gfd b]pm . -u_ laGb' (2,5) df klg 2 PsfO pbu\\ d laGba' f6 bfof“ OX lt/ hfpm . 5 PsfO 7f8f] hfpm / To; laGbn' fO{ C gfd b]pm . -3_ laGb' (3, -5) df klg 3 PsfO pbu\\ d laGba' f6 bfof“ OX lt/ hfpm . -5 PsfO tn OY' lt/ hfpm / To; laGbn' fO{ D gfd b]pm . pbfx/0f 2 nv] flrqdf lbOPsf] laGbx' ¿ A, B, C / D sf] lgbz{] fªs\\ kQf nufpm M B A O C -s_ pbu\\ d laGb' O af6 XX' sf] bfof“ laGb' A ;Ddsf] b/' L 1 PsfO / pbu\\ d laGba' f6 laGb' A sf] YY' sf] 7f8f] /v] f;Ddsf] b/' L 2 PsfO 5 . To;}n] laGb' A sf] lgbz{] fªs\\ A(x,y) = A(1,2) x'G5 . -v_ ‘s’ df h:t} u/L laGb' B sf] lgbz{] fªs\\ B(x,y) = B(-3, 4) x'G5 . -u_ To;} u/L C laGbs' f] lgbz{] fªs\\ C(x,y) = C(-2,-5) x'G5 . -3_ To;} u/L laGb' D sf] lgbz{] fªs\\ D(x,y) = D(3,-3) xG' 5 . 218 ul0ft, sIff – &

3. bO' { rnoS' t /v] Lo ;dLs/0fsf] nv] flrq (Graph of Simultaneous Equation in Two Variables) tnsf] ljm| ofsnfk cWoog u/L 5nkmn u/ M dfgf“} sg' } bO' { rnoS' t ;dLs/0f y = x + 1 5 . -s_ o;af6 x / y sf dfgx¿sf] tflnsf agfpm M x0 1 23 4 y1 2 34 5 oxf“ x sf] ;b:odf 1 hf8] b\\ f y sf] ;b:o cfp“5 . ;dx\" x df hg' ;s' } cªs\\ /fVg ;lsG5 t/ x sf] ;dx\" g} lbOPsf] 5 eg] ToxL ;dx\" sf ;b:o dfq /fVg'k5{ . To;}n] ;d\"x y sf ;b:o ;dx\" x df ePsf ;b:odf lge{/ ub{5g\\ . ctM ;dx' X sf ;b:onfO{ :jtGq (3,4) (4,5) rn /flz (independent variables) / ;dx\" Y sf ;b:onfO{ (2,3) k/fwLg rn /flz (dependent (0,1) (1,2) variables) elgG5 . O ca, y = x + 1 ;DaGwdf, x sf] dfg 0 /fVbf y sf] dfg 1 x'G5 . oxf,“ y sf] dfg 1 xg' klxnf x sf] dfg 0 x'g'k5{ . cGoyf y sf] dfg 1 xg' ;Sbg} g\\ . dflysf] tflnsfaf6 ags] f jm| dhf8] fx¿ jm| dzM nv] M (0,1), (1,2), (2,3), (3,4), (4,5) x'g\\ . -v_ dflysf jm| dhf8] fnfO{ nv] flrqdf k:| tt' u//] bv] fpm . pbfx/0f 3 y = 2x ;DaGwnfO{ input (x) 0 bl] v 4 ;Dd /fvL output (y) lgsfNbf aGg] jm| dhf8] fnfO{ nv] flrqdf b]vfpm . ;dfwfg oxf“ y= 2x nfO{ tflnsf agfpm M x0 1 2 3 4 y0 2 4 6 8 ul0ft, sIff – & 219

