111

VqdM+s ;k iwjs \VqdM+s ;k iwjs \VqdM+s ;k iwjs \VqdM+s ;k iwjs \VqdM+s ;k iwjs \

ikB & 8ikB & 8ikB & 8ikB & 8ikB & 8 fdl iw.kZ ds fgLls\fdl iw.kZ ds fgLls\fdl iw.kZ ds fgLls\fdl iw.kZ ds fgLls\fdl iw.kZ ds fgLls\

ifjp; & vk/kkfjr ;kfu fdruk \ iw.kZ vkSj iw.kZ ds VqdM+s & lkjka'kA

ikB & 9ikB & 9ikB & 9ikB & 9ikB & 9 fHkUu dh fdLesafHkUu dh fdLesafHkUu dh fdLesafHkUu dh fdLesafHkUu dh fdLesa

ifjp;&fHkUu dh rLohj cukuk& fHkUuksa dk ekiu ,oa fHkUuksa dk iSekuk & tfVyfHkUu&lkjka'kA

ikB & 10ikB & 10ikB & 10ikB & 10ikB & 10 n'keyon'keyon'keyon'keyon'keyo

ifjp;& fHkUuksa ds fy, nl dk iSekuk& n'keyoksa dk xf.kr & lkjka'kA

bl bdkbZ dh 'kq:vkr ge igsyh ls djrs gSa&

,d xksy cQhZys tes rkykc ds chpksachp ,d igyoku cSBk gS vkSj mls Nyksaxs yxkdj rkykc ls ckgjfudyuk gSA ,d 'krZ gS % igyh Nykax rkykc ds fdukjs rd dh nwjh ls vk/kh ls T;knk ugha gks ldrhAnwljh Nykax igyh Nykax dh nwjh ls vk/kh ls T;knk ugha gks ldrhA ,sls gh] rhljh] pkSFkh NykaxAloky gS % D;k og igyoku cQZ ds fi?kyus ls igys ¼;kfu xfeZ;k¡ vkus ls igys½ rkykc ls ckgj vkldrk gS\ lkspdj ns[kk tk,A igyh Nykax fdukjs ls vk/kh nwjh rd ys vk;sxhA nwljh Nykax ckdhvk/kh nwjh dh vk/kh nwjh rd gksxhA rhljh Nykax cph nwjh dh vkSj vk/kh nwjh rd gksxhA blh rjg pkSFkh]ik¡poha] Nykaxsa-----A lkQ gS] og igyoku dHkh Hkh fdukjs rd ugha igq¡p ik;sxk& xfeZ;ksa esa cQZ fi?kytk,xh vkSj og ikuh esa Mwc tk,xkA

bl igsyh esa [kkl ckr gS % iwjs ds VqdM+ksa dh ckrA blesa igyoku dks nwjh dk vk/kk VqdM+k gh gkflygSA ge VqdM+ksa dks vPNh rjg tkurs gSa & 1@2] 1@3] 2@3] 5@6--- vkfnA budks fHkUu dgk tkrk gSA

vxj dqN iwjk ugha ekStwn gksrk] rc D;k VqdM+s ekStwn gksrs\ vxj iwjk #i;k ugha gksrk] rc D;k vBUuh]poUuh gksrs\ vxj iwjk lsj ugha gksrk] rc D;k iko] v/klsjh] gksrs\ vxj ,sls& ;kfu cktkj dh utj ls&ns[ksa rks yxrk gS tokc gksxk % gk¡] gksrs! vBUuh] poUuh vius esa Hkh iwjs gSa& buls mruk gh dke pyrkgS ftruk iwjs #i;s ls! ;kfu] 1@2] 1@3] 2@3] 5@6--- vkfn fHkUu VqdM+s Hkh gSa] iwjs vad Hkh gSaA cktkjcgqr dqN lqy>krk gSA vkf[kj xf.kr cktkj ls gh mitk Fkk] vkSj vkt Hkh xf.kr ds ukscsy iqjLd`rfo}ku vkt ds cktkj dh my>us lqy>kus esa yxs gSaA

112

ikB&8ikB&8ikB&8ikB&8ikB&8fdl iw.kZ ds fgLlsfdl iw.kZ ds fgLlsfdl iw.kZ ds fgLlsfdl iw.kZ ds fgLlsfdl iw.kZ ds fgLls

ifjp;ifjp;ifjp;ifjp;ifjp;

oSls rks f“Uu la[;kvksa ls cPpkas dk lkeuk jkst+kuk gksrk gS exj vke rkSj ij buds okLrfod vFkZ dksysdj muds fopkj dkQ+h my>s gq, gksrs gSaA mnkgj.k ds rkssSj ij ckrphr eas] tgk¡ okLro easa fgLlk* 'kCndk bLrseky gksuk pkfg,] ogk¡ cPps xyrh ls a^vk/kk* 'kCn dk bLrseky djrs gSaA gesa vk/kk dsd rHkh feyldrk gS tc dsd dks nks cjkcj Hkkxksa esa ckaVk tk,A ijUrq gdhdr esa gj fgLlk gh rdjhcu vk/kk gksrkgSA tc ge vk/kk fdyksxzke pk; [kjhnrs gSa rks] okLro esa geus ,d iSdsV pk; [kjhnh gksrh gSA ;gk¡ dbZcPpksa ds fy, vk/ks dk eryc flQZ ,d yscy gks tkrk gSA vk/ks dks ysdj cPpksa esa ,d vkSj vkexyrQgeh ;g gksrh gS fd vk/kk rHkh feyrk gS tc ,d iw.kZ ¼;kuh ,d iwjh oLrq½ ds fgLls fd, tk,aAos ;g ugha le> ikrs fd ^iw.kZ^] phtksa dk ,d lewg Hkh gks ldrk gSA ,d iwjs dks nks vk/kksa esa ckWaVukcPPkksa ds fy, eqf’dy gksrk gSA vdlj ;g ns[kk tkrk gS fd os nks fgLls djds :dus dh ctk; fgLlsdjrs pys tkrs gSaA os lksprs gSa fd ,d ckj dkVus ls ,d fgLlk feyrk gS vkSj nks ckj dkVus ls nksfgLlsA ;g Hkh ns[kk x;k gSS fd cPps fdlh oLrq] tSls fd dsd ds fgLls djrs oDr nks NksVs VqdM+s fudkyysrs gSa vkSj ,d cM+k fgLlk vfoHkkftr gh NksM+ nsrs gSaA ,slk blfy, gksrk gS D;ksafd vdlj cPpksa esafgLlksa o iw.kZ ds chp laca/k dh le> ugha gksrhA vxj fdlh cPps ds ikl vk/kk Hkkx gksrk gS rks og ;gugha le> ikrk fd nwljk fgLlk Hkh vk/kk gh gksxkA dkj.k ;g gS fd ,slk le>us ds fy, fgLls vkSjiw.kZ ds vkilh laca/k dks le>uk vko’;d gksrk gSA cPPksa ds fopkj my>s gq, D;ksa gksrs gSa \ bl ikBesa geus dqN ,slh f’k{k.k fof/k;ksa ds lq>ko fn, gSa ftuls cPpksa dks bu my>uksa ls ckgj fudyus esa ennfey ldrh gSA

D;k vk/kk lpeqp vk/kk gS\D;k vk/kk lpeqp vk/kk gS\D;k vk/kk lpeqp vk/kk gS\D;k vk/kk lpeqp vk/kk gS\D;k vk/kk lpeqp vk/kk gS\

ml fnu js.kq ds nksuksa cPps] 10 lky dh ehuk vkSj 8 lky dk jfo [kkuk [kk jgs FksA nksuksa dk [kkuk iwjkgks x;k Fkk ysfdu ,d pikrh cp xbZ FkhA js.kq us muls dgk fd mls Hkh vkil esa ckWaVdj [kRe dj nsaAjfo us pikrh yh] ,d dksus ls NksVk lk VqdM+k rksM+dj ehuk dks ns fn;kA eSaus jfo ls iwNk fd mlusviuh cgu dks fdruk fgLlk fn;k gSA mlus csfgpd tokc fn;k ^vk/kk*A

fp=&1 % lksuw ;g yks rqEgkjk vk/kk fxykl nw/kfp=&1 % lksuw ;g yks rqEgkjk vk/kk fxykl nw/kfp=&1 % lksuw ;g yks rqEgkjk vk/kk fxykl nw/kfp=&1 % lksuw ;g yks rqEgkjk vk/kk fxykl nw/kfp=&1 % lksuw ;g yks rqEgkjk vk/kk fxykl nw/k

eSus ,d fcLdqV fy;k vkSj ,d NksVk lk VqdM+k mls nsdj iwNk fd mls fdruk fcLdqV feykA mldktokc ogh Fkk] ^vk/kk^ A ;kfu jfo iwjh pht ds fdlh Hkh VqdM+s dks ^vk/kk^ ekurk gSA

bl vk;q leqg ds cPpksa ds lkFk ;g fnDdr vke ckr gSA iw.kZ dk dksbZ Hkh VqdM+k muds fy;s vk/kk gksrk

113

gSA exj ;g xyrQgeh gksrh D;ksa gS \ ,d otg rks ;g gks ldrh gS fd mUgksaus cpiu esa viuh ekWdks blh <ax ls vk/kh pikrh ;k vk/kk fxykl nw/k nsrs ns[kk gksxk A exj dkSrwgyo'k esa rhljh d{kk ds,d oxZ esa igqap xbZ tgka f’kf{kdk ,u-lh-bZ-vkj-Vh- dh ikB~; iqLrd ls ^fHkUu^ i<+kuk 'kq: djus okyhFkhA mUgksaus fofHkUu vkd`fr;kWa cukbZA ¼fp= 2½

vkÑfr;k¡ cukus ds ckn mUgksaus cPpks ls iwNk fd dkSu lh vkÑfr;k¡ nks cjkcj fgLlksa esa ckaVh xbZ gSa vkSjdkSu lh vkÑfr;k¡ pkj cjkcj fgLlksa esa ckaVh xbZ gSaA vf/kdka’k cPpksa ds mÙkj lgh FksA

rc mUgksaus dqN vkSj vkÑfr;k¡ cukbZA ¼fp= 3½

fp= 3fp= 3fp= 3fp= 3fp= 3

gj vkÑfr nks cjkcj Hkkxksa esa caVh gqbZ FkhA ,d fgLlk Nk;knkj Fkk vkSj nwljk lkQA mUgksaus Nk=ksa dkscrk;k fd gj vkÑfr esa Nk;knkj Hkkx vkSj lkQ Hkkx iwjs dk vk/kk&vk/kk gS rFkk ge gj ,sls fgLls dks^vk/kk^ dgrs gSaA blds ckn mUgksaus ,d dkxt ysdj] mlds nks fdukjksa dks feykrs gq, eksM+dj nks cjkcjfgLlksa esa dkV fn;kA

fQj mUgksaus nks Nk=ksa dks cqyk;k vkSj izR;sd dks ,d&,d VqdM+k ns fn;kA vc mUgksaus iwjh d{kk ls iwNkfd nksuksa Nk=ksa ds ikl fdruk&fdruk dkxt gSA iwjh d{kk us tokc fn;k] ^vk/kk^A rc mUgksaus nksuksaVqdM+s fy, vkSj mUgsa ,d ds Åij ,d j[kdj crk;k fd nksuksa VqdM+s cjkcj gSaA blh <ax ls mUgksaus,d&pkSFkkbZ ¼;k iko½ dh ladYiuk Hkh le>kbZA vUr esa mUgkssaus fdrkc ls dqN loky d{kk esa djus dks

fp= 2fp= 2fp= 2fp= 2fp= 2

fp= 4fp= 4fp= 4fp= 4fp= 4

114

rFkk dqN gkseodZ ds :i esa ns fn,A f’k{kd dkQh larq"V fn[k jgh FkhasA ,slk yxrk Fkk fd os tks dqNdjuk pkgrh Fkha] mls djus esa lQy jghaA ysfdu eq>s FkksM+k lansg FkkA eq>s ;dhu ugha Fkk fd ;g ckrlpeqp cPps le> x, gSa fd fdlh Hkh iwjh pht dk vk/kk izkIr djus ds fy, nks cjkcj Hkkx djus dkegRo D;k gSaA blds vykok ;g le>kuk Hkh t:jh Fkk fd nks cjkcj Hkkx djus ds dbZ rjhds gks ldrsgSaA ;kuh ;g dksbZ t:jh ugha gS fd foHkktd js[kk ljy js[kk gh gksA

eSaus r; fd;k fd izs{k.kksa ds vk/kkj ij dqN ewY;kadu djuk pkfg, rkfd ;g irk yxk;k tk lds fdf’kf{kdk o cPpksa ds chp okLro esa fdruk laokn gqvk gSA nks fnuksa ckn eSa vuhrk ds ?kj pyh xbZA vuhrkesjh lgsyh dh fcfV;k Fkh FkksM+h b/kj&m/kj dh ckrphr ds ckn eSaus vuhrk dks iakp vkÑfr;k¡ fn[kkbZ¼fp=&5½

fp=&5fp=&5fp=&5fp=&5fp=&5

mnkgj.k 1mnkgj.k 1mnkgj.k 1mnkgj.k 1mnkgj.k 1

eSaeSaeSaeSaeSa %%%%% vuhrk tjk crkvks buesa ls dkSu&lh vkÑfr;k¡ nks cjkcj Hkkxksa esa ca¡Vh gS\

vuhrkvuhrkvuhrkvuhrkvuhrk % vkÑfr A, B, vkSj E nks cjkcj fgLlksa esa caWVh gSA vkÑfr C ugha cWaVh gS vkSj D, gka-------- D Hkh nks cjkcj Hkkxksa esa cWaVh gSA

eSaeSaeSaeSaeSa % D;k rqe iDdk dg ldrh gks fd C nks cjkcj Hkkxksa esa ugh caVh gS vkSj E nks cjkcjHkkxksa esa caVh gSA

vuhrkvuhrkvuhrkvuhrkvuhrk % gka] vkUVh] eSa iDdk dg ldrh gw¡A

eSaeSaeSaeSaeSa % vPNkA pyks ge C dh vkÑfr dk ,d dkxt ysrs gSaA eSa bls chp okyh oØ js[kk ijls dkV nsrh gw¡A yks] gekjs ikl nks VqdM+s gks x,A

vc bUgsa ,d ds Åij ,d tek,¡ rks D;k gksxk\

D;k ,d VqdM+k nwljs ij iwjk te tkrk gS\

vuhrkvuhrkvuhrkvuhrkvuhrk % gka vkUVhA

eSaeSaeSaeSaeSa % eryc nksuksa VqdM+s cjkcj gSaA

vuhrkvuhrkvuhrkvuhrkvuhrk % gka] ;s VqdM+s Hkh cjkcj gSA vc eq>s irk py x;k fd vkd`fr C Hkh nks cjkcj Hkkxksa esac¡Vh gSA

