=Sekfld ifj{kk 2014 d{kk & 12 oha fo’k; & xf.krle;& 3 ?k.Vs iw.kkZad 100funsZ”k &lHkh Á”u gy djuk vfuok;Z gS & Á”uksa ds vad lEeq[k vafdr gSAÁ”u 1- lgh fodYi pqudj fyf[k, ¼10½1-lehdj.k x+2 y=5 es ;fn x=1 rks y dk eku v½ 3 c½ &3l½ 2 n½ &12- jsf[kd lehdj.k a1 x+b1 y+c1=0 , a2 x+b2 y+c2=0 vf}rh; gy dk ÁfrcU/k gSA

v½ a1a2≠b1b2 c½

a1a2

=b1b2

l½ a1a2

=b1b2

=c1c2 n½

a1a2

=b1b2≠c1c2

3- x−1x dk ;ksT; Áfrykse gS

v½ x+ 1x c½ −x−1x

l½ 1x−x n½ −1x +x

4- x2−4

( x+2 )2 dk U;wure ifjes; :i gksxkA

v½ x−2x+2 c½ x+2x−2

l½ x−1x+2 n½ x+2x−1

5- 9]12 dk r`rh;kuqikr gksxkAv½ 12 c½ 20l½ 16 n½ 246- 6 :10∷ x :25 es x dk eku gksxkAv½ 5 c½ 15l½ 25 n½ 357- oxZ lehdj.k 2 x2+4 x+6=0 es ewyksa dk ;ksxQy gksxkAv½ &2 c½ &4l½ 6 n½ 3

8- oxZ lehdj.k x2+5x+6=0 ds fofoDrdj dk eku gSav½ 1 c½ &1l½ 5 n½ &69- ÁR;{k dj gSv½ vk;dj c½ fcØh dj l½ euksjatu dj n½ bues ls dksbZ ugh10- f”k{kk midj dh Ápfyr nj gSaAv½ 10% c½ 20%

l½ 3% n½ 2%

Á”u 2 fjDr LFkkuksa dh iwfrZ dhft,& ¼5½1-ÁR;sd cgqin ,d -------------------- O;atd gksrk gSA2- a :b dk Áfryksekuqikr --------------- gSA3- og lehdj.k ftles vKkr jkf”k dh /kkr vf/kdre nks gks --------------- dgykrk gSA4- pØo`f) C;kt dk eku lk/kkj.k C;kt ls --------------------- gksrk gSaA5- ;fn nks f=Hkqtksa ds laxr dks.k cjkcj gks]rks os f=Hkqt ------------------ gksrs gSAÁ”u 3- lR; @vlR; fyf[k,& ¼5½1- nks pj okys ,d ?kkr lehdj.k dks jsf[kd lehdj.k dgrs gSA2- HkkT;¿Hkktd× HkkxQy $ “ks’kQy

3- oxZ lehdj.k a x2+bx+c=0 ds ewyksa dk xq.kuQy −ba gksrk

gSA4- euksjatu dj ÁR;{k dj gSA5- ;fn nks f=Hkqt ledksf.kd gks rks f=Hkqt le#i gksxkAÁ”u 4- vfry/kqmÙkjh; Á”u

1- ifjes; O;atd x+2x−2,x−2x−2 dk ;ksx Kkr dhft,

2- oxZ lehdj.k cukus dk lw= tcfd ewyksa dk ;ksxQy ,oa xq.kuQy fn;k gksA3- oxZ lehdj.k es ewy okLrfod vkSj leku dh ÁfrcU/k fy[kks4- ;fn C;kt dh x.kuk N% ekgh dh tkrh gS rks nh xbZ nj dks fdruk xquk djrs gSA

5- f=Hkqt ds {ks=Qy dk gSjks dk lw= fy[kksaAÁ”u 5- dk eku Kkr dhft,] ftuds fy, fudk; ax+ y=5 ,3 x+ y=1 dk ,d vf}rh; gy gks ¼2½Á”u 6- oxZ lehdj.k cukb, ftlds ewy 5] &5 gSA ¼2½Á”u 7- ÁR;{k dj ,oa vÁR;{k dk ds mnkgj.k lfgr fyf[k, ¼2½Á”u 8-le:i f=Hkqtksads vk/kkjHkwr vkuqikfrd Áes; dk dFku fyf[k, ¼2½Á”u 9- le:i f=Hkqtksa ds ifjeki Øe”k% 30 ls-eh- vkSj 20 ls-eh- gS ;fn ,d f=Hkqt dh ,d Hkqtk dh yEckbZ Kkr dhft, ¼2½Á”u 10- fuEu lehdj.k dks ÁfrLFkkiu fof/k ls gy djks 7 x−2 y=1 ,3 x+4 y=15 ¼4½

vFkoklehdj.k x+ y=5 ,

5 x−3 y=1dks oztxq.ku fof/k ls gy djksÁ”u 11- nks la[;k dk ;ksx 7 gSaA ;fn budk ;ksx buds varj dk lkr xquk gks rks la[;k,¡ Kkr dhft, ¼4½ vFkok2 dqlhZ ,oa 3 estksa dk ewY; # 800 gS vkSj 4 dqlhZ rFkk 3 estksa dk ewY; Kkr dhft,A