pSt tflnsfnfO{ nv] flrqdf bv] fpb“ f, (4,8) (3,6) (2,4) (1,2) cEof; 24.4 1. tnsf laGbx' ¿nfO{ nv] flrqdf bv] fpm M -s_ A(3,2) -v_ B(-2,3) -u_ C(-5,2) -3_ D(-3,-4) -ª_ E(-6,-1) -r_ F(0,6) -5_ G(-5,0) -h_ H(5,-2) -em_ I(4,1) -`_ J(6,-6) 2. tn nv] flrqdf lbOPsf laGbx' ¿sf lgbz{] fªs\\ kQf nufpm M D B C A J E F H I G 3. tnsf ;DaGwdf input (x) 0 bl] v 5 ;Dd /fvL nv] flrqdf k:| tt' u/ M -s_ y = x + 3 -v_ y = x - 2 -u_ y = 2x -3_ y = 3x -ª_ y = 2x + 1 -r_ y = 3x - 1 -5_ y = 2x -3 -h_ y = 2x + 3 -em_ y = x + 8 -`_ y = 4x - 1 220 ul0ft, sIff – &

pQ/dfnf cEof; 1.1 ;a} pQ/ lzIfsnfO{ bv] fpm . cEof; 1.2 ;a} pQ/ lzIfsnfO{ b]vfpm . cEof; 1.3 ;a} pQ/ lzIfsnfO{ bv] fpm . cEof; 1.4 1. -s_ a = 1200, x =600, y = 1200 -v_ x =450, y = 300 -u_ x = 200, -3_ x = 450, a = 450, z = 450, y = 1350 2. pQ/ lzIfsnfO{ bv] fpm . cEof; 2.1 pQ/ lzIfsnfO{ b]vfpm . cEof; 2.2 1. -s_ x'G5g\\ -v_ x'“b}gg\\ -u_ x“'b}gg\\ -3_ ldNb}gg\\ 2. -s_ ;Ddv' eh' fx¿ a/fa/ xG' 5g\\ . -v_ ljs0fx{ ¿ cfk;df ;dlåeflht xG' 5g\\ . 3. pQ/ lzIfsnfO{ b]vfpm .4. pQ/ lzIfsnfO{ bv] fpm . 5. pQ/ lzIfsnfO{ bv] fpm . cEof; 2.3 pQ/ lzIfsnfO{ bv] fpm . cEof; 2. 4 1. -s_ 600 -v_ 900 -u_ 1080 -3_ 1200 -ª_ 1350 -r_ 1400 -5_ 1440 -h_ 1500 2. -s_1200 -v_ 900 -u_ 720 -3_ 600 -ª_ 450 -r_ 400 -5_ 360 -h_ 300 3. -s_ 500 -v_ 1130 -u_ 850 -3_ 2350 -ª_ 720 -r_1100 -5_ 1100 -h_ 980 -em_ 600 4. -s_ 1800 -v_ 1200 -u_ 1200 -3_ 600 -ª_ 600 -r_ 5 -5_ aflx/L sf0] f = leqL cgf;Gg sf0] fsf] ofu] -h_ Y + Z -em_ QYZ ;“u cEof; 3.1 -s_ 1. ;d¿k 5 2. ;d¿k 5 3. 5g} g\\ 4. 5g\\ 5. 5g} g\\ 6. 5g\\ 7. 5g} g\\ -v_ 1. 5g\\ 2. 5g} g\\ 3. 5g\\ 4. 5g} g\\ 5. 5g\\ 6. 5g} g\\ 7. 5g\\ 8. 5g\\ -u_ pQ/ lzIfsnfO{ bv] fpm . -3_ pQ/ lzIfsnfO{ bv] fpm . -ª_ pQ/ lzIfsnfO{ bv] fpm . -r_ 1. x'“b}gg\\ 2. xG' 5g\\ 3. x'G5g\\ 4. xb“' g} g\\ 5. xb“' g} g\\ 6. xb“ g} g\\ -5_ lzIfsnfO{ bv] fpm . cEof; 4.1 1. pQ/ lzIfsnfO{ b]vfpm . ul0ft, sIff – & 221

2. pQ/ lzIfsnfO{ bv] fpm . 3. jT[ tsf] sG] b| laGbb' l] v kl/lw;Ddsf] b/' LnfO{ cwJ{ of; elgG5 . lrq lzIfsnfO{ bv] fpm . 4. jT[ tsf] cwJ{ of; egs] f] sG] bl| aGbb' l] v kl/lw;Ddsf] b/' L jf nDafO xf] eg] Jof; egs] f] sG] bl| aGb' eP/ hfg] hLjf xf] . lrq lzIfsnfO{ bv] fpm . jT[ tsf] Jof; ;w“} cwJ{ of;sf] bfA] a/ xG' 5 . 5. hLjf kl/lwsf sg' } bO' { laGbx' ¿ hf8] g\\ ] /v] f xf] t/ cwJ{ of; jT[ tsf] sG] bl| aGbb' l] v kl/lw;Ddsf] b/' L xf] . lrq lzIfsnfO{ bv] fpm . 6. ;a} hLjf Jof; x'g ;Sbg} g\\ . j[Ttsf] s]Gbl| aGb' eP/ hfg] hLjf dfq Jof; x'G5 . 