115

eq>s cgqr vPNk yxk fd vuhrk us tokc [kqn c [kqn fn;kA vc eSaus vkÑfr E dks fy;kA gkykafdmlds nks Hkkxksa ds chp cgqr T;knk vUrj ugha FkkA exj dkxt dks dkVdj eSa mls le>k ikbZ fd bldsnks Hkkx cjkcj ugha gSaA eSus mlds lkFk fp= &6 esa fn[kkbZ nks vkSj vkÑfr;ksa ds ckjs esa ckrphr dhA

fp=&6fp=&6fp=&6fp=&6fp=&6

vc vuhrk fo’okl ds lkFk lgh tokc ns jgh FkhA

E1) vuhrk dks ,slk D;ksa yxk Fkk fd vuhrk dks ,slk D;ksa yxk Fkk fd vuhrk dks ,slk D;ksa yxk Fkk fd vuhrk dks ,slk D;ksa yxk Fkk fd vuhrk dks ,slk D;ksa yxk Fkk fd C ds nks cjkcj Hkkx ugha fd, x, gSa \ ds nks cjkcj Hkkx ugha fd, x, gSa \ ds nks cjkcj Hkkx ugha fd, x, gSa \ ds nks cjkcj Hkkx ugha fd, x, gSa \ ds nks cjkcj Hkkx ugha fd, x, gSa \

vkÑfr E dks ysdj vuhrk dks tks fnDdr vkbZ] og dksbZ vuks[kh ckr ugha gSA izk;% ;g ns[kk x;k gSfd tc rd nks Hkkxksa ds chp vUrj ,dne Li"V u gks tk, rc rd cPps mUgsa vk/kk gh dgrs gSaA fp=&7dh rhljh vkÑfr rd os nksuksa Hkkxksa dks cjkcj crkrs jgrs gSaA bldk eryc ;g gS fd d{kk esa iw.kZ dsvk/ks dh ckr i<+krs oDr nks cjkcj Hkkx djus ds egRo ij tksj nsuk pkfg,A cPpksa dks ;g Hkh fn[kk;ktkuk pkfg, fd dc nks fgLls lpeqp cjkcj gksrs gSaA bl lanHkZ esa ge ;gka nks xfrfof/k;k¡ ns jgs gSaAf’k{kd bUgsa viuh d{kk esa djok ldrs gSaA

nks Hkkx rc cjkcj gksrs gSa tc ,d dks nwljs ij j[kus ij og iwjk <d tk,Anks Hkkx rc cjkcj gksrs gSa tc ,d dks nwljs ij j[kus ij og iwjk <d tk,Anks Hkkx rc cjkcj gksrs gSa tc ,d dks nwljs ij j[kus ij og iwjk <d tk,Anks Hkkx rc cjkcj gksrs gSa tc ,d dks nwljs ij j[kus ij og iwjk <d tk,Anks Hkkx rc cjkcj gksrs gSa tc ,d dks nwljs ij j[kus ij og iwjk <d tk,A

fp= & 7fp= & 7fp= & 7fp= & 7fp= & 7

xfrfof/k xfrfof/k xfrfof/k xfrfof/k xfrfof/k (i) % % % % % ,d cM+k dkxt vkSj rhu&pkj VqdM+s ysaA cPpksa ls ;g irk yxkus dks dgsa fd dkSu lsVqdM+s cM+s dkxt ds vk/ks gSaA

xfrfof/k xfrfof/k xfrfof/k xfrfof/k xfrfof/k (ii) % % % % % ,d fjcu ysaA nks cPpksa ls dgsa fd os bls vkil esa bl rjg ckaVsa fd nksuksa dks vk/kk&vkèkkfeysA tc os vkil esa ckaV ysa rks muls dfg, fd os tkap djsa fd D;k lpeqp nksuksa fgLls cjkcj gSaA

116

blds vykok Nk=ksa ls fdlh o`Ùk] oxZ ;k f=dks.k ds nks cjkcj Hkkx djus tSlh xfrfof/k djokuh pkfg,Anks cjkcj Hkkx 3&4 vyx&vyx <ax ls djus dks dg ldrs gSaA flQZ o`Ùk] oxZ ;k f=dks.k ds nks fgLlsdjus dk gh vH;kl ugha djokuk pkfg,A cPpksa dks ;g Hkh le>uk pkfg, fd ;fn 10 dkjksa dh nkSM+esa ikap dkjsa vkf[kj rd ugha igq¡prh rks bldk eryc ;g gS fd vk/kh dkjsa vkf[kj rd ugha igq¡phA

'kq:vkr esa vki ,slk mnkgj.k ys ldrs gSa tgk¡ cjkcj caVokjk lEHko gksA tSls& vxj 10 xksfy;k¡ nkscPpksa esa cjkcj&cjkcj cakWVh tk,a rks nksuksa dks xksfy;ksa dk vk/kk&vk/kk Hkkx feykA ;kfu 10 dk vk/kk5-

cPpksa ls 6 ;k 14 'khf’k;ksa ds <Ddu ;k pkWd ;k dksbZ vU; pht ysus dks dgsaA vc muls dgsa fd vk/kh phtsa vyx djsaA vc fdruh pht muds ikl gSa\ bl ij ppkZ djsaA

E1) ,slh nks vkSj xfrfof/k;k¡ crkb, ftuds }kjk ;g irk py lds fd cPps lpeqp bl ckr dksle> x, gSa fd fdlh iwjs dk vk/kk irk yxkus ds fy, nks cjkcj fgLls djuk t:jh gSA

1 1 1, ,

4 3 6 vkfn dh ladYiuk Hkh blh rjg ls i<+kbZ tk ldrh gSA

;gk¡ dqN xfrfof/k;ksa ds lq>ko fn, x, gSa] tks 'kk;n vkidks mi;ksxh yxsaA

mnkgj.k 2 % mnkgj.k 2 % mnkgj.k 2 % mnkgj.k 2 % mnkgj.k 2 % fp=&8 esa fn[kkbZ xbZ fdlh Hkh vkÑfr dk dkxt ysaA

fp=&8fp=&8fp=&8fp=&8fp=&8

bls nks foijhr fdukjs feykrs gq, eksM+ ysaA eksM+ ij vPNs ls nck ysaA vc bls okfil [kksy ysa A vkins[ksaxs fd ,d js[kk }kjk dkxt nks cjkcj fgLlksa esa caV x;k gSA ;kfu ,d&nwljs ds Åij j[ks tkus ij;s fgLls ,d&nwljs dks iwjk&iwjk <ad ysaxsA izR;sd fgLlk iwjs dk vk/kk gSA vc dkxt dks blh rjg,d ckj vkSj eksfM+,A dkxt vc pkj fgLlksa esa caV tk,xkA

bl rjg vki cPpksa dks 1/2, 1/4, 1/8, 1/16 vkfn ls ifjfpr djk ldrs gSaA

1 1 1 1, , ,

2 4 8 16

;g /;ku j[ksa fd oxZ vkSj vk;r dks dbZ <axksa ls vkB Hkkxksa esa ckaVk tk ldrk gSA dqN <ax fp=&10esa fn[kk, x, gSaA

117

cPpksa dks bl izdkj dh xfrfof/k;k¡ vklku o jkspd yxrh gSaA exj bl xfrfof/k }kjk 1

3 fn[kk ikuk

'kk;n muds fy, vklku u gksA ;gka vki cPpksa dh enn dj ldrs gSaA dkxt dks rhu cjkcj Hkkxksa

esa eksM+uk fl[kkdj vki fQj

1

3

1

6

vkfn fn[kk ldrs gSaA

fp=&9fp=&9fp=&9fp=&9fp=&9

vafdr pkSFkh esa i<+rk gS vkSj mls xf.kr esa :fp gSA og xf.kr dk lfØ; Nk= gSA og xf.kr dh dqNfnDdrsa ysdj esjs ikl vk;k FkkA mlls ckr djrs gq, eq>s irk pyk fd mudh d{kk esa fHkUu la[;kvkasdk vH;kl vHkh&vHkh iwjk gqvk gSA rks eSaus lkspk fd D;ksa u mlls dqN loky djokdj ns[kk tk,A eSausdqN vkÑfr;k¡ cukdj mlls iwNk fd izR;sd esa Nk;knkj fgLlk iwjs dk fdruk va’k gS] fHkUu ds :i esafy[kks ¼fp=&10½

fp= 10fp= 10fp= 10fp= 10fp= 10

bldk tokc Fkk ¼d½

3

4

¼[k½

2

5

RkFkk ¼x½

1 1,

4 4

d

[k

x

118

E2) ¼d½ vkids fopkj esa vafdr dh fnDdr D;k Fkh\

¼[k½ D;k ;g cPpksa dh vke fnDdr gS \

¼x½ vki mldh enn dSls djsaxs \

E3) dkxt eksM+dj

1

3

1

6

fn[kkus esa vki cPps dh enn dSls djsaxs \

E4) D;k vki dksbZ ,slh xfrfof/k lq>k ldrs gSa ftlls cPps dks

1

5

ladYiuk le>us esa enn feys\

E5) d{kk esa fHkUu i<+kus ds vius rjhds dh lQyrk dk ewY;kadu vki dSls djsaxs\

Åij dh xbZ ppkZ ls vki le> gh x, gksaxs fd fgLls dks iwjs ds lanHkZ esa ns[k ikuk cPpksa dsfy, ,d vkSj my>u dk fo"k; lkfcr gksrk gSA vxys [k.M esa ge blh leL;k ij xkSj djsaxsA

iw.kZ vkSj mlds fgLlsiw.kZ vkSj mlds fgLlsiw.kZ vkSj mlds fgLlsiw.kZ vkSj mlds fgLlsiw.kZ vkSj mlds fgLls

fHkUu dks le>us esa ,d vM+pu ;g vkrh gS fd bls vyx ls Lora= bdkbZ ds :i esa ugha ns[kk tkldrkA fHkUu dk eryc rHkh gS tc mls ml iwjs ls tksM+dj ns[kk tk, ftldk og Hkkx gSA fdlh phtdk fgLlk le>us ls igys t:jh gS fd ge ml iwjh pht dks tkurs gksa ftldk og fgLlk gSA vki blckr ls rks lger gksaxs fd rhu&pkSFkkbZ ¼ikSu½ dk eryc ;g gS fd fdlh iw.kZ dks pkj cjkcj Hkkxksa esackaVdj muesa ls rhu Hkkx fy, x, gSaA ;k ;g Hkh gks ldrk gS fd lewg esa pkj oLrq,a ;k lnL; Fks ftuesarhu ys fy, x, gSaA ;k FkksM+k vyx :i ls ns[kus ij bldk eryc ;g Hkh gks ldrk gS fd rhu iw.kZdks pkj cjkcj Hkkxksa esa ckaV fn;k x;k gSA bu lkjs rjhdksa ls urhtk ,d gh fudysxk exj /;ku j[kusdh ckr ;g gS fd ;s vyx&vyx ladYiuk,a gSaA bUgsa le>us esa cPpksa dks ekxZn’kZu dh vko’;drk gksrhgSA

dqN f’k{kdksa o cPpksa ds ekrk&firk ls ckrphr djds ,slk yxrk gS fd tc dsoy ,d iw.kZ fn;k tk,rks cPps ^fgLls^ o ^iw.kZ^ dh ladYiuk vklkuh ls le> ikrs gSaA exj tc ^iw.kZ^ phtksa dk ,d lewg gks]rks mUgsa blds fgLls fy[kus esa fnDdr gksrh gSA bl leL;k ls fuiVus dk ,d rjhdk ;g Hkh gks ldrkgS fd ge fgLlksa dh ckr djrs gq, gj ckj mlls lacaf/kr iw.kZ dk Hkh mYys[k djsaA flQZ pkSFkkbZ ¼iko½dgus ds ctk; ge lsc dk pkSFkkbZ fgLlk] ehVj dk pkSFkkbZ fgLlk] ;k ckjg dk pkSFkkbZ fgLlk oxSjgdgsaA blds vykok fgLls dh ladYiuk dh 'kq:vkr esa ,d iw.kZ rd gh lhfer j[ksaA

bl lanHkZ esa f’k{kd d{kk esa dqN xfrfof/k;k¡ djok ldrs gSaA ;gka ,d xfrfof/k nh tk jgh gS tks ,dd{kk esa dh xbZ FkhA

fp= &11fp= &11fp= &11fp= &11fp= &11

119

mnkgj.k 3mnkgj.k 3mnkgj.k 3mnkgj.k 3mnkgj.k 3

f’kf{kdkf’kf{kdkf’kf{kdkf’kf{kdkf’kf{kdk %%%%% ;g ,d lsc gS ftls pkj cjkcj Hkkxksa esa dkVk x;k gSA eSa tc bu pkj VqdM+ksa dks ,dlkFk tksM+rh gw¡ ¼fn[kkrs gq,½] rks iwjk lsc cu tkrk gSA ¼fp=&12½ eksgu] ;gk¡ vkdj ,dVqdM+k ys yksA rqEgkjs ikl lsc dk fdruk fgLlk gS\

eksgueksgueksgueksgueksgu %%%%% ,dA

f’kf{kdkf’kf{kdkf’kf{kdkf’kf{kdkf’kf{kdk %%%%% fdrus fgLlksa esa ls\

eksgueksgueksgueksgueksgu %%%%% pkj esa ls ,d fgLlkA

f’kf{kdkf’kf{kdkf’kf{kdkf’kf{kdkf’kf{kdk %%%%% D;k rqe crk ldrs gks fd rqEgkjs ikl ,d lsc dk fdruk Hkkx gS\

eksgueksgueksgueksgueksgu %%%%% th eSMe] esjs ikl ,d lsc dk pkSFkkbZ fgLlk gSA

f’kf{kdkf’kf{kdkf’kf{kdkf’kf{kdkf’kf{kdk %%%%% Bhd gSA vc ;g ,d vkSj VqdM+k ys yksA vc crkvks rqEgkjs ikl fdruk lsc gS\

eksgueksgueksgueksgueksgu %%%%% vc esjs ikl nks VqdM+s gSaA

f’k{kdf’k{kdf’k{kdf’k{kdf’k{kd %%%%% fdrus VqdM+ksa esa ls\

eksgueksgueksgueksgueksgu %%%%% esjs ikl pkj esa ls nks VqdM+s gSaA

f’kf{kdkf’kf{kdkf’kf{kdkf’kf{kdkf’kf{kdk %%%%% rqEgkjs ikl pkj esa ls nks VqdM+s gSaA D;k rqe bl ckr dks vk/ks ds :i esa crk ldrs gks\