Á”u 12- ;fn P= X+1X−1 vkSj x−1x+1 rks P+Q Kkr dhft,A ¼4½

vFkok

X3−1X2+2es dksu lk ifjes; O;atd tksMk tk, fd 2x

3−x2+3x2+2 ÁkIr gks

Á”u 13- ;fn ab=cd= ef gks rks fl) dhft, fd

a2+c2+e2

b2+d2+ f 2=a

2

b2 ¼4½

vFkok

;fn xb+c

= yc+a

= za+b rks fl) djks ¿ (b−c ) x+( (−a ) y )+(a−b ) z=0

Á”u 14- leh- 6 x2−13 x+6=0 xq.ku[k.M fof/k ls gy djks ¼4½ vFkoklehdj.k x2−6 x−55=0 lw= fof/k ls gy djksÁ”u 15- ;fn α vkSj β oxZ lehdj.k a x2+b x2+c=0 ds ewy gks rks α 2+ β2 dk eku Kkr dhft, ¼4½ vFkoklehdj.k 2 x2+3 x−p=0 dk P dk eku Kkr djks tcfd lehdj.k ds ewy cjkcj gS Á”u 16- 1000 # ij 3 % Áfro’kZ dh nj ls 2 o’kZ dk feJ/ku Kkr dhft, ¼4½ vFkok40]000 # dh eksVj lk;dy 10 % /klkjs dh nj ls 3 o’kZ ckn eksVj lk;dy dk ewY; rFkk ?klkjk Kkr dajks Á”u 17- ∆ PQR es ∠P=X ,∠Q=3 X vkSj ∠R= y gSA ;fn 3 y−5 x=30 rks ∆ PQR ds ÁR;sd dks.k Kkr dhft, ¼5½ vFkokfdlh ifjes; la[;k ds gj es 5 tksMus vkSj va”k es ls 5 ?kVkus

ij 17 ÁkIr gksrk gSA ;fn va”k es ls 4 ?kVk;k tk;s rks 13 ÁkIr

gksrk gS og la[;k Kkr dhft,Á”u 18- xq.ku[k.M dhft, a2 (b+c )+b2 (c+a )+c2 (a+b )+3abc ¼5½

vFkok

x2−3x+1x+3 es dkSu lk ifjes; O;atd tksMk tk;s fd x

2+1x−2 ÁkIr gks

tk;s

Á”u 19- ;fn x= 4aba+b gks rks fl) djks fd x+2ax−2a+ x+2bx−2b

=2++++++++

¼5½ vFkok abcvkSj d for vuqikr es gks rks fl) dhft,

a2+ab+b2

b2+bc+ c2 =a

c

Á”u 20- ;fn oxZ lehdj.k 2 x2+Px+4=0 dk ewy 1 gks rks nqljk ewy Kkr dhft, vkSj P dk eku Kkr dhft, ¼5½ vFkok x4−35x2+300=0 lehdj.k gy dhft,Á”u 21- 1500 ij 5% Áfr”kr dh nj ls 3 o’kZ dk feJ/ku ,oa pØo`f) C;kt Kkr dhft, ¼5½ vFkok,d flykbZ e”khu # 1600 uxn ;k # 1200 uxn Hkqxrku nsdj “ks’k N% eghus ckn # 460 nsdj feyrh gSA rks fd”r ds vk/kkj ij C;kt dh nj dh x.kuk dhft,Á”u 22- ,d ledks.k f=Hkqt dh ledks.k cukus okyh Hkqtk,¡ ¼ls-eh- es½ x rFkk x+1 gS ;fn f=Hkqt dk {ks=Qy 6 oxZ ls-eh- gS] f=Hkqt dh Hkqtk,¡ Kkr dhft, ¼6½ vFkok

,d la[;k vkSj mlds O;wRde dk ;ksx 507 gS la[;k Kkr dhft,

Á”u 23- # 2000 ij 3 o’kZ ds fy, 5% dh nj ls lk/kkj.k ,oa pØo`f) C;kt es varj Kkr dhft,

¼6½ vFkok,d ?kMh # 960 uxn ;k # 480 vkaf”kd Hkqxrku dj # 245 dh nks ekfld fd”rksa ij nh xbZA fd”r ;kstuk dh C;kt dh nj Kkr dhft,A