7. pQ/ lzIfsnfO{ bv] fpm . ko| fu] fTds sfo{ lzIfsnfO{ bv] fpm . cEof; 5.1 pQ/ lzIfsnfO{ bv] fpm . cEof; 6.1 1. A(-5, 8) , B(-5, -5) , C(7, -5), D(-2 , 0) , E(4, 0), F(-5,-8) 2. lqe'h M A(3, 4) , B(-1, -2) , C(4, -2), cfot M D(-3, -6) , E(-3, -9) F(4, -9), G(4, -6) ju{ M P(-9, 4), Q(-9, -3), R(-3,-3), S(-3,-4)\\ 3. pQ/ lzIfsnfO{ bv] fpm . 4. pQ/ lzIfsnfO{ b]vfpm . cEof; 6.2 1. pQ/ lzIfsnfO{ bv] fpm . 2. E / P, A / S, G / H tyf Q / B 3. Q / G, F / H, R / E, B / S 4. nv] flrq lzIfsnfO{ bv] fpm . -s_ lqeh' -v_ cfot -u_ gk] fnsf] /fli6o« emG8f 5. -s_ R (2,0) -v_ PQ = 10 PsfO 6. -s_ nv] flrq lzIfsnfO{ bv] fpm -v_ nv] flrq lzIfsnfO{ bv] fpm, laGb' J sf] lgbz{] fªs\\ J(5, 5) x'G5 . cEof; 7.1 1. pQ/ lzIfsnfO{ b]vfpm . 2. -s_ 52cm -v_ 72cm -u_ 258cm -3_ 16m 3. -s_ 28m -v_ 224cm 4. 56.25cm 5. 286cm 6. 120m 7. -s_ 20m -v_ 160m 8. -s_ 88m -v_ 352m 9. pQ/ lzIfsnfO{ b]vfpm . cEof; 7.2 1. -s_ 103cm2 -v_ 661.5cm2 -u_ 20cm2 -3_ 9cm2 2. -s_ 102cm2 -v_ 170.12cm2 3. -s_ 216cm2 -v_ 73.5cm2 -u_ 864cm2 4. -s_ l = 12cm -v_ h= 6.73cm 222 ul0ft, sIff – &

5. -s_ 10cm -v_ 30cm 6. -s_ 0.5m -v_ 0.75m2 7. -s_ 50650cm2 -v_ 10625cm2 8= -s_ pQ/ lzIfsnfO{ bv] fpm . -v_ 1032cm2 -u_ 180cm2 -3_ 852cm 9. -s_ 10cm -v_ 412cm2 cEof; 8.1 pQ/ lzIfsnfO{ bv] fpm . cEof; 8.2 1. -s_ 360° -v_ 180° -u_ 90° -3_ 120° -ª_ 270° 2. -s_ 15 ldg6] 36L -v_ 30 ldg6] a9L -u_ 1 306f 36L -3_ 3 306f a9L -ª_ 45 ;]s]G8 36L 3. pQ/ lzIfsnfO{ b]vfpm . 4. pQ/ lzIfsnfO{ b]vfpm . cEof; 8.3 pQ/ lzIfsnfO{ bv] fpm . cEof; 9.1 1. -s_ >0] fL 2 -v_ >0] fL 3 -u_ ;dldlt gx'g] -3_ >0] fL 4 -ª_ >0] fL 6 -r_ >0] fL 2 -5_ >0] fL 4 -h_ >0] fL 2 -em_ >0] fL 3 -`_ >0] fL 6 2. kl/jm| d0fx¿ lzIfsnfO{ bv] fpm . -s_ >0] fL 1 -v_ >0] fL 1 -u_ >0] fL 1 -3_ >0] fL 2 -ª_ >0] fL 2 -r_ >0] fL 2 3. /v] Lo ;dldlt lzIfsnfO{ bv] fpm . -s_ >0] fL 1 -v_ >0] fL 2 -u_ >0] fL 2 -3_ >0] fL 2 cEof; 9.2 1. axe' h' sf 9fr“ fx¿ lzIfsnfO{ bv] fpm . 2. -s_ lqeh' -v_ lqeh' / ;dfgfGt/ rte' h{' -u_ lqeh' , ju{ / if6e\\ h' -3_ lqe'h, if6e\\ h' , ;dnDa rte+'{h -ª_ lqeh' , ju{ / if6e\\ h' 3. lzIfsnfO{ bv] fpm . 4. lzIfsnfO{ bv] fpm . 5. lzIfsnfO{ bv] fpm . 6. 