EkksguEkksguEkksguEkksguEkksgu %%%%% th eSMe] esjs ikl vc vk/kk lsc gSA

f’kf{kdkf’kf{kdkf’kf{kdkf’kf{kdkf’kf{kdk %%%%% ,d vkSj VqdM+k ysdj crkvks fd vc rqEgkjs ikl lsc dk fdruk fgLlk gS\

eksgueksgueksgueksgueksgu %%%%% vc esjs ikl pkj esa ls rhu VqdM+s gSaA

f’kf{kdkf’kf{kdkf’kf{kdkf’kf{kdkf’kf{kdk %%%%% eryc vc rqEgkjs ikl lsc dk rhu&pkSFkkbZ Hkkx gSA

eksgueksgueksgueksgueksgu %%%%% th eSMeA

f’kf{kdkf’kf{kdkf’kf{kdkf’kf{kdkf’kf{kdk %%%%% eksgu ds ikl lsc ds pkj VqdM+ksa esa ls rhu VqdM+s gSaA vkSj bu pkj VqdM+ksa dks tksM+usls iwjk lsc cu tkrk gSA rks bl <ax ls gesa iwjs dk rhu&pkSFkkbZ Hkkx feyrk gSA ;gk¡iwjs dk eryc gS ,d lscA

blds ckn f’kf{kdk us lkjs cPpksa dks dkxt] czsM] fcLdqV] pikrh tSlh vyx&vyx phtksa] tks Hkh d{kkesa miyC/k Fkha] ds lkFk rjg&rjg dh xfrfof/k;k¡ djokbZA bu phtksa dh enn ls mUgksaus lkjs cPpksa dks

1 1 3, ,

2 4 4

fn[kk;kA chp&chp esa mUgksaus cPpksa ls loky iwNsA

cPpksa ls lkjs lokyksa ds tokc fey tkus ds ckn os dkQh larq"V utj vk jgh FkhaA

tSlk fd geus igys ftØ fd;k Fkk fd tc iw.kZ^ dbZ oLrqvksa dk ,d lewg gksrk gS] rc cPpksa dks mldsfgLlksa dks ml iw.kZ ls tksM+dj ns[kus esa fnDdr gksrh gSA blfy, ;g t:jh gS fd ge Nk=ksa dks fofHkUurjg ds ^iw.kZ^ ls ifjfpr djk,aA tc gesa ;dhu gks tk, fd cPps ,d gh oLrq ls cus ^iw.kZ^ ds lanHkZ esa^va’k&iw.kZ^ laca/k dks HkyhHkkafr le> pqds gSaA

120

vkb, vc ,d ckj fQj iw.kZ ds rhu&pkSFkkbZ dh leL;k dks mBkrs gSaA ge ns[kus dh dksf’k’k djsaxs fdNk=ksa dks fdruh rjg ds ^iw.kZ^ ls ifjfpr djk;k tk ldrk gSA

1- ,d ^iw.kZ^ ftlesa ,d ls T;knk exj pkj ls de phtsa gksaA

3 1 1 1

4 4 4 4= + +3 1

3 44

× = ÷

2- pkj phtksa ls cuk iw.kZ ftlesa gj pht iw.kZ gksA

3- Pkkj ls T;kn phtksa ls cuk ^iw.kZ^ ftlesa phtksa dh dqy la[;k pkj ls foHkkftr gksA

;gka ge ,d xfrfof/k ns jgs gSaA

121

mnkgj.k 4 & mnkgj.k 4 & mnkgj.k 4 & mnkgj.k 4 & mnkgj.k 4 & f'kf{kdk d{kk esa dqN VkfQ;ka vkSj fcLdqV ysdj vkbZ vkSj cPpksa ls ckrphr 'kq: djrsgq, mUgksaus eksgu dks vius ikl cqyk;kA

f’kf{kdkf’kf{kdkf’kf{kdkf’kf{kdkf’kf{kdk % ;s pkj fcLdqV gSaA eSaus eksgu dks rhu fcLdqV ns fn,A mlds ikl fdrus fcLdqV gSa \

Nk=Nk=Nk=Nk=Nk= %%%%% rhu fcLdqVA

f'kf{kdkf'kf{kdkf'kf{kdkf'kf{kdkf'kf{kdk %%%%% fdrus esa ls\

Nk=Nk=Nk=Nk=Nk= %%%%% pkj esa lsA

f’kf{kdkf’kf{kdkf’kf{kdkf’kf{kdkf’kf{kdk %%%%% eksgu] D;k rqe cksMZ ij fy[k ldrs gks fd fcLdqVksa dk fdruk fgLlk rqEgsa feyk\

eksgueksgueksgueksgueksgu %%%%% th] eSMe ¼cksMZ og ckSMZ ij

3

4

fy[krk gSA½

f’kf{kdkf’kf{kdkf’kf{kdkf’kf{kdkf’kf{kdk %%%%% rks D;k ge dg ldrs gSa fd eksgu ds ikl fcLdqV dk rhu&pkSFkkbZ fgLlk gS\

eksgueksgueksgueksgueksgu %%%%% th] eSMe

f’kf{kdkf’kf{kdkf’kf{kdkf’kf{kdkf’kf{kdk %%%%% ;kfu bl mnkgj.k esa rhu&pkSFkkbZ dk eryc gqvk pkj esa ls rhu fcLdqVA D;k rqe crkldrs gks fd ;gka ^iw.kZ^ D;k gS\

¼d{kk esa FkksM+h nsj pqIih jgrh gSA½

,d yM+dk,d yM+dk,d yM+dk,d yM+dk,d yM+dk %%%%% fcLdqVA

f’kf{kdkf’kf{kdkf’kf{kdkf’kf{kdkf’kf{kdk %%%%% fdrus fcLdqV\

yM+dkyM+dkyM+dkyM+dkyM+dk %%%%% pkj fcLdqVA

lHkh Nk=lHkh Nk=lHkh Nk=lHkh Nk=lHkh Nk= %%%%% th] eSMeA

f’kf{kdkf’kf{kdkf’kf{kdkf’kf{kdkf’kf{kdk %%%%% 'kkck’k! ;kuh ;gka gekjk iw.kZ phtksa dk ,d lewg gS ftlesa pkj fcLdqV gSaA

vc f’kf{kdk us ikap VkfQ;ka mBkbZa vkSj js.kq dks mlesa ls nks ns nhaA fQj mUgksaus Åij xbZ xfrfof/knksgjkbZA mUgksaus cPpksa ls dbZ loky iwNsA cPpksa dks vc ;g Bhd ls le> vk x;k Fkk fd ;gka iw.kZ dkeryc ikap VkfQ;ka gSaA blds ckn vH;kl ds fy, mUgksaus cPpks dks dqN loky gj djus dks fn,A

bl rjg ls Nk=ksa dks fofHkUu iw.kZ ls ifjfpr djk;k tk ldrk gSA

E6) blh izdkj Åij of.kZr lHkh iw.kZ ds lanHkZ esa ,d&,d xfrfof/k crkb,A

lkjka'klkjka'klkjka'klkjka'klkjka'k

bl ikB esa geus fuEukafdr igyqvksa ij ppkZ dh%

1) 10 o"kZ rd cPpksa esa vke rkSj ij ^vk/ks^ dks ysdj dkQh my>s gq, fopkj gksrs gSaA iw.kZ dk dksbZHkh fgLlk muds fy, vk/kk gksrk gSA os bl ckr dk vFkZ ugha le> ikrs fd fdlh Hkh iw.kZ dk^vk/kk^ irk yxkus ds fy, nks cjkcj Hkkx djuk vko’;d gksrk gSA blds vykok dbZ cPpksa dksyxrk gS fd foHkktd js[kk dsoy ljy js[kk gh gks ldrh gSA ;fn cPpksa dks muds bnZ&fxnZmiyC/k izR;sd phtksa ds lkFk xfrfof/k;ka djokbZ tk,a] rks dkQh gn rd ,slh xyrQgfe;ksa lscpk tk ldrk gSA mUgsa o`r] oxZ] f=dks.k vkfn vkÑfr;ksa dks vyx&vyx <ax ls nks

122

cjkcj&cjkcj fgLlksa esa ckaVus dks dgk tk ldrk gSA tc os fdlh pht dks nks fgLlksa esa ckaVysa rks muls bl ckr dh tkap djus dks dg ldrs gSa fd fgLls cjkcj gSa ;k ughaA

2) bl vk;q ds cPpksa dks ,d vkSj fnDdr ;g vkrh gS fd os va’k dk laca/k iw.kZ ls ugha tksM+ ikrsAos ;g ugha le> ikrs fd va’k dk eryc iw.kZ ds lanHkZ esa gSaA bl leL;k ls fuiVus ds fy,gesa va’k ds lkFk lnSo lEcfU/kr iw.kZ dk mYys[k djuk pkfg,A ;g Hkh t:jh gS fd ge cPpksadks vyx&vyx xfrfof/k;ksa ds tfj;s fofHkUu fdLe ds iw.kZ ls ifjfpr djk,aA

123

ikB&9ikB&9ikB&9ikB&9ikB&9

fHkUu dh fdLesafHkUu dh fdLesafHkUu dh fdLesafHkUu dh fdLesafHkUu dh fdLesaifjp;ifjp;ifjp;ifjp;ifjp;

vdlj ns[kk x;k gS fd fHkUu dks ysdj cPpksa dk Kku cgqr lhfer gksrk gSA bls ,d la[;k ds :i esale> ikuk muds fy, vlaHko&lk gksrk gSA QyLo:i os fHkUu dks la[;k ls tksM+ ugha ikrsA ;fn vkifdlh cPph ls iwNsa fd ^vk/kk* D;k gksrk gS] rks vdlj ;g tokc feysxk fd vk/kk eryc dsd ;k jksVh;k fdlh vU; fdlh pht dk ,d fgLlk gksrk gSA ;gh fLFkfr ,d&frgkbZ] ,d&pkSFkkbZ ;k fdlh HkhvU; fgLls ds lkFk Hkh gksrh gSA cPps fHkUuksa vkSj la[;kvksa ds chp ds laca/kksa dks ugha le> ikrsA bldh,d otg ;g gks ldrh gS fd cPpksa ls fHkUUkksa dh ckr djrs gq, ftl Hkk"kk dk bLrseky gqvk gS] og=qfViw.kZ gksA ;k fQj cPpksa us 'kk;n vius f'k{kd dks ;g dgrs dHkh u lquk gks fd fHkUu la[;k,a gksrhgSaA cPps fHkUuksa dks ek= mlds izR;{k :i esa gh tkurs&le>rs gSa vkSj blfy, os mudk izrhdu ughadj ikrsA

bl ikB esa ge dqN xfrfof/k;ka lq>k jgs gSa ftuds iz;ksx ls vki cPpksa dks ;g le>k ik,axs fd fHkUuksadks vewrZ jkf'k;ksa ds :i esa dSls ns[ksa vkSj mUgsa ladsrksa ds :i esa dSls O;Dr djsaA ;gka geus fHkUu la[;kvksadh rqY;rk rFkk Øe.k dh Hkh ckr dh gSA

fHkUUkksa dk izrhdufHkUUkksa dk izrhdufHkUUkksa dk izrhdufHkUUkksa dk izrhdufHkUUkksa dk izrhdu

,d fnu eSa viuh Hkrhth vafdrk vkSj mldh lgsyh jek ds ckrphr dj jgh FkhA nksuksa d{kk pkj esai<+rh gSaA rHkh eq>s ;kn vk;k fd esjh ,d f'k{kd fe= us dgk Fkk fd cPpksa dks fHkUuksa ds izrhdu esafnDdr vkrh gSA eSaus lkspk fd D;ksa u bu nks cPpksa dk ijh{k.k fd;k tk,A

mnkgj.k 1

eSa % gj vkÑfr esa Nk;knkj Hkkx D;k fn[kkrk gS\

fp= 1fp= 1fp= 1fp= 1fp= 1

vafdrk % 1 ¼d½ esa Nk;knkj Hkkx rhu cVk lksyg gS vkSj 1 ¼[k½ esa pkj cVk lksyg gSA

jek % 1 ¼d½ esa rhu cVk lksyg gS vkSj 1 ¼[k½ esa ,d&pkSFkkbZ gSA

;s dkQh fnypLi mRrj FksA eSaus lkspk fd fHkUuksa ds izrhdu ds ckjs esa jek dh le>dks vkSj xgjkbZ ls vkaduk pkfg,A

eSa % jek] rqeus ,slk D;ksa dgk fd 1 ¼[k½ esa Nk;knkj Hkkx ,d pkSFkkbZ gS\

jek % ¼fgpfdpkrs gq,½ D;ksafd ------ iwjs dkxt ij lksyg gSa vkSj gj rjQ ---------------- gj ,d -------------- esa pkj gSaA ;fn vki bls dkVsaxs rks ¼gj ckj pkj&pkj oxksZa ds lewg dh vksj

124

b'kkjk djrs gq,½ ;g ,d pkSFkkbZ gS] ;g ,d pkSFkkbZ gS] ;g ,d pkSFkkbZ gS] vkSj ;g ,dpkSFkkbZ gSA

ijUrq mls ns[kdj esjs eu esa 'kadk iSnk gqbZA tc mlus dgk fd ^gj ,d esa pkj gSa-------------gj rjQ* rksmlds gkoHkko ls yx jgk Fkk fd og ?ksjs ds vanj ds pkjksa vk;rksa dks fxu jgh FkhA eq>s 'kadk ;g gqbZfd D;k og ;g dg jgh gS fd ?ksjsnkj Hkkx ,d pkSFkkbZ gS D;ksafd mlesa pkj vk;r gSa ;k og dg jghgS fd ;g ,d pkSFkkbZ gS D;ksafd iwjs dkxt ij cjkcj lkbt ds ,sls pkj fgLls gSaA esjk 'kd rc lghlkfcr gks x;k tc jek vkSj vafdrk us ;g crk;k fd dksbZ fgLlk vkBoka Hkkx dc gksrk gSA

jek % ;g vkBoka Hkkx gS D;ksafd blesa vkB vk;r gSaA

fp= 2fp= 2fp= 2fp= 2fp= 2

vafdrk % ugha] vkBoka Hkkx ;g gS D;ksafd iwjs dks ,sls vkB Hkkxksa esa ckaVk tk ldrk gSA

fp= 3fp= 3fp= 3fp= 3fp= 3

;kuh fdlh fHkUu dk izrhdu djuk vkSj mls ladsrksa esa O;Dr djuk cPpksa ds fy, vkSj cM+hleL;k gSA