3 ks| f/sf . kl/efiff / pbfx/0f lzIfsnfO{ bv] fpm . 7. lzIfsnfO{ bv] fpm . cEof; 10.1 1. -s_ klZrd -v_ blIf0f klZrd -u_ ldNbg} . -3_ pQ/ lzIfsnfO{ bv] fpm . 2. -s_ pQ/ klZrd -v_ kj\" { blIf0f -u_ blIf0f klZrd -3_ pQ/ kj\" { -ª_ pQ/ lzIfsnfO{ bv] fpm . 3. -s_ pQ/ -v_ k\"j{ blIf0f -u_ klZrd -3_ pQ/ kj\" { 4. pQ/ lzIfsnfO{ bv] fpm . cEof; 10.2 1. lrq lzIfsnfO{ bv] fpm . 2. lrq lzIfsnfO{ bv] fpm . 3. 180 m 4. 52.5 m 5. 3.75 m 6. pQ/ lzIfsnfO{ b]vfpm . ul0ft, sIff – & 223

cEof; 11.1 1. pQ/ lzIfsnfO{ bv] fpm . 2. U = {30 ;Ddsf k0\" f{ ;ªV\\ ofx¿sf] ;d\"x} 3. U = {12 ;Ddsf kf| sl[ ts ;ªV\\ ofx¿sf] ;dx\" } cEof; 11.2 1. -s_ bl] v -3_ ;Dd pQ/ lzIfsnfO{ bv] fpm . -ª_ 64 cf6] f 2. bl] v 6. ;Dd pQ/ lzIfsnfO{ b]vfpm . 7. pQ/ lzIfsnfO{ bv] fpm . pk;dx\" sf] ;ª\\Vof = 2n cEof; 11.3 1. pQ/ lzIfsnfO{ b]vfpm . 2. eg] lrq lzIfsnfO{ bv] fpm . 3. pQ/ lzIfsnfO{ b]vfpm . cEof; 11.4 1. -s_ A / B cnlUuPsf ;dx\" x¿ -v_ A / C cnlUuPsf ;dx\" x¿ -u_ B / C vlK6Psf ;dx\" x¿ -3_ A / D vlK6Psf ;d\"xx¿ -ª_ A / E vlK6Psf ;dx\" x¿ -r_ B / D vlK6Psf ;dx\" x¿ -5_ B / E vlK6Psf ;dx\" x¿ -h_ C / D vlK6Psf ;dx\" x¿ -em_ C / E vlK6Psf ;dx\" x¿ 2. -s_ B = [ 1, 2, 3, 4, 5,6, 7, 8, 9, 10, 11 ] -v_ C = [ 0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20 } -u_ D = { 1, 3, 5, 7, 9 } -3_ E = { 1, 2, 5, 10 } -ª_ -c_ vlK6Psf = B / C, B / D, B / E, C / E -cf_ cnlUuPsf = C / D 3. pQ/ lzIfsnfO{ b]vfpm . cEof; 11.5 1. eg] lrq lzIfsnfO{ bv] fpm . 2. -s_ U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}, A = {2, 4, 6, 8,10,12}, B = {1, 3, 5, 7, 9, 11} -v_ -c_ A U B = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12} -c_ B U A = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12} -O_ B U B = {1, 3, 5, 7, 9, 11} -O_{ A U A = {2, 4, 6, 8, 10, 12} -u_ kd| fl0ft u//] lzIfsnfO{ bv] fpm . 3. -s_ eg] lrq lzIfsnfO{ bv] fpm . -v_ kd| fl0ft u//] lzIfsnfO{ bv] fpm . 4. -s_ M = {1, 2, 4, 8} -v_ eg] lrq lzIfsnfO{ bv] fpm . -u_ M U N = {1, 2, 4, 8 } -3_ ;lsG5 . kd| fl0ft u//] lzIfsnfO{ bv] fpm . 224 ul0ft, sIff – &

5. -s_ eg] lrq lzIfsnfO{ bv] fpm . -v_ ;lsG5 . kd| fl0ft u//] lzIfsnfO{ bv] fpm . cEof; 11.6 1. -s_ A ∩ B = { d, e, f, } -v_ B ∩ A = { d, e, f, } -u_ A ∩ A = { a, b, c, d, e, f } -3_ U ∩ A = { a, b, c, d, e, f } -ª_ U ∩ B = { d, e, f, g, h , i } 2. -s_ A ∩ B = { 1, 2, 3 } eg] lrq lzIfsnfO{ bv] fpm . 3. -s_ A ∩ B = { 3, 9 } -v_ B ∩ C = { 6 } -u_ A ∩ C = { } eg] lrq lzIfsnfO{ bv] fpm . 4. P ∩ Q = { a, b, c } eg] lrq lzIfsnfO{ bv] fpm . 5. -s_ eg] lrq lzIfsnfO{ bv] fpm . -v_ M ∩ N = { 2, 4, 8 } -u_ ;lsG5 . kd| fl0ft u//] lzIfsnfO{ bv] fpm . cEof; 12.1 -s_ 1. 8 2. 14 3. 18 4. 20 5. 35 6. 54 7. 75 8. 108 9. 143 10. 196 11. 168 12. 125 2. 144 -v_ 1. 64 3. 225 4. 361 5. 625 6. 5929 7. 9025 8. 10000 9. 42025 10. 250000 5. 99 6. 105 7. 309 8. 408 9. 804 10. 1012 -u_ 1. 13 2. 25 3. 48 4. 94 -3_ 12 25 35 46 80 1. 13 2. 32 3. 54 4. 45 5. 27 -ª_ 1. 400m2 2. 25m -u_ 2197 -h_ 91,125 cEof; 12.2 -u_ 7 1. -s_ 216 -v_ 1331 -3_ 3375 -ª_ 5832 -r_ 13824 -5_ 27000 -em_ 5,12,000 -`_ 10,00,000 2. -s_ 2 -v_ 5 -3_ 10 -ª_ 15 3. 1728m3 4. 91,125m3 5. 15,625m3 6. 16m 7. 40m cEof; 12.3 1. -s_ 3 -v_ 2 -u_ 3 -3_ 3 -ª_ 6 -r_ 9 -5_ 7 -h_ 4 -em_ 5 -`_ 2 2. -s_ 6 -v_ 6 -u_ 10 -3_ 5 -ª_ 16 -r_ 12 -5_ 18 -h_ 3 -em_ 5 3. 9 4. 25 hgf ljBfyL,{ 5 cf6] f ;G' tnf, 6 cf6] f df;} d / 9 cf6] f cDaf 5. 10 hgf, 8 cf6] f sDan, 9 :jL6/ / 12 Kofs]6 6. 12 cEof; 12.4 1. -s_ 144 -v_ 60 -u_ 144 -3_ 245 -ª_ 300 -r_ 600 -5_ 168 -h_ 216 -em_ 44520 -`_ 1200 2. 720 3. 7560 cm 4. 75 6. lzIfsnfO{ bv] fpm . 5. 185 ul0ft, sIff – & 225

cEof; 12.5 1. -s_ 10112 -v_ 110012 -u_ 10011112 -3_ 11010002 -ª_ 111110102 -3_ 21 -ª_ 25 -r_ 31 -5_ 51 -h_ 32 -em_ 67 -`_ 121 -r_ 101101110 2 2. -s_ 3 -v_ 5 -u_ 7 3. -s_ 415 -v_ 2105 -u_ 422 -3_ 10100 -ª_ 14003 -r_ 104100 4. -s_ 11 5 5 5 5 -v_ 19 -u_ 38 -3_ 98 -ª_ 283 -r_ 194 cEof; 13.1 1. ;ªV\\ of /v] f lzIfsnfO{ bv] fpm . 1. -s_ (+7) -v_ (+3) -u_ (-3) -3_ (-7) -ª_ (-8) -r_ (+4) -5_ (+8) -h_ (+2) -em_ (+2) -`_ -2 2. -s_ (+5), (-15) -v_ (+7, -13) -u_ (+10), (-10) -3_ (+14), (-6) -ª_ (+17), (-3) -r_ (20), 0 3. -s_ (-4) -v_ (-1) -u_ (+3) -3_ (+5) -ª_ 0 -r_ (-7) 4. -s_ 6 -v_ 4 -u_ 10 -3_ 3 -ª_ 5 -r_ 7 5. -s_ 13 -v_ 7 -u_ -6 -3_ 4 -ª_ 8 -r_ 0 -5_ -11 -h_ -30 6. -s_ (+49) -v_ 0 -u_ (+30) -3_ (+41) -ª_ (-32) 7. (-50) 8. (-15) 9. gfkmf ?= 71 10. 