E1) Åij fn, x, fp=ksa o O;k[;kvksa esa ls dkSu lh lgh gS\ lgh gy ij /;ku dsfUnzr djus ds fy,vki D;k djsaxs\

;g cgqr t:jh gS fd fHkUuksa ds izrhdu ds rjhds dks ysdj vxj cPps ds fnekx esa dksbZ Hkze gS rks mlsnwj fd;k tk,A mlds ckn gh bl fo"k; esa vkxs c<+uk pkfg,A tc cPpk ^vk/kk*] ^frgkbZ*] ^pkSFkkbZ* tSlsfHkUuksa ds uke ls lqifjfpr gks tk,a vkSj bu 'kCnksa dks lacaf/kr iw.kZ ¼dsd dk ,d frgkbZ½ ds lanHkZ esale>us yxsa rc oks fHkUuksa ds ladsr fl[kkus ds fy, rS;kj gks tkrs gSaA ,slk ns[kk x;k gS fd ge vkerkSj ij mUgsa crk nsrs gSa fd nks frgkbZ* fy[kus ds fy, os 2 ds uhps ,d ykbu [khapdj mlds uhps rhu

125

bl izdkj

2

3

fy[k nsa exj ;g ugha le>krs fd ge ,sls D;ksa fy[k jgs gSaA cPps dbZ ckj Hkzfer gks tkrs

gSa vkSj nks frgkbZ

3

2

fy[k nsrs gSaA gesa mudks ;g le>kuk pkfg, fd ykbu ds uhps dh la[;k ¼gj½ ls

irk pyrk gS fd iw.kZ dks dqy fdrus Hkkxksa esa ckaVk x;k gS tcfd Åij dh la[;k ¼va'k½ ls irk pyrk

gS fd ge muesa ls fdrus Hkkxksa dks ysrs gSaA fHkUu

2

3

ls irk pyrk gS fd iw.kZ dks dqy rhu cjkcj Hkkxksa

esa ckaVk x;k gS vkSj ge muesa ls nks Hkkx ys jgs gSaA fHkUu

2

3

ds gj ls gesa ^frgkbZ* 'kCn feyrk gS vkSj

va'k ls irk pyrk gS fd fdruh frgkb;ksa ij /;ku fn;k tkuk gSA

fHkUuksa dks la[;k ds :i esa fy[kus ij gesa tksj nsuk pkfg,A tSls ,d dkxt dks nks cjkcj VqdM+ksa esa ckaVk

tkrk gSA bu nks VqdM+ksa esa ls ,d VqdM+s dks la[;k

1

2

ls O;Dr fd;k tkrk gSA bl rjg cPps la[;k

o fHkUu ds vkilh laca/k dks izR;{k :i ls ns[k le> ldrs gSaA

blh izdkj cPpksa dks fHkUu ds izrhdu dks ladsrksa esa rCnhy djus dk Hkh vH;kl djkuk t:jh gSA 'kq:vkresa mUgha fHkUuksa ij /;ku nsuk vPNk jgrk gS ftuesa va'k 1* gksA blls cPpksa dk /;ku gj ds egRo ij dsfUnzrdjus esa enn feyrk gSA cPpksa dks fuEufyf[kr rkfydk Hkjus ds fy, dgk tk ldrk gS %

iw.kZ ds cjkcj fgLlksa dh la[;k 2 3 4 5 6

gj fgLls dk izrhdu vk/kk frgkbZ pkSFkkbZ & &

,d fgLls dk ladsr

1

2

1

3

& & &

/khjs&/khjs cPps fofHkUu ^va'k* ls lacaf/kr vH;kl@xfrfof/k;ka dj ldrs gSaA

E2) D;k vki d{kk esa 40 cPpksa ds fy, dksbZ ,slh xfrfof/k lq>k ldrs gSa ftlls ;g irk yx ldsfd fHkUuksa ds izrhdu vkSj ladsr dh ladYiuk os le> x, gSa ;k ugha\

tc ,d ckj cPps ;g le> ysa fd fHkUu okLro esa la[;k,a gSa rks gks ldrk gS os mu la[;kvksa ij xf.krh;lafØ;kvksa ds ckjs esa Hkh lkspsaA exj blls igys fd vki mUgsa fHkUuksa ds tksM+ ;k ?kVk vkfn fl[kk,a ;gt:jh gS fd mUgsa fHkUu laca/kh vU; ladYiuk,a tSls fd fHkUu dh rqY;rk vkSj Øe.k vkfn dh iwjh le>gksA fHkUuksa ds tksM+ ?kVk vkfn le>us esa bu ladYiukvksa dk cgqr egRo gSA cgqr ls f'k{kdksa dk vuqHkogS fd cPps ;s ladYiuk,a vklkuh ls ugha le> ikrsA

fp=&4

126

fHkUuksa dh rqY;rkfHkUuksa dh rqY;rkfHkUuksa dh rqY;rkfHkUuksa dh rqY;rkfHkUuksa dh rqY;rk

cPpksa ds lkeus ,sls dbZ mnkgj.k vkrs gSa tc ,d gh fHkUu dks ,d ls vf/kd <ax ls O;Dr fd;k tk

ldrk gSA dbZ cPps dgsaxs fd fp=&4 esa

2

8

fgLlk Nk;knkj gS tcfd vU; cPps dgsaxs fd Nk;knkj

fgLlk

1

4

gSA

nksuksa gh mRrj lgh gSaA exj dbZ ckj cPps bl ckr dks vklkuh ls Lohdkj ugha dj ikrs fd

vyx&vyx fHkUu ,d gh ek=k ;k cjkcj fgLlksa dks fu:fir dj ldrs gSaA tSls

2 4 6 8, , , ,...............

3 6 9 12

,d gh ek=k dks fu:fir djrs gSaA bl rjg ;s fHkUu ijLij rqY; ;k cjkcj gSaA

mnkgj.k&2 ,d ckj eSa vius iM+ksl ds 4 cPpksa nqdku esa dqN f[kykus ys xbZA lHkh cM+h isLVªh [kkukpkgrs FksA

eSa % vxj eSa 3 isLVªh [kjhnwa] rks rqe yksx mUgsa vkil esa cjkcj&cjkcj dSls ckaVksxs\

,d cPpk % eSa gj ,d isLVªh ds pkj cjkcj VqdM+s djds lcdks gj isLVªh dk ,d&,d VqdM+k ns nwaxkArks ge lcdks cjkcj&cjkcj isLVªh fey tk,xhA

nwljh cPpk % ugha] eSa igys ,d&,d isLVªh rhu yksxksa dks ns nwaxkA fQj bu rhuksa ls dgwaxk fd os pkSFksdks viuh&viuh isLVªh dk pkSFkkbZ fgLlk ns nsaA rc ge lcdks cjkcj fgLlk fey tk,xkA

eSa % BhdA rqe nksuksa us 3 isLVªh dks pkj cjkcj&cjkcj fgLlksa esa bl rjg ckaVkA ¼fp=&5½

fp= 5 ¼[k½

D;ksa u lc yksx tjk fy[k dj crk,a fd gj ,d dks isLVªh dk fdruk fgLlk feysxk\

igyk cPpk % gj ,d dks

1

4

feysxkA

nwljk cPpk % gj ,d dks

3

4

feysxkA

rhljk cPpk % gj ,d dks

3

12

feysxkA

fp= 5 ¼d½

127

vki bu cPpksa ds mRrjksa ds ckjs esa D;k dgsaxs\ dkSu lgh Fkk vkSj dkSu xyr] vkSj D;ksa\

Åij fy, x, mnkj.k esa igys cPps us rhu isfLVª;ksa dks ,d ^iw.kZ* ds :i esa ns[kk] blfy, mls bldk

1

4

feykA nwljs cPps ds fy, iw.kZ dk eryc rhu vyx&vyx isfLVª;ka Fkha vkSj mldk fgLlk bu rhu

isfLVª;ksa dk

1

4

FkkA rhljs cPps us Hkh rhu isfLVª;ksa dks ,d ^iw.kZ* ds :i esa ns[kk] ftls 12 cjkcj Hkkxksa

esa ckaVk x;k Fkk vkSj mls buesa ls rhu Hkkx feys FksA

bl mnkgj.k ls irk pyrk gS fd cPpksa ds fy, ;g le>uk t:jh gS fd fHkUu dks uke nsrs oDr ^iw.kZ*dk mYys[k vfuok;Z gSA ,d ckj os bl ckr dks le> x,] rks mUgsa ,d gh ek=k dks vyx&vyx fHkUula[;kvksa ds :i esa O;Dr djus esa dksbZ fnDdr ugha gksxhA

'kq:vkr esa] dksbZ vkSipkfjd uke crk, cxSj] ge muls dg ldrs gSa fd os FkksM+h tklwlh djds ;g rksirk yxk,a fd fdlh fHkUu ds fdrus vkSj uke gks ldrs gSaA exj ;g tklwlh FkksM+s O;ofLFkr <ax lsdjuh gksxhA 'kq:vkr fuEufyf[kr xfrfof/k ls dh tk ldrh gSA

mnkgj.k 3

dkxt dh ,d iV~Vh ysdj mls vkB fgLlksa esa eksM+ nhft,A vc cPpksa ls dfg, fd vk/kh iV~Vh dks

vyx&vyx uke nsaA mUgsa ;s irk yxkus nhft, fd iV~Vh dk

1

2

ogh gS tks iV~Vh dk

2

4

gS ;k

4

8

gSA blh izdkj ls ,d oxZ dks vkB fgLlksa esa eksM+dj irk yxk ldrs gSa fd oxZ dk 1

2

gh oxZ dk 2

4vkSj oxZ dk

4

8 Hkh gksrk gSA vc bl le; vki vk/ks] nks&pkSFkkbZ] pkj&vkBosa dh rqY;rk ¼lekurk½

le>k ldrs gSaA vkSj fy[k ldrs gSa fd

1 2

2 4=

ftldk eryc gS fd ,d&vk/kk vkSj nks&pkSFkkbZ cjkcj

gSaA vc vki cPpksa ls dgsa fd os vius fu"d"kZ dks fuEukuqlkj fy[kdj c;ku djsa&

1 2 4

2 4 8= =

cPps bl lwph dk v/;;u djds va'k o gj dk iSVuZ ns[k ldrs gSaA [kkldj os ;g ns[k ldrs gSa fdizR;sd fHkUu esa gj] va'k ls nqxquk gSA vki cPpksa ls blh Øe dk ikyu djus okyh vU; fHkUu la[;k,a

crkus dks dg ldrs gSaA 'kq:vkr djus ds fy, vki viuh vksj ls

6

12

dk lq>ko ns ldrs gSaA

bl izdkj ,d ckj cPpksa dks fn, x, fHkUu ds rqY; fHkUu [kkstus dk dkQh vuqHko gks tk, vkSj os gjckj rqY; fHkUuksa ds chp ds iSVuZ dks ns[k le> ysa rks os [kqn c [kqn rqY; fHkUu fy[kus dk fu;e ;kuhva'k o gj nksuksa dks ,d gh la[;k ls xq.kk djuk ;k nksuksa dks muds xq.ku[kaM ls Hkkx nsuk [kkst ysaxsA

E3) ,d&,d xfrfof/k ,slh lq>kb, ftldh enn ls cPpksa dks ,d frgkbZ] ,d&pkSFkkbZ vkSjnks&frgkbZ ds rqY; fHkUu irk djus esa enn feysA

xfrfof/k ftlesa f'kf{kdk us viuh d{kk esa miyC/k fofHkUu izR;{k phtksa dk iz;ksx rqY; fHkUu dhladYiuk le>kus easa fd;k gSA

128

mnkgj.k 4

f'kf{kdk % esjs ikl 32 daps gSaA eSa eksgu vkSj lksgu dks 16&16 daps ns jgh gwaA

eksgu] bu 16 dapksa dks 4 cjkcj Hkkxksa esa ckaVksA

eksgu % ¼bl rjg ckaVdj f'kf{kdk dks fn[kkrk gS½

00 00 00 00

00 00 00 00

;s pkj cjkcj fgLls gks x,A

f'kf{kdk % gj fgLls esa fdrus daps gSa\

eksgu % pkj daps gSaA

f'kf{kdk % ,d fgLlk dapksa dk fdruk Hkkx gS\

eksgu % ;g 16 dapksa dk

1

4

gSA

f'kf{kdk vc ,d vU; Nk=k jkuh dks cqykrh gSA

f'kf{kdk % eksgu] pkj esa ls nks fgLls jkuh dks ns nksA

eksgu % th] eSMeA

00 00

00 00

;kuh nks fgLls jkuh dks ns nsrk gSA

f'kf{kdk % eksgu] ;g crkvks fd jkuh dks rqeus dapksa dk fdruk Hkkx fn;k gS\

eksgu % eSaus mls lksyg dapksa dk

2

4 fn;k gSA

f'kf{kdk % 'kkck'k! lksgu] vc rqe vius 16 dapksa ds 8 cjkcj fgLls djksA

lksgu % ¼ 00 00 00 00 00 00 00 00 ds :i esa ckaVrkgS½ gks x;kA

rc f'kf{kdk us mlls bl rjg ds loky iwNs fd gj fgLls esa fdrus daps gSa\ ,dfgLlk dapksa dk fdruk Hkkx gS\ vkfnA blds ckn mUgksaus jhrk uke dh ,d Nk=kdks cqykdj lksgu ls dgk fd og mls 8 fgLlksa esa ls pkj fgLls ns nsA lksgu us ¼0000 00 00½ 4 fgLls jhrk dks ns fn,A

f'kf{kdk % lksgu] ;g crkvks fd rqeus jhrk dks dapksa dk fdruk Hkkx fn;k gS\

lksgu % eSaus mls 16 dapksa dk

4

8

fn;k gSA

f'kf{kdk % Bhd gSA ;kuh jkuh dks 16 dapksa dk

2

4

feyk vkSj jhrk dks 16 dapksa dk

4

8

feykA

rqe nksuksa ds ikl fdrus&fdrus daps gSa ¼jkuh vkSj jhrk ls loky½\

jkuh % eSMe] vkB dapsA

129

jhrk % eq>s Hkh vkB daps feysA

f'kf{kdk % D;k bldk eryc ;g gqvk fd 16 dapksa dk

2

4

vkSj

4

8

cjkcj gksrk gS\

iwjh d{kk % th gka] eSMeA

f'kf{kdk % fcYdqy lghA vUrj flQZ bruk gS fd muds lewg vyx&vyx <ax ls cuk, x,gSaA blh rjg ls os ;g Hkh le>krh gSa fd ;fn nks pikfr;ksa dks pkj cjkcj VqdM+ksaesa ckaVk tk, ¼fp=& 6½A

fp= 6fp= 6fp= 6fp= 6fp= 6

rks 2 pikrh dk

2

4

,d iwjh pikrh gksxkA vkSj ;fn 2 pikfr;ksa dks 8 Hkkxksa esa ckaVk tk, ¼fp= 7½A

fp= 7

rks 2 pikrh dk

4

8

Hkh ,d iwjh pikrh gksxkA ;kuh 2 pikrh dk

2

4

ogh gS tks 2 pikrh dk

4

8

A

,slh xfrfof/k;ksa ls cPps ;g le> ik,axs fd iw.kZ dqN Hkh gks] exj nks&pkSFkkbZ fulansg :i ls pkj&vkBosa;k N%&ckjgosa ds cjkcj gksrk gSA

E4) D;k vki lger gSa fd ,slh xfrfof/k;ksa ls cPpksa dks fHkUu dh rqY;rk dh ladYiuk le>us esaenn feyrh gS\ ;fn gka] rks D;ksa\ ;fn ugha] rks vkidk D;k lq>ko gS\

tc ge cPpksa dks ,d fHkUu nsdj mlds rqY; fHkUu fy[kus dks dgrs gSa rks cPps vke rkSj ij xq.kk dkrjhdk viukrs gSaA ;kfu os va'k vkSj gj nksuksa dks ,d gh la[;k ls xq.kk djus dk rjhdk viukrs gSaA va'kvkSj gj ds xq.ku[kaM ls Hkkx nsus dk rjhdk mUgsa dfBu yxrk gSA 'kk;n blh otg ls fdlh fHkUu dksmlds y?kqre in esa fy[kus esa cPpksa dks fnDdr gksrh gSA ,slk gh vuqHko esjh viuh Hkrhth vafdrk dslkFk tks vafdrk pkSFkh esa i<+rh gSA ,d fnu ge fHkUu ij ppkZ dj jgs FksA

130

mnkgj.k 5

eSa % D;k rqe ds

8

12

rqY; dksbZ fHkUu crk ldrh gks\

vafdrk % gkaA

vafdrk % f'kf{kdk us D;k crk;k Fkk\ gka] ;kn vk;kA 2 ls xq.kk djds

16

24

feysxk] 3 ls xq.kk

djds

24

36

feysxk] 4 ls xq.kk djds

32

48

feysxkA bl rjg ls

8

12

ds cjkcj dbZ

fHkUu fy[k ldrh gw¡A

eSa % cf<+;kA lgh crk;k rqeusA vc ;g crkvks fd D;k

2

3

Hkh

8

12

ds cjkcj gS\

vafdrk % vHkh djds ns[krh gw¡A

eSa mls /;ku ls ns[k jgh FkhA eSaus ns[kk fd ;gka Hkh og xq.kk ds rjhds dk mi;ksx dj

jgh FkhA mlus

2

3

¼va'k o gj nksuksa½ dks 2 ls xq.kk fd;kA blls ckr ugha cuhA fQj

mlus 3 ls xq.kk fd;k ij ckr ugha cuhA rc mlus 4 ls xq.kk fd;k vkSj ph[k iM+hA

vafdrk % gkaA 2

3

Hkh 8

12

ds cjkcj gSA ge 2 dks 4 ls vkSj 3 dks Hkh 4 ls xq.kk djsa rks 8

12

vkrk

gSA

eSa % exj bldk ,d T;knk vklku rjhdk gSA rqEgsa irk gS fd 8 vkSj 12 dk ,d lkekU;

xq.ku[kaM 4 gSA rks cl] 8 dks 4 ls Hkkx ns nks vkSj 12 dks 4 ls Hkkx ns nks vkSj

2

3

fey tk,xkA

vafdrk % gka --------------------- yxrk rks vklku gS exj D;k ,sls dj ldrs gSa\

eSa % D;ksa ugha\ pyks] rqedks ,d pht+ fn[kkrh gw¡A ;g dkxt+ ns[kksA bls eksM+ fn;kA ;s nkscjkcj fgLls gks x, ¼fp= 8½A crkvks] izR;sd fgLlk fdruk Hkkx gSa\

fp= 8

131

vafdrk %

1

2

A

eSa % ,d ckj vkSj eksM+ nsa rks pkj cjkcj fgLls gks tk,axsA ¼fp= 9 ns[ksa½ vc dkxt+ fdrusfgLlksa esa caV x;k\

fp= 9fp= 9fp= 9fp= 9fp= 9

vafdrk % pkj fgLlksa esaA gj fgLlk

1

4

gSA

eSa % vc eSa dkxt+ dks [kksy nsrh gw¡A D;k rqe ;g ekurh gks fd

1

2

dkxt+ 2 ,d&pkSFkkbZ

fgLlksa ds cjkcj gS\

vafdrk % gkaA

eSa % rks eSa

1

2

=

2

4

fy[k ldrh gw¡A vc ;fn eSa bl dkxt dks ,d ckj vkSj eksM+dj [kksy

nw¡ rks ;g ,slk fn[ksxk ¼fp= 10½A

fp= 10

vc crkvks fd dkxt+ ds

1

2

fgLls esa fdrus vkBosa Hkkx gSaA

vafdrk % ,d] nks -------------- pkjA pkj Hkkx gSaA

eSa % ;kuh

4 1

8 2=

A

132

vafdrk % gkaA

eSa % D;k vc ge dg ldrs gSa fd

4

8

ds rqY;

2

4

vkSj

1

2

gS\ D;k ge ,slk fy[k ldrs

gSa&

4 2 1?

8 4 2= =

vafdrk % gka] ,slk fy[k ldrs gSaA

eSa % ;kuh 4

8 ds rqY; fHkUu ge fuEu va'k vkSj gj ds lkFk fy[k ldrs gSaA ge fy[krs

4

8

=

2

4

=

1

2

gSa rks D;k rqEgsa dksbZ iSVuZ fn[kkbZ iM+rk gS\

vafdrk % th gkaA ck,a ls nk,a pyrs gq, ge va'k vkSj gj nksuksa dks nks&nks ls Hkkx nsrs tk jgsgSaA

eSa % D;k bldk eryc ;g gqvk fd gesa nks ls Hkkx nsrs gq, ,d&,d dne gh pyuk

gksxkA D;k ge lh/ks

4

8

= ugha fy[k ldrs\

vafdrk % D;ksa ugha\ ;fn ge 4 vkSj 8 dks lh/ks 4 ls Hkkx ns nsa rks 1

2 vk tk,xkA

eSa % D;k vc rqe ekurh gks fd rqY; fHkUu fy[kus ds fy, ge va'k o gj nks dks mudslkekU; xq.ku[kaM ls Hkkx ns ldrs gSa\

vafdrk % thA

eq>s [kq'kh Fkh fd vafdrk dk lansg nwj gks pqdk Fkk vkSj mls esjs lkFk xfrfof/k djus esa etk Hkh vk;k

FkkA blds ckn eSaus mls

5,

10 2=

14 2

56=

vkfn esa [kkyh MCcksa esa vad Hkjus ds vH;kl djok,A vafdrk

us bUgsa lgh&lgh dj fn;kA eSaus ekSds dk Qk;nk mBk;k mls ;g Hkh le>k fn;k fd tc ge

4

8

=

2

4

=

1

2

fy[krs gSa rks

1

2

y?kqre :i gS D;ksafd vc va'k vkSj gj dk dksbZ lkekU; xq.ku[kaM ugha gSA blfy,

vc ge bUgsa vkSj foHkkftr ugha dj ldrsA

E 5) vki fdl rjhds ls irk djsaxs fd va'k vkSj gj dks muds xq.ku[kaM ls foHkkftr djds rqY; fHkUuirk djus dh fof/k vkids Nk= le> x, gS ;k ugha\

vkius ns[kk gksxk fd cPps dHkh&dHkh iwNrs gSa fd rqY; fHkUu irk djus ds fy, ge ftl rjg ls va'ko gj esa xq.kk ;k Hkkx djrs gSa] mlh rjg va'k vkSj gj nksuksa esa ,d gh la[;k tksM+ ;k ?kVkdj rqY; fHkUuD;ksa irk ugha dj ldrs\ ,sls lokykssa ds tokc cPpksa dks [kqn gh [kkstus dks dguk pkfg,A muls dfg,

133

fd os ,d fHkUu la[;k fy[ksaA elyu

1

2

vkSj mlesa va'k vkSj gj nksuksa esa 2 tksM+dj ns[ksa fd D;k

1

2

=

1 2

2 2

++

=

3

4

gksrk gS\

E 6) cPpksa dks ;g le>kus ds fy, vki D;k djsaxs fd

5

6

=

5 2

6 2

−−

=

3

4

ds cjkcj ugha gS\

cPpksa dks ;g le>us esa Hkh fnDdr vkrh gS fd

4 5,

4 5

vkfn 1 ds rqY; gSaA mUgsa ;g dguk eqf'dy yxrk

gS fd

4

4

= 1 ;k

5

5

= 1A ns[ksa mnkgj.k 6A

mnkgj.k 6

f'kf{kdk % ;g ,d lsc gSA eSa blds pkj cjkcj fgLls djrh gw¡A vxj bu pkjksa fgLlksa dks ,dlkFk j[ksa rks iwjk lsc curk gSA js.kq ;gka vkdj ,d VqdM+k ys yksA

js.kq % th eSMeA

f'kf{kdk % lsc dk fdruk fgLlk rqEgsa feyk\

js.kq % ,d fgLlkA

f'kf{kdk % fdrus fgLlksa esa ls\

js.kq % pkj esa ls ,d fgLlkA

f'kf{kdk % bls cksMZ ij fy[k nksA

js.kq %

blh rjg ls f'kf{kdk us js.kq dks nwljk o rhljk fgLlk fn;k vkSj cksMZ ij

2

4

o

3

4

fy[kok;kA vkf[kj esa pkSFkk fgLlk Hkh js.kq dks ns fn;kA

f'kf{kdk % lsc ds fdrus fgLls rqEgkjs ikl gSa\

js.kq % pkj fgLlsA

f'kf{kdk % fdrus fgLlksa esa ls pkj fgLls rqEgkjs ikl gSa\

js.kq % 4 esa ls 4A

f'kf{kdk % D;k blds fy, ge fHkUu

4

4

fy[k ldrs gSa\

js.kq % th eSMeA

f'kf{kdk % BhdA rks cPpksa ;g crkvks fd js.kq ds ikl fdruk lsc gS\

Nk= % iwjk@,d@lewpkA

f'kf{kdk % rks D;k ge

4

4

= 1 fy[k ldrs gSa\

134

Nk= % th eSMeA

f'kf{kdk % blh izdkj ls

5 61, 1

5 6= =

oxSjg gksrs gSaA Åij dh xbZ xfrfof/k dks pkj cjkcj

fgLlksa esa dkVdj ;k fQj pkj dapksa vkfn ds lkFk Hkh djk;h tk ldrh gSA

,d ckj cPps ;g le> x, fd

4

4

= 1,

5

5

= 1 vkfn gksrs gSa] rks mUgsa ;g le>us esa enn feysxh fd

5 pkSFkkbZ fgLls

5

4

og fHkUu gS tks 1 ls T;knk gSA ;fn ,d dkxt dks pkj cjkcj Hkkxksa esa ckaVk x;k

gS rks bl izdkj ds 5 pkSFkkbZ fgLls bl dkxt dks iwjk <d ysaxs vkSj vfrfjDr dkxt dh Hkh t:jriMs+xhA blfy, 5 pkSFkkbZ ,d ls cM+k fHkUu gSA

E 7) d{kk pkj ds cPpksa dks

5

4

le>kus gsrq dksbZ vH;kl lq>kb,A

vki bl ckr ls lger gksaxs fd cPpksa fHkUuksa dk ?kVkuk fl[kkus ls igys] ;g t:jh gS fd os fHkUuksa dkØe.k vPNh rjg ls le> ysaA vc ge blh fo"k; ij ppkZ djsaxsA

fHkUuksa dk Øe.kfHkUuksa dk Øe.kfHkUuksa dk Øe.kfHkUuksa dk Øe.kfHkUuksa dk Øe.k

nks fHkUuksa dk Øe.k] ;kuh ;g r; dj ikus dh le> fd D;k os cjkcj gSa ;k ,d NksVk ,d cM+k gS vkSj;fn gka rks dkSu lk NksVk o dkSu lk cM+k gS] ds fy, t:jh gksrk gS fd cPps igys bdkbZ fHkUuksa ds Øe.kdh le> gkfly djsaA blds fy, uhps nh xbZ dqN vklku xfrfof/k;k¡A

mnkgj.k 7mnkgj.k 7mnkgj.k 7mnkgj.k 7mnkgj.k 7

,d gh eki dh dkxt dh nl ifV~V;ka ysaA igys iV~Vh dks oSlh gh jgus nsaA nwljh iV~Vh dks nks cjkcjHkkxksa esa ckaV nsa] rhljh iV~Vh dks rhu cjkcj Hkkxksa -------------------------- blh izdkj ls nloha iV~Vh dks nlcjkcj Hkkxksa esa ckaV nsaA vc bUgsa ,d xRrs ij ,d&nwljs ds uhps fpidk nsa vkSj gj iV~Vh ds ,d&,dHkkx dks jax nsaA ¼fp= 11½

cjkcj eki dh ifV~V;ks a ds vyx&vyx jaxs fgLlks a dks ns[kdj cPps le> ik,axs fd

1 1 11 .............

2 3 10> > > >

A

fp= 11

135

1 1 11 .............