266km. 11. -296 12. -s_ +47 -v_ +108 13. -s_ (-7) -v_ (+7) 14. -s_ -27 -v_ -40 cEof; 13.2 1. -s_ (+25) -v_ (-40) -u_ (-56) -3_ (+72) -ª_ (+120) -r_ (-336) -5_ (-192) -h_ (-140) -em_ (+144) -`_ (-480) 2. -s= (+210) -v_ (+105) -u_ (-27) -3_ (-120) -ª_ (-336) 3. -s= (+72) -v_ (-150) -u_ (-126) -3_ (+180) -ª_ (+288) 4. -s_ (+5) -v_ (-5) -u_ (-8) -3_ (-5) -ª_ (+5) -r_ (+6) 5. (+7) 6. (+12) 7. (-16) 8. (+8) 9. (-15) 10. (+4) cEof; 13.3 1. -s_ 29 -v_ -360 -u_ 78 -3_ 424 -ª_ 5 2. 37 3. 83 4. 15 5. 18 cEof; 14.1 -v_ x'g\\ -u_ xg' \\ -3_ xf] -ª_ xfO] gg\\ 1. -s_ x'g\\ -v_ cGTo -u_ kg' /fjt[ -3_ cGTo -ª_ k'g/fj[t 2. -s_ cGTo -5_ cGTo -h_ cGTolxt -em_ k'g/fs[t -`_ cGTo -r_ cGTo 3. -s_ 2 , 5 -v_ -u_ -3_ -ª_ 52 4. pQ/ lzIfsnfO{ b]vfpm . 226 ul0ft, sIff – &

cEof; 15.1 1. -s_ cgk' flts -v_ cgfgk' flts -u_ cgfg'kflts -3_ cgk' flts -5_ cgk' flts -h_ cgk' flts -ª_ cgk' flts -r_ cgk' flts -em_ cgk' flts 2. xfO] gg\\ . 3. xfO] gg\\ . 4. xg' \\ . cEof; 16.1 1. efu 2. 4 efu s6] f 3 efu s]6L 3. 1 efu / ?= 900 4. vfgfdf 5. 150 10 6. ?= 562.50 7. ?= 3,00,000 8. 3500 nL6/ 9. 100 lbg cEof; 16.2 -v_ 7.4 -u_ 4.431 -3_ 16.982 -ª_ 1.6975 1. -s_ 14.5168 -5_ 1.735 -h_ 10 -em_ 51.6375 -`_ 66.73 -r_ 41.54 2. 388.18125 cm2 3. 76.5m 4. 276m 5. 60.5 m 6. 3. 2.m 7. 75 cf6] f cEof; 17.1 1. -s_ 2 -v_ 14.85 -u_ 448kg -3_ 525l -ª_ 1170 hgf -u_ 60% -3_ 20% -ª_ 5% 2. -s_ 33.33% -v_ 50% 3. 60%, 40% 4. 64%, 36% 5. 675 cª\\s 6. ?= 10,200 7. 25% 2 8. ?= 6,642 9. ?= 20,000 3 cEof; 17.2 1. -s_ 1 -v_ ?= 3 -u_ 27 -3_ 1 -ª_ 1 20 4 100 6 4 2. 1: 5 3. ?. 100 / ?= 150 4. 108 5. ?= 10,000 6. -s_ 12 -v_ 3 -u_ 27 -3_ 5 -ª_ 60 7. 16 hgf 10. 60 lbg 8. ?. 3000 9. 240 km cEof; 18.1 1. -s_ gfkmf 10% -v_ gfS] ;fg 10% -u_ gfkmf 30% -3_ gf]S;fg 25% -ª_ gfkmf 25% 2. ?= 4345 3. 25% 4. ?= 1105 5. 4% gf]S;fg 6. ? 18400 7. 23.2% 8. ?= 1200 9. ?= 1750, ?= 1837.5 10. ?= 6000 cEof; 19.1 1. -s_ k|ToIf kl/jt{g -v_ k|ToIf kl/jt{g -u_ ck|ToIf kl/jt{g -3_ ck|ToIf kl/jt{g -ª_ k|ToIf kl/jt{g 2. ? 200 3. ?= 60 4. ?= 24,000 5. 3 ln6/ 6. 75 kg. 7. 4 lbg 8. 30 lbg 9. 12 306f 10. 37.5 lbg 11. 28 lbg cEof; 20 -u_ ?=360 -3_ ?=233.33 1. -s_ ?= 45 -v_ ?= 270 ul0ft, sIff – & 227

2. -s_ 3% -v_ 5% -u_ 22.22% 3. -s_ 2 jif{ 6 dlxgf -v_ 2 jif{ -u_ 3 jif{ 4. -s_ ?= 400 -v_ ?=1,000 -u_ ?= 6,000 5. ?=700, ?= 2450 6. 10% 7. 2 jif{ 6 dlxgf 8. gfkmf, ?= 240 cEof; 21.1 ;l~rt af/Daf/tf tflnsf lzIfsnfO{ bv] fpm . cEof; 21.2 1. lzIfsnfO{ bv] fpm . 2. -s_ :ofp 50 cf6] f, gf;kftL 45 cf]6f -v_ :ofp 30 cf6] f, gf;kftL 55 cf6] f -u_ a'waf/ ;aeGbf a9L 50 cf]6f / dª\\unaf/ ;aeGbf sd 27 cf6] f :ofp -3_ lzIfsnfO{ b]vfpm . 3. lzIfsnfO{ b]vfpm . 4. lzIfsnfO{ bv] fpm . 5. lzIfsnfO{ bv] fpm . cEof; 21.3 pQ/ lzIfsnfO{ bv] fpm . cEof; 21.4 1. -s_ 6 -v_ 11.2 -u_ 6.33 -3_ 20 -ª_ 65 2. -s_ 5 -v_ 14.32 -u_ 30 -3_ 31.5 -ª_ 93.33 3. -s_ 11.73 -v_ 17.5 -u_ 32.5 -3_ 129.25 -ª_ 92.39 4. 94 cEof; 22.1 1. -s_ lqkbLo -v_ Ps kbLo -u_ b'O{ kbLo -3_ lqkbLo -ª_ lqkbLo -r_ Ps kbLo 2. -s_ l8uL| 3 -v_ l8uL| 5 -u_ l8u|L 7 -3_ l8uL| 12 -ª_ lzIfsnfO{ bv] fpm . cEof; 22.2 1. -s_ 3a2 – 2ab -v_ 2 xy2) -u_ 2 bc -3_ 6mp – 9 np 3 (x3 – 3 ac + 2. -s_ 10x3 + 27x2 – 18x -v_ 23 m2 – 11 -u_ 2y + 21x -15 -3_ 0 3. -s_ x2 + 2xy + y2 6 2m -v_ p2 – 2pq + q2 -u_ m2 – n2 -3_ 9x2 – 25y2 -ª_ 2a3 -3a2b + 2ab2 – 3b3 -r_ 15c2 – 34cd +15d2 -5_ k2/9 – ¼ -h_ 15.5a4 + 38.74a2b2 + 13.52 b4 4. (15p2 – p – 6), 22 5. (10a2 + 25 a2b – 8ab2 – 20b3), 176 6. -s_ 12a2 + 3ab -v_ 6x2 + 13xy -u_ p2 -3_ 2y2 -ª_ 3x2+ 9.5xy + 5y2 -r_ 5.2a+ 2.5b + ab + 13 -5_ 21m2 + 20.75mn + 3.75n2 -h_ 1.5x2 + 5.5xy + 4yz + 2zx + 5y2 228 ul0ft, sIff – &

7. -s_ (20a2 + 3ab - 2b2) m2 -v_ 190m2 8. -s_ (72a2 – 42ab – 24ac + 6bc + 6b2)m2 -v_ 1512m2 cEof; 22.3 1. -s_ 2a - 3b + 6 -v_ 5m3 - 3m2 + 5 -u_ 2x -3_ (m+2) -ª_ (a + 4) -r_ (m-4) -5_ (2y+3) -h_ (4p + 3q) -em_ l2 - 4l – 6 -`_ pQ/ lzIfsnfO{ bv] fpm . 2. -s_ 5x + 4, -v_ A = 335cm2, l = 15cm b = 29cm 3. -s_ l = 6xy, A = 12960cm2 l = 432cm b = 30cm 4. -s_ ?= (x+4) -v_ jf:tljs /sd = ?= 323, dflg;sf] ;ªV\\ of = 17 hgf, kT| os] sf] efudf k/s] f] /sd = ?. 19, 5. -s_ (x- 7) -v_ l = 28m, b = 3m / A = 84m2 cEof; 22.4 1. -s_ (a2 +2a + 1) -v_ b2 + 4b + 4 -u_ c2 – 2c + 1 -3_ c2 - 10c + 25 -ª_ 4p2 + 12pq + 9q2 -r_ 36m2 -60mn + 25n2 2. pQ/ lzIfsnfO{ bv] fpm . 