2 3 10> > > > le>kus dh bl xfrfof/k dks la[;k js[kk (number line) dh enn ls Hkh

fd;k tk ldrk gSA

E8) la[;k js[kk dh enn ls d{kk esa ;g le>kb, fd 1 1 1

1 .............2 3 10

> > > > gksrk gSA vkids

fo|kfFkZ;ksa dh D;k izfrfØ;k jgh\ D;k la[;k js[kk ij fHkUu la[;kvksa ds fu:i.k dks le>ukmUgsa T;knk eqf'dy yxrk gS ;k ;g muds fy, ,d mi;ksxh pk{kq"k midj.k dk dke djrhgS\

fHkUuksa dk Øe.k le>us ds fy, ;g le>uk fugk;r t:jh gS fd iw.kZ* dk eki D;k gS vkSj mls fdrusHkkxksa esa ckaVk x;k gSA ;fn cPps dks bl pht+ dh le> gS] rks mlds fy, bdkbZ fHkUuksa] leku va'k okyhfHkUuksa vkSj leku gj okyh fHkUuksa dk Øe.k djuk vklku gks tkrk gSA ijUrq dbZ ckj cPps eki vkSj Hkkxksads chp ds laca/k dh xyr O;k[;k dj cSBrs gSaA bl lanHkZ esa eq>s viuh 8 o"khZ; Hkrhth vafdrk ds lkFkgqvk vuqHko ;kn vkrk gSA

,d ckj eSa mlls fHkUuksa ds Øe.k ds ckjs esa ckrphr dj jgh FkhA bdkbZ fHkUuksa ds Øe.k dks ysdj vafdrk

esa dkQh vkRefo'okl ut+j vk jgk Fkk mlus vklkuh ls ;g dg fn;k fd 1 1

,8 5

ls NksVk gSA blus ;g

Hkh crk;k fd og ,slk D;ksa le>rh gSA mlus crk;k fd ;fn og ,d dsd dks 7 vkSj cPpksa ds lkFkckaVsxh rks mls de fgLlk feysxk tcfd ;fn mlh dsd dks og 4 vkSj cPpksa ds lkFk ckaVsxh rks mls

T;knk fgLlk feysxkA mlus 1 1 1 1

, , ,3 6 11 20

vkfn fHkUuksa dks Hkh vklkuh ls Øec) dj fn;kA exj tc

mlus ;g dgk fd

7 4,

8 8 ls de gS rks eSa vk'p;Z pfdr jg xbZA mldk dguk Fkk fd 7 fgLlksa dk

eryc gqvk T;knk fgLls vkSj tc fgLlksa dh la[;k T;knk gksxh rks gjsd fgLlk eki esa NksVk gksxkA eSausdgk fd pyks ns[krs gSaA eSaus dkxt dh nks cjkcj ifV~V;ka yh vkSj nksuksa dks 8 cjkcj fgLlksa esa ckaVk ¼fp=12½A vafdrk us bl dke esa esjh lgk;rk dhA

fp= 12

mnkgj.k 8

eSa % vafdrk] vc igyh iV~Vh ysdj mlds 8 Hkkxksa esa ls 4 esa yky jax Hkj nksA

vafdrk % thA yhft,] gks x;k] ¼fp= 13½

fp= 13

136

eSa % yky Hkkx fdruk fgLlk gS\

vafdrk %4

8

eSa % BhdA vc nwljh iV~Vh yks vkSj mlds 8 Hkkxksa esa ls 7 dks xzs dj nksA

vafdrk % yhft,] gks x;k ¼fp= 14½A

fp= 14

eSa % xzs Hkkx fdruk fgLlk gS\

vafdrk %

7

8

eSa % dkSu lk Hkkx cM+k gS & yky jax okyk Hkkx ;k xzs jax okyk HkkxA

vafdrk % xzs jax okyk Hkkx T;knk gSA

vkSj blls igys fd eSa mlls dksbZ loky d:¡] mlus [kqn gh Bhd tokc ns fn;kA vc mls bl dkeesa etk vkus yxk Fkk vkSj og pkgrh Fkh fd eSa bl rjg dh vkSj xfrfof/k;ka mlds lkFk d:¡A vr% eSaus

dkxt dh enn ls mls

4

4

vkSj

5

4

fn[kk;kA bl chp eSaus mlls dqN loky iwNs] tSls fd

4

4

vkSj

5

4

esa

ls dkSu lk cM+k gS\ vkSj D;ksa gS\ mlus cf<+;k tokc fn,A

vc mls ;g Li"V Fkk fd

4 4,

13 8

ls de gSA ijUrq mlds fy, ;g r; dj ikuk vHkh Hkh eqf'dy Fkk

fd

7

8

de gS ;k

12

13

A eSaus lkspk fd tokc mlh ls izkIr djuk pkfg,A eSa fuEufyf[kr <ax ls vkxs c<+hA

eSa % vafdrk D;k vc rqEgsa

7

8

vkSj

11

8

;k

3

7

vkSj

4

7

tSlh la[;kvksa dh rqyuk djus esa dksbZ

fnDdr gS\

vafdrk % th ugha vk.Vh] ;g rks cgqr ljy gSA blesa dksbZ fnDdr ugha gSA

eSa % rqEgsa ,slk D;ksa yxrk gS fd

7

8

vkSj

11

8

dh rqyuk djuk vklku gS vkSj

7

8

o

12

13

dh

rqyuk djuk T;knk dfBu gS\

vafdrk % ;g blfy, vklku gS D;ksafd nksuksa esa gj leku gS vkSj gesa flQZ va'k dh fpark djuhgksrh gSA

eSa % BhdA exj D;k rqe

7

8

vkSj

12

13

dks cnydj ,slh la[;k ugha cuk ldrh ftuesa gj

leku gksaA ¼FkksM+k lkspdj½

137

vafdrk % gka] dj ldrh gw¡A

mlus dqN ifjdyu fd;k vkSj mRrj fudky fy;kA

vafdrk %

7

8

vkSj

12

13

ds la[;k,a

91

104

vkSj

96

104

gSaA

eSa % Bhd D;k vc rqe crk ldrh gks fd fHkUu

7

8

cM+k gS ;k

12

13

\

vafdrk % ¼eqLdjkrs gq,½ gka]

12

13

cM+k gSA

vafdrk [kq'k vkSj jksekafpr FkhA mls ,slk vH;kl djds etk vk;k Fkk vkSj mlesa vkRefo'okl utj vkjgk FkkA ;g ns[kdj eq>s Hkh [kq'kh gqbZA

cPpksa dks izR;{k o fp=kRed lk/kuksa ls cPps fHkUuksa ds Øe.k dh ladYiuk le>us ds ckn mUgsa ,dlkekU; fu;e crk ldrs gSaA bls vke rkSj ij lkekU; gj dk fu;e dgrs gSaA fHkUuksa dk Øe irk yxkusesa bldk iz;ksx gksrk gSA bl fu;e ds vuqlkj nks ;k nks ls T;knk fHkUuksa dh rqyuk djus ds fy, mUgsa,slh rqY; la[;kvksa esa cnyk tkrk gS ftuesa lcds gj cjkcj gksaA rc fHkUu dk va'k lcls cM+k gks] oglcls cM+h fHkUu gksxhA

E9) lkekU; gj fu;e dk iz;ksx fd, cxSj vki cPpksa dks dSls le>k,axs fd

12

13

vkSj

7

8

esa ls

dkSulh la[;k cM+h gS\

vc ge fo"ke fHkUu dks fefJr fHkUu esa cnyus dhA ,d ,slh leL;k ds ckjs esa ppkZ djsaxs tks izk;% cPpksads lkeus vkrh gSA

fo"ke fHkUufo"ke fHkUufo"ke fHkUufo"ke fHkUufo"ke fHkUu

izk;ejh Ldwy ds f'k{kd vdlj ;g crkrs gSa fd fo"ke fHkUu dks fefJr fHkUu esa cnyrs oDr cPps vkerkSj ij fefJr fHkUu esa iw.kkZad okys LFkku ij HkkxQy dh ctk; 'ks"kQy fy[k nsrs gSaA

ftu fHkUu la[;kvksa esa va'k] gj ls cM+k gksrk gS mUgsa fo"ke fHkUu dgrs gSaAftu fHkUu la[;kvksa esa va'k] gj ls cM+k gksrk gS mUgsa fo"ke fHkUu dgrs gSaAftu fHkUu la[;kvksa esa va'k] gj ls cM+k gksrk gS mUgsa fo"ke fHkUu dgrs gSaAftu fHkUu la[;kvksa esa va'k] gj ls cM+k gksrk gS mUgsa fo"ke fHkUu dgrs gSaAftu fHkUu la[;kvksa esa va'k] gj ls cM+k gksrk gS mUgsa fo"ke fHkUu dgrs gSaA

fiNys jfookj dks ,d fe= ds ?kj ij eq>s ;gh ns[kus dks feykA mldh 9 o"khZ; csVh feuh viuk x`gdk;Zdj jgh FkhA eSaus mldh uksVcqd ij ;ksa gh fuxkg MkyhA og fo"ke fHkUu dks fefJr fHkUu esa cnyus ds

loky dj jgh FkhA mlus 7 esa 4 dk Hkkx bl rjg fd;k

14 7

4

3

vkSj

7

4

dks

13

4

fy[k fn;kA eSa pqipki

ns[krh jghA mlus fQj

11

6

=

16 11

6

5

=

15

6

fy[kkA

fefJr fHkUu iw.kkZad la[;k vkSj mfpr fHkUu dk ;ksx gksrs gSaAfefJr fHkUu iw.kkZad la[;k vkSj mfpr fHkUu dk ;ksx gksrs gSaAfefJr fHkUu iw.kkZad la[;k vkSj mfpr fHkUu dk ;ksx gksrs gSaAfefJr fHkUu iw.kkZad la[;k vkSj mfpr fHkUu dk ;ksx gksrs gSaAfefJr fHkUu iw.kkZad la[;k vkSj mfpr fHkUu dk ;ksx gksrs gSaA

138

mlls ckr djrs gq, le> esa vk;k fd fo"ke fHkUu dks fefJr fHkUu esa cnyus ds ckjs esa mlds f'k{kdus mls tks dqN crk;k gksxk] mls mldk /kqa/kyk lk vglkl FkkA og ,d e'khu dh rjg ;s loky djjgh Fkh vkSj og tks dqN dj jgh Fkh] mldk dksbZ Bksl fp= mlds fnekx esa ugha FkkA eSaus ckr dks Li"Vdjus ds fy, fuEufyf[kr rjhdk viuk;kA

mnkgj.k 9

eSaus ikap o`Rrkdkj dkxt ds VqdM+s fy,A gj ,d VqdM+s dks pkj cjkcj Hkkxksa esa ckaVk x;k Fkk ¼fp= 15ns[ksa½A

fp=&15fp=&15fp=&15fp=&15fp=&15

eSa % dk

1

2

fdruk gksxk\

feuh % 4 Hkkxksa esa ls ,d HkkxA

eSa % D;k ;g gksxk\

feuh % gk¡A

eSa % ;g crkvks fd

eSa % ;g fdruk fgLlk n'kkZrk gS\

feuh % ;g

2

4

gSA

eSa % cf<+;kA ;kuh ;g nks ,d&pkSFkkbZ gSA D;k blh rjg ls ge dg ldrs gSa fd

dk

1

4

gSA

;kuh rhu ,d pkSFkkbZ ¾

3

4

gS vkSj

139

dk

1

4

;kuh pkj ,d pkSFkkbZ ¾ 1 gSA

feuh % gkaA

eSa % vc crkvks fd

dk

1

4

;kuh ikap ,d&pkSFkkbZ D;k gksxk\

feuh FkksM+h Hkzfer fn[k jgh FkhA eSaus FkksM+h enn djus dk lkspkA

eSa % feuh D;k

5

4

vkSj 5 dk

1

4

,d gh ckr ugha gS\

feuh % gka----- gka----A vc eSa crk ldrh gwa fd 5 dk

1

4

D;k gksxkA 5 dk

1

4

gksxkA

eSa % D;k bls ge ,sls ugha dg ldrs\

$

11 ?

4= +

feuh % gka vk.VhA nksuksa cjkcj gSaA

eSa % BhdA bldk eryc gqvk fd 5

4 cjkcj gSaA iwjs ds vkSj

1

4

vkSj 1 bls ge

fy[krs gSaA tc ge 5 dks 4 ls Hkkx nsrs gSa

rks HkkxQy ls gesa fefJr

14 5

4

1

140

fHkUu dk iw.kkZad okyk fgLlk feyrk gS vkSj 'ks"kQy@Hkktd ls gesa mldk

mfpr fHkUu okyk fgLlk feyrk gSA ;kuh

5

4

¾ HkkxQy

'k"s k

Hkktd

¾

11

4

gksrk

gSA

vc crkvks

7

4

ds ckjs esa D;k dgrh gks\

feuh % vc ;g ckr eq>s le> vk xbZ gSA vkius tSlk crk;k mlds fglkc ls

7

4

gqvk

,d iwjk vkSj

3

4

vkSj blfy, ;g

31

4

gksxkA

feuh us viuh xyrh le> yh FkhA blh rjg ds dqN vkSj loky gy djus dsckn mldk vkRefo'okl c<+ x;k FkkA

E 10) feuh dh leL;k D;k Fkh\

E 11) D;k vki dksbZ vkSj rjhdk lq>k ldrs gSa ftldk mi;ksx djds feuh dh xyrh dks lq/kkjk tkldrk Fkk\

lkjka'klkjka'klkjka'klkjka'klkjka'k

bl ikB esa geus fuEufyf[kr fcUnq mHkkjus dh dksf'k'k dhA

1- vkerkSj ij ;g ns[kk x;k gS fd cPpksa dks fHkUuksa ds izrhdu o mUgsa ladsr :i esa n'kkZus esafnDdr gksrh gSA fHkUuksa ds ladsr :i esa n'kkZus ds fu;e le>uk muds fy, eqf'dy gksrk gSAfHkUuksa ds izrhdu ds rjhds dks ysdj cPps ds fnekx esa dksbZ my>u gks] rks mls nwj djus dsckn gh bl fo"k; esa vkxs c<+uk pkfg,A tc cPps ^vk/kk*] ^frgkbZ*] ^pkSFkkbZ*] tSls fHkUuksa ds ukeo iw.kZ ls muds laca/k esa Hkyh Hkkafr ifjfpr gks tk,a rHkh mUgsa fHkUuksa ds ladsrksa ls ifjfpr djk;ktkuk pkfg,A mUgsa ;g Li"V gks tkuk pkfg, fd tc ge 2 ds uhps ykbu [khapdj ykbu ds

uhps 3 fy[krs gSaA ;kuh

2

3

fy[krs gSa rks fHkUu

2

3

dk gj gesa crkrk gS fd iw.kZ ds rhu cjkcj

Hkkx fd, x, gSa vkSj va'k crkrk gS fd ge buesa ls 2 Hkkxksa dks ys jgs gSaA mUgsa fHkUuksa ds ukedks ladsr esa cnyus dk dkQh vH;kl djkuk pkfg,A blds fy, f'k{kd d{kk esa dbZ xfrfof/k;ka djok ldrs gSaA

2- fHkUuksa dks va'k&gj ds :i esa fy[kdj ,d gh fHkUu dks vyx&vyx <ax ls n'kkZ ldrs gSaA cPpksals dgk tk ldrk gS fd os fdlh ,d fHkUu dks n'kkZus ds fy, vf/kd ls vf/kd la[;k,a [kkstsaA;g dj ysus ds ckn mUgsa rqY; fHkUu dh ladYiuk ls ifjfpr djk;k tk ldrk gSA dkxt+ eksM+usrFkk blh rjg dh vU; xfrfof/k;ka djus o fofHkUu fdLe ds iw.kZ ls ifjfpr gksus ds ckn mUgsa;g le>us esa dfBukbZ ugha gksrh gS fd D;ksa bruh la[;k,a ijLij rqY; gSaA tc cPps ,d fHkUuds rqY; vU; fHkUu [kkstus dk dkQh vH;kl dj pqdsa rc mUgsa gj mnkgj.k esa iSVuZ [kkstus nsavkSj rqY; fHkUu fy[kus dk fu;e [kqn c [kqn irk djus nsaA

3- tc cPps rqY; fHkUu fy[kus ds fu;e ls ifjfpr gks tk,a rks mUgsa va'k o gj ds xq.ku[kaM ls Hkkxnsdj rqY; fHkUu irk djus dks dkQh vH;kl djok,a D;ksafd blesa cPpksa dks izk;% fnDdr gksrh gSA

141

4- iw.kZ dks dqy fdrus fgLlksa esa ckaVk x;k gS rFkk izR;sd fgLls ds vkdkj ds ijLij laca/k dksle>us esa cPps dbZ erZck xyrh dj cSBrs gSaA bldk vlj fHkUuksa dk Øe.k djus ij Hkh iM+rkgSA dkxt dks jaxus dh xfrfof/k ds tfj;s mUgsa ;g le>us esa enn fey ldrh gS fd dkSu lhla[;k cM+h gSA f'k{kd bdkbZ fHkUu ls 'kq: djds leku va'k ;k leku gj okys fHkUu ij tk

ldrs gSaA bl rjg ls cPps [kqn c [kqn vU; fHkUuksa tSls

5

6

o

7

8

rFkk

3

4

o

6

7

vkfn dh rqyuk

dk fu;e ;kuh lkekU; gj fu;e [kkst ik,axsA

5- 8&10 o"kZ ds cPpksa dks fo"ke fHkUu dks fefJr fHkUu esa cnyus esa dfBukbZ gksrh gSA blls fuiVus

ds fy, izR;{k phtksa ds lkFk xfrfof/k ds tfj;s fn[kk;k tk ldrk gS fd

7

4

¼;kuh lkr

,d&pkSFkkbZ ;k 7 dk

1

4

½ dk okLro esa vFkZ D;k gS\ blls mUgsa ,d izR;{k fp= gkfly gksxk

vkSj os ladYiuk dks le> ik,axsA

142

ikB&10ikB&10ikB&10ikB&10ikB&10n'keyon'keyon'keyon'keyon'keyo

ifjp;ifjp;ifjp;ifjp;ifjp;

fiNys ikB esa geus mu leL;kvksa dh ckr dh Fkh tks cPpksa dks fHkUu la[;kvksa ij lafØ;k,a djrs le;gksrh gSA bl ikB esa ge mu leL;kvksa ij fopkj djsaxs tks cPpksa dks fHkUu la[;kvksa dks n'keyo ds :iesa fy[kus esa gksrh gSa n'keyo la[;k,a os la[;k,a gSa ftUgsa n'keyo fcUnq ds lkFk fy[kk tkrk gSA

n'keyo dh vo/kkj.kk ,d egRoiw.kZ vo/kkj.kk gSA bls le>us esa cPpksa dks vDlj fnDdr gksrh gSAblfy, n'keyo la[;kvksa ls fuiVus esa os vDlj xyfr;ka djrs gSaA mnkgj.k ds fy, 15 lky dh ,dcPph ls iwNk x;k fd -05] -5] -5808 rFkk -056 esa ls lcls NksVh la[;k dkSu lh gS rks og ml fu;edks ;kn djus dh dksf'k'k djus yxh tks mlus izkbejh Ldwy esa lh[kk FkkA FkksM+k lkspdj mlus -5808dks lcls NksVh la[;k crk;k tc mlls dkj.k iwNk x;k] rks mlus crk;k fd mlds f'k{kd us mlsle>k;k Fkk fd n'keyo fcUnq ds ckn ftrus T;knk vad gksrs gSa] la[;k mruh gh NksVh gksrh gSaA

blh izdkj tc 12 ls 15 o"kZ ds cPpksa dks

40 0.8÷

djus dks dgk tkrk gS rks muds mRrj 5 ;k -5 gksldrs gSaA

bl ikB esa ge cPpksa dks n'keyo esa bruh fnDdr D;ksa gksrh gS\ rFkk ge bu fnDdrksa dks gy djusds fy, dqN mi;qDr rjhds Hkh fodflr djus dh dksf'k'k djsaxsA

'kCnkoyh ds vuqlkj ls n'keyo la[;kvksa dks n'keyo ;k n'keyo fHkUu Hkh dgk tkrk gSA ge bl ikBesa n'keyo la[;k dk gh mi;ksx djsaxsA

igys ge dqN ,slh leL;kvksa ij ppkZ djsaxs tks blfy, iSnk gksrh gSa D;ksafd cPps n'keyo ds ladsrksadks le> ugha ikrs gSaA

n'keyo la[;k D;k gS\n'keyo la[;k D;k gS\n'keyo la[;k D;k gS\n'keyo la[;k D;k gS\n'keyo la[;k D;k gS\

tc ge n'keyo lh[krs@fl[kkrs gSa] rks geesa ls fdrus yksx ;g loky iwNrs gSa fd ^^D;ksa 1-5] 1-50]1-500 leku gSa** exj 1-05 ls vyx D;ksa gS** ;fn vki fdlh ,sls cPps ls ;g loky iwNsa ftlus n'keyolh[k fy;k gks] rks og vkidks dqN vfuf'pr vkSj pdjk;k gqvk utj vk,xkA

bl Hkkx esa ge ,sls dqN rjhdksa ij ckr djsaxs ftuls cPpksa dks n'keyo lh[kus esa enn feysxh] rFkk,slh xyrQgfe;ksa ls cpk tk ldsxkA

mnkgj.k 1 %mnkgj.k 1 %mnkgj.k 1 %mnkgj.k 1 %mnkgj.k 1 % d{kk 4 dh f'k{kd ls iwNk fd os cPpksa dks n'keyo dSlh i<+krh gSaA mUgksaus eq>s crk;k fdlcls igys rks os 10 ls Hkkx dk fu;e crkdj mUgsa n'keyo i)fr ls ifjfpr djkrh gSA tSls&

7.7

10=27

2.710

=

12512.5

10=

bl rjg fu;e ;g gS fd 10 ls Hkkx nsuh] vkSj la[;k ds vkf[kjh vad ds igys n'keyo gksuk ,d ghckr gS blds ckn os blh fu;e dks gj 100 o gj 1000 okyh fHkUu la[;kvksa ij Hkh ykxw dj nsrh gSaA

143

os 27

.27,100

= 205

2.05,100

= 127

.1271000

= vkfn fy[kdj crkrh gSaA lkFk gh og ;g Hkh le>krh gS

fd -7 ¾ -70 blds ckn os <sj lkjs vH;kl nsrh gSa ftuesa n'keyo la[;k dks fHkUu esa vkSj fHkUu la[;kvksadks n'keyo esa cnyus dk vH;kl Hkh gksrk gS ftlls fd os mudh le> dks ij[k ldsaA dqN Nk=ksa dks

3

100 dks n'keyo ds :i esa fy[kus dks dgk x;kA dbZ cPps pDdj esa iM+ x, D;ksafd mUgsa ;g le>

ugha vk jgk Fkk fd nwljk vad dgka ls yk,a\ rc f'k{kd us mUgsa le>k;k fd os la[;k ls 'kq: djdsckbZa vksj pyrs tk,aA tgka dksbZ vad u gks ogka 'kwU; fy[k nsaA mUgksaus cPpksa dks ;g Hkh le>k;k fd-03

o -3 esa D;k vUrj gSA blds ckn cPpksa dks dbZ vH;kl djus dks fn, tSls fd

19

1000

dks n'keyo :i

esa fy[kukA ge vHkh vkxs crk,axs fd f'k{kd us gesa vkSj D;k&D;k crk;kA

E1 eku yhft, dksbZ cPph 0-06 dks 'kwU; n'keyo N% i<+rh gSA vki mls dSls le>k,axs fd mlusxyrh dh gS vkSj okLro esa bls 'kwU; n'keyo 'kwU; N% i<+uk t:jh gS\

vH;kl ls irk pyrk gS fd n'keyo i)fr dks iwjh rjg le>us ds fy, t:jh gS LFkkuh; eku dh vo/kkj.kk dk Kku gksA

vkb, ns[krs gSa fd f'k{kd n'keyo la[;kvksa ds LFkkuh; eku :i dh ckr fdl rjg le>krh gSaA ;g/;ku nsa fd mUgksaus fHkUu la[;kvksa dks n'keyo la[;k esa vkSj n'keyo la[;kvksa dks fHkUu esa cnyus dsdkQh lkjs loky djok Mkyus ds ckn gh ;g dke 'kq: fd;k gSA lcls igys mUgksaus cPpksa dks dqNiw.kkZad la[;kvksa tSls fd 324] 271 vkSj 450 dks 100] 10 vkSj 1 ds xq.kt ds :i esa fy[kus dks dgkA;g rks mUgksaus vklkuh ls dj fy;k vkSj fy[kk324 3 100 2 10 4 1= × + × + ×271 2 100 7 10 1 1= × + × + ×450 4 100 5 10 0 1= × + × + ×

fQj mUgksaus lkFk j[ks vadksa ds LFkku dk laca/k bl rjg crk;k] lSdM+s ds LFkku vkSj ngkbZ ds LFkku dksns[kksA rqEgsa 100 ls 10 dSls feysxk\ 100 dks 10 dks Hkkx nsdjA vc ngkbZ ds LFkku vkSj 1 ds LFkku dksyksA rqEgsa 10 ls 1 dSls feysxk\ 10 dks 1 ls Hkkx nsdj\ bl rjg gjsd LFkku dh rjQ /;ku fnyk djmUgksaus dgk ^^bl rjg tSls&tSls ge nk;ha rjQ c<+rs gSa** ge 10 ls Hkkx nsrs gSaA blh rjg gj ckj 10ls Hkkx nsdj ge bdkbZ ds ckn okys LFkkuksa dh vksj c<+uk tkjh j[krs gSaA rc bdkbZ ds nkfguh vksjnloka Hkkx gksxk] fQj lkSoka Hkkx vkfnA vkSj ;g fn[kkus ds fy, fd bl LFkku ij ^bdkbZ* lekIr gksrh

gS] ge bdkbZ la[;kvksa ds vkxs fcUnq yxk nsrs gSaA tSls& 2-5 dk eryc gS

12 1 5

10× + ×

-7 dk eryc gS&

7

10

11-47 dk eryc gS

1 11 10 1 1 4 7

10 100× + × + × + ×

bl rjg 2-5 gS 1 5

2 1 5 2 2.510 10

× + × = + = vkSj blh rjg 16-7 gSa 16 $ -7 bl rjg n'keyo

fcUnq iw.kkZad dks fHkUu la[;k dks fHkUu la[;k ls vyx djrh gS] blds ckn mUgksaus crk;k fd cPpksa

144

dks ;g lc fl[kkus ds ckn os muls n'keyo la[;kvksa dks LFkkuh; eku ds :i esa fy[kokrh gSaAtSls &

6 151.6 51 5 10 1 1 6

10 10= = × + × + ×

blh rjg ls os LFkkuh; eku ds :i esa izLrqr la[;k dks n'keyo ds :i esa fy[kokus dk vH;kl Hkhdjokrh gSA tSls]

1 12 100 0 10 7 1 8 3 207.83

10 100× + × + × + × + × =

LFkkuh; eku :i fl[kkus ds ckn os cPpksa ls <sj lkjs vH;kl djokrh gSaA buesa bckjrh loky Hkh gksrsgSaA tSls] dksbZ est 92-3 lseh yEch gSA crkvks ;g est fdrus ehVj yEch gS\ eSaus muls iwNk fd os blrjg ds loky igys D;ksa ugha nsrh\ mudk tokc Fkk fd igys bl rjg ds loky fn, tk,a rks cPpsxyfr;ka djrs gSaA tSls] tc muls 8 iSls dks :i, ds :i esa fy[kus dks dgk tkrk gS rks os 0-08 fy[kusdh ctk; -8 fy[k nsrs gSaA blfy, ,sls loky rHkh nsuk vPNk jgrk gS tc os LFkkuh; eku ds :i esala[;k izLrqr djuk lh[k pqds gksaA rks bl rjg ls os cPpksa dks n'keyo la[;kvksa ls ifjfpr djkrh gSaA

E2 mnkgj.k 1 esa of.kZr rjhds ds ldkjkRed o udkjkRed igyw D;k gS\

E3 vius vuqHko ds vk/kkj ij crkb, fd D;k cPpksa dks n'keyo fHkUu dk rdZ ¼;kuh 1

10 dh ?kkr

dk Øe½ le>kus ls mUgsa enn feysxh ;k os pdjk tk,axsA vius mRrj dk dkj.k Hkh nsaA

mnkgj.k 2 %mnkgj.k 2 %mnkgj.k 2 %mnkgj.k 2 %mnkgj.k 2 % f'k{kd 5 isaflysa vkSj 5 jcj ysdj vkbZA gj isafly dh yEckbZ jcj ls djhc nl xquh gS¼fp= 1½ os vyx&vyx yEckbZ dk /kkxk Hkh ykbZA

fp= 1

mUgksaus Nk=ksa dks ikap Vksfy;ksa easa ckaV fn;kA gj Vksyh dks mUgksaus ,d isafly] ,d jcj vkSj /kkxs dk,d&,d VqdM+k ns fn;kA vc mUgksaus Nk=ksa dks dgk fd isafly o jcj dh enn ls /kkxs dh yEckbZ ukisaA'kq:vkr esa FkksM+h enn Hkh dhA vkb, ns[krs gSa fd os Vksyh 1 ls fdl <ax ls ckrphr djrh gSaA

f'k{kd % isafly dh enn ls bl /kkxs dh yEckbZ ukiksA ;g /kkxk isafly ls fdrus xquk yEck gS\