3. -s_ a4 – 6a2y + 9y2 -v_ x2y2 + 2abxy + a2b2 -u_ p4q2 + 2p2q3r + q4r2 -3_ 25p8 + 60p4a + 36a2 -ª_ m4 – 2m + 1/m2 1 -r_ 9q6 + 1 + 36q6 4. -s_ 47 -v_ 49 5. -s_ 146 -v_ 148 6. -s_ 34c2 – 48cd + 40d2 -v_ (15k2 – 172k + 485) 7. -s_ g3 + h3 -v_ x3 + y3-u_ l 3 – m3 8 / 9. kd| fl0ft u//] lzIfsnfO{ bv] fpm . cEof; 23.1 1. -s_ 57 -v_ (-15)4 -u_ (3x)4 -3_ (-64)6 2. -s_ 6 x 6 x 6 -v_ 3 x 3 x 3 x 3 x 3 x 3 x 3 x 3 x 3 x 3 x 3 x 3 x 3 x 3 x 3 -u_ (-6) x (-6) x (-6) x (-6) x (-6) x (-6) x (-6) x (-6) -3_ (2x) x (2x) x (2x) x (2x) x (2x) x (2x) x (2x) -ª_ (-2b) x (-2b) x (-2b) x (-2b) x (-2b) x (-2b) x (-2b) x (-2b) x (-2b) 3. -s_ 102 -v_ 2 x 102 -u_ 5 x 103 -3_ 35 x 104 -ª_ 69 x 106 4. -s_ 200 -v_ 5,00,000 -u_ -15,000 -3_ 1152 -ª_ -625 -r_ 128 5. -s_ 22 ;fgf] / 32 7n' f] -v_ 53 ;fgf] / 35 7n' f] -u_ 42 ;fgf] / 34 7n' f] -3_ 102 ;fgf] / 210 7n' f] -ª_ 0100 ;fgf] / 1001 7n' f] -r_ 28 ;fgf] / 103 7n' f] 6. -s_ 26 -v_ 22 x 53 -u_ 157 x 23 -3_ 26 x 33 -ª_ 28 x 33 x 53 7. -s_ 37 -v_ 512 -u_ x8 -3_ a-1 -ª_ x9 -r_ (-b)8 -5_ q5 -h_ (5x)2 8. -s_ 1 -v_ 2 -u_ 1 -3_ 1 -ª_ 105 -r_ 2 9. -s_ 27 -v_ 425 -u_ 18 -3_ 2 -ª_ 1 ul0ft, sIff – & 229

cEof; 24.1 1. -s_ 12 -v_ 85 -u_ -6 -3_ 2 -ª_ 15 -r_ -5_ 5 6 2. -s_ p = -30 -v_ k = -35 -u_ r = 1.25 -3_ t = 24 3. -s_ ;To -v_ c;To -u_ c;To -3_ ;To 4. -s_ Ps rnoS' t ;dLs/0f -v_ pQ/ lzIfsnfO{ bv] fpm . -u_ 1 -3_ 4 5. 2x + 4 = 28, 5fq = 12 hgf / 5fqf = 16 hgf 6. 5fq = 305 hgf / 5fqf = 250 hgf 7. -s_ gdg' f lrq lzIfsnfO{ b]vfpm . -v_ 4x + 4 = 132 -u_ nDafO = 34m rf8} fO = 32m -3_ Ifq] kmn = 1088m2 8. -s_ nDafO = 20m rf8} fO = 10m -v_ gdg' f lrq lzIfsnfO{ b]vfpm . -u_ 6x + p = 0 -3_ kl/ldlt = 60m 9. -s_ x - 18 = 0 -v_ 12 hgf 10. -s_ 2x +1 = 51 -v_ 25 / 26 11. -s_ 4x - 120 = 0 -v_ 30 cf6] f / 90 cf6] f 12. -s_ 4x - 48 = 0 -v_ 12 / 36 13. -s_ 4x - 20 = 110 -v_ nDafO = 32.5m rf8} fO = 22.5m cEof; 24.2 1. pQ/ lzIfsnfO{ bv] fpm . 2. -s_ al] 7s -v_ al] 7s -u_ al] 7s -3_ l7s -ª_ al] 7s -r_ l7s -5_ al] 7s -h_ l7s 3. -s_ x<1 -v_ x>-1 -u_ x>-3 -3_ x>4 cEof; 24.3 1-5 pQ/ lzIfsnfO{ bv] fpm . cEof; 24.4 1. lzIfsnfO{ bv] fpm . 2. A (1,2), B (5,8) , C (-3,4), D(-5,8), E (-4,0), F (-2,-3), G (-5,-5), H(3,-2), I (1,-6), J(5,0) 3. pQ/ lzIfsnfO{ b]vfpm . 230 ul0ft, sIff – &