¼Nk=ksa us ukidj fn[kk;k vkSj dgk 3 xqukA exj /kkxs dk dqN fgLlk cpk gqvk FkkA½

f'k{kd % cps gq, fgLls dk D;k djsa\

Vksyh % ;g ,d isafly ls de gSA

f'k{kd % D;k ml fgLls dks jcj ls uki ldrs gks\

Vksyh % ¼djds fn[kkrs gq,½ ;g jcj ls N% xquk gSA

f'k{kd % ;kuh /kkxk isafly ls rhu xquk vkSj jcj ls N% xquk gSA pyks bls rkfydk esa fy[k nsrsgSa ¼rkfydk 1 dh igyh iafDr ns[ksa½A

145

rkfydk 1

isafly jcj

3 6

2 5

1 3

4 7

5 1

f'k{kd % vc bl rkfydk dks ns[kksA ¼Vksyh 1 us /kkxs dh yEckbZ isafly dh rhu xquk vkSjjcj dh N% xquk ukih gSA½ vc ;g crkvks fd isafly jcj ls fdrus xquk yEch gSAukidj ns[kksA

,d Nk= % nl xqukA

f'k{kd % dSls fudkyk\

¼Nk= us isafly dks jcj ls ukidj fn[kk;kA½

f'k{kd % rks jcj isafly dk fdruk fgLlk gS\ ¼dksbZ tokc ughaA½ ;fn nl jcj ,d isafly dscjkcj gSa] rks ,d jcj fdruh isafly ds cjkcj gksxk\

,d vU; Nk=%

1

10

\

f'k{kd % gka]

1

10 gksxkA

vc f'k{kd us ,d js[kk cukbZ ftldh yEckbZ iasfly ds cjkcj Fkh vkSj ,d NksVk vk;rcuk;kA fp= 2 esa nsf[k,A

fp= 2

mUgksaus jcj dks fp= ij j[krs gq,

1 2 10, ,...............,

10 10 10

vkfn fu'kku yxk fn,A

f'k{kd % rks jcj isafly dk

1

10

gSA rc jcj ds N% xqus dk eryc gS N% xquk

1

10

tks

16

10×

gSA ;kuh isafly dk

6

10

;kfu /kkxs dh yEckbZ iasfly dh yEckbZ dh 3 xquk vkSj isafly

dh yEckbZ ds

1

10

dh 6 xquk gSA

146

vc f'k{kd us isafly ds uhps bdkbZ fy[kk vkSj jcj ds uhps nloka Hkkx ¼;k

1

10

½ fy[kkA

rkfydk 2rkfydk 2rkfydk 2rkfydk 2rkfydk 2

isafly ¼bdkbZ½isafly ¼bdkbZ½isafly ¼bdkbZ½isafly ¼bdkbZ½isafly ¼bdkbZ½ jcj ¼nloka Hkkx½jcj ¼nloka Hkkx½jcj ¼nloka Hkkx½jcj ¼nloka Hkkx½jcj ¼nloka Hkkx½

3 6

mUgksaus rkfydk ds cktw esa gh rkfydk 2 cuk nh rkfd nksuksa lkFk&lkFk fn[ksaA vc mUgksaus bdkbZ ds LraHkesa 3 vkSj nlosa Hkkx ds LrEHk esa 6 fy[k fn;kA

f'k{kd % vc crkvks isafly dh yEckbZ ds inksa esa /kkxs dh yEckbZ D;k fy[ksaxsA

,d Nk= %

63

10

f'k{kd % 'kkck'k! vkSj vU; Vksfy;ksa ds /kkxksa dh yEckb;ka D;k gSa\

dqN Nk= %

5 3 72 ,1 ,4

10 10 10

vkSj

15

10

-

f'k{kd % lgwfy;r ds fy, gj ckj

1

10

fy[kus dh ctk; ,d fcUnq yxk ldrs gSaA tSls

63

10

dks 3-6 fy[k ldrs gSaA blls irk pyrk gS fd 3 bdkb;ka gSa vkSj 6 nlosa Hkkx gSaA

;kuh 1 63.6 3 1 6 3

10 10= × + × =

rks] geus 6

310

dks ,d fcUnq dh enn ls 3-6 fy[kkA D;k vc gj Vksyh crk ldrh gS

fd bl rjg fcUnq ds lkFk muds /kkxs dh yEckbZ fdruh gS\

Vksfy;ka % 2-5] 1-3] 4-7] 5-1

f'k{kd % cgqr cf<+;kA bu la[;kvksa dks eSa rkfydk esa fy[k nsrh gwa ¼mUgksaus rkfydk 2 dh cktwesa rkfydk 3 Hkh cuk nhA½A

rkfydk 3

isafly ¼bdkbZ½isafly ¼bdkbZ½isafly ¼bdkbZ½isafly ¼bdkbZ½isafly ¼bdkbZ½ jcj ¼nloka Hkkx½jcj ¼nloka Hkkx½jcj ¼nloka Hkkx½jcj ¼nloka Hkkx½jcj ¼nloka Hkkx½

3 6

2 5

1 3

4 7

5 1

147

bl fcUnq dks n'keyo fcUnq dgrs gSaA bl rjg ls fcUnq dk bLrseky djds la[;k fy[kus ds rjhds dksn'keyo iz.kkyh dgrs gSaA

vc rkfydk 3 dks ns[kksA ;fn eSa bdkbZ ds LrEHk esa 1 vkSj nlosa Hkkx ds LrEHk esa 4 fy[k nwa rks n'keyoi)fr esa og la[;k D;k gksxh\

,d Nk= % ;g la[;k ,d n'keyo pkj gksxhA

f'k{kd % fHkUu ds :i esa bl la[;k dks dSls fy[ksaxs\

ogh Nk= %

41

10

fy[ksaxsA

f'k{kd % bls bdkbZ vkSj nlosa Hkkx ds :i esa rksM+dj dSls fy[ksaxs\

dbZ Nk= %

11 1 4

10× + ×

fy[ksaxsA

f'k{kd % eku yks fd eSa bdkbZ ds LrEHk esa 0 vkSj nlosa Hkkx ds LrEHk esa 5 fy[k nwa rks n'keyoi)fr esa ;g la[;k D;k gksxh\

,d vU; Nk= % ¼dqN lkspdj½ D;k ;g 'kwU; n'keyo ikap gksxh\

f'k{kd % gkaA vc crkvks bl la[;k dks fHkUu esa dSls fy[kksxs\

Nk= %

50

10f'k{kd % ;kuh D;k\

ogh Nk= % eryc

5

10

f'k{kd % dSls\

ogh Nk= %

10.5 0 1 5

10= × + ×

bl rjg ls ckrphr djrs gq, f'k{kd us bl ckr dks ij[kk fd Nk=ksa us vyx&vyx la[;kvksa dhn'keyo i)fr le>h ;k ughaA

rks bl rjg ls f'k{kd us cPpksa dk ifjp; n'keyo la[;k ls djk;kA blds ckn mUgksaus n'keyola[;kvksa dk lSdM+s] ngkbZ] bdkbZ] nlosa] lkSosa ds xq.kdksa ds :i esa fy[kuk fl[kk;kA

Åij fn;s x;s mnkgj.k ls tkfgj gS fd n'keyo la[;k dh vo/kkj.kk dk vglkl cukus ds fy, gefdl rjg dh xfrfof/k;ksa dk bLrseky dj ldrs gSaA

E4 ,sls nks vH;kl ;k xfrfof/k;ka lq>kb, ftUgsa 20 cPpksa ds lewg ds lkFk fd;k tk lds rFkkftuls n'keyo i)fr le>us esa enn feysA

E5 mnkgj.k 1 o 2 esa geus n'keyo fl[kkus ds nks vyx&vyx rjhdksa dh ppkZ dhA vkidseqrkfcd cPpksa dks n'keyo dh cqfu;knh le> gkfly djus ds fygkt ls dkSu lk rjhdkT;knk dkjxj jgsxk\

148

E6) ;fn dksbZ cPpk fHkUu la[;k dks n'keyo la[;k esa rFkk n'keyo la[;k dks fHkUu esa cny ys rks;g ekuk tk ldrk gS fd mls n'keyo i)fr le> vk xbZ gSA ;g dFku lgh gS ;k xyr\dkj.k lfgr crkb,A

vc rd vki ;g rks le> gh x, gksaxs fd n'keyo fcUnq dh vo/kkj.kk rFkk la[;k dh n'keyo i)frdks le>us esa cPpksa dks le; yxrk gSA

n'keyo la[;kvksa dh fofHkUu xf.krh; lafØ;k,a djus ds fy, ;g vo/kkj.kkRed le> fugk;r t:jhgSA vxys Hkkx esa ge bl ls lacaf/kr dqN leL;kvksa ij ns[ksaxsA

n'keyo la[;kvksa ij lafØ;k,an'keyo la[;kvksa ij lafØ;k,an'keyo la[;kvksa ij lafØ;k,an'keyo la[;kvksa ij lafØ;k,an'keyo la[;kvksa ij lafØ;k,a

D;k vkius dHkh fdlh cPps dks n'keyo dk tksM+ xq.kk fl[kkus dh dksf'k'k dh gS\ D;k vkidh dksf'k'k;gh Fkh fd og fofHkUu fu;eksa dks rst xfr ls vkSj lgh&lgh ykxw djus yxs\ cnfdLerh ls ge vDlj;gh djrs gSaA ge izk;% bu fØ;kvksa esa fufgr vo/kkj.kkvksa dh le> ij tksj ugha nsrsA exj] t:jrbl ckr dh gS fd le> cukus ij /;ku fn;k tk,A gesa ;g Hkh vknr cukuh pkfg, fd muls ,sls lokyiwNrs pysa ftuls mUgsa vkSj gesa mudh le> dks ij[kus esa enn feysA mUgsa ,sls vH;kl nsa ftuls mudhcqfu;knh le> dh tkap gks ldsA tc Hkh os fdlh fØ;k dks djus ds fy, dksbZ ,Yxksfjn~e ykxw djsa rksgesa muls iwNuk pkfg, fd mUgsa dSls ekywe fd mudk mRrj lgh gSA

bl [k.M esa ge bl ckr ij fopkj djsaxs fd n'keyo dh pkj cqfu;knh lafØ;kvksa ds fu;e le>us omUgsa ykxw djus esa cPpksa dh enn dSls dh tk,A

vkb,] lcls igys tksM+ o ckdh ls lacaf/kr dqN fnDdrksa ij xkSj djsaA

tksM+@ckdhtksM+@ckdhtksM+@ckdhtksM+@ckdhtksM+@ckdh

izkbejh Ldwy ds dqN f'k{kdksa ls ckrphr djrs gq, gesa irk pyk fd n'keyo ds tksM+&ckdh esa cPps[kkl rkSj ls rc fnDdr eglwl djrs gSa tc bu la[;kvksa ds n'keyo okys fgLls esa vadksa dh la[;kvyx&vyx gksrh gSA tSls 0-123 $ 1-1 $ 1-101 tSlk tksM+A muesa ls ,d f'k{kd us gesa foLrkj lscrk;k fd os d{kk 5 ds cPpksa dks n'keyo la[;kvksa dk tksM+ dSls fl[kkrh gSaA vkb, mudk rjhdk ns[ksaA

mnkgj.k 3 %mnkgj.k 3 %mnkgj.k 3 %mnkgj.k 3 %mnkgj.k 3 % f'k{kd d{kk esa 2-7 vkSj 1-8 rFkk 18-75 vkSj 20-65 tSls tksM+ igys gh fl[kk pqdh FkhaA vcvxyk dne ;g Fkk fd mUgsa 18-7 $ 20-65 tSls tksM+ fl[kkuk FkkA os bl rjg vkxs c<+haA

mUgksaus cksMZ ij 18-7 $ 20-65 fy[kkA la[;kvksa dh vksj b'kkjk djrs gq, mUgksaus cPpksa ls dgk] ^^igyhla[;k esa n'kryo fcUnq ds ckn ,d vad gS vkSj nwljh la[;k esa nks vad gSaA blfy, ge 18-7 ¾ 18-70 fy[k nsaxsA vc bUgsa ,d ds uhps ,d fy[kdj tksM+ nsaxsA fQj mUgksaus cksMZ ij fy[kk &

18.70

20.65

39.35

+

vkSj crk fn;k fd 18-7 vkSj 20-65 dk tksM+ 39-35 gSA mUgksaus blh rjg dk ,d vkSj loky djkus dsckn cPpksa dks fuEufyf[kr loky fn;k &

0-05 $ 0-101 $ 0-3

149

mUgksaus ns[kk fd dbZ cPpksa us bls ;ksa fy[k fy;k Fkk %

0.005

0.101

0.300+ ;k

0.05

0.101

0.003+

gj ckj mUgsa dbZ&dbZ erZck cPpksa dh xyfr;ka lq/kkjuh iM+haA

E7 vkids [;ky esa cPps xyfr;ka D;ksa dj jgs Fks\ vki mudh enn dSls djsaxsA

E8 vius vklikl ds cPpksa ls iwfN, fd jkstejkZ dh ,slh fLFkfr;ka lkspsa tgka mUgsa n ' k e y ola[;kvksa dh t:jr iM+sxhA muds tokc uksV dhft,A

;fn vki mnkgj.k 3 esa cPpksa }kjk dh xbZ xyfr;ksa ij /;ku nsaxs rks vkidks irk pysxk fd mUgsa okLroesa ;g le> ugha vk;k gS fd D;ksa 18-7 vkSj 18-70 ;k 18-700 ,d gh ckr gS tcfd 18-07 vyx gSAnwljs 'kCnksa esa os ;g ugha le> ik, gSa fd n'keyo fcUnq ds ckn la[;k ds vUr esa tc pkgs rc 'kwU;D;ksa yxk;k ;k gVk;k tk ldrk gS\ vr% tksM+ dk fu;e fl[kkrs oDr ;s ckrsa Hkh mUgsa lkQ rkSj ijcrkuh gksaxhA cPps dks ;g vglkl djkuk gksxk fd ml fu;e ds ihNs D;k le> gSA dqN yksxksa us ns[kkgS fd ;fn Nk=ksa dks n'keyo fl[kkus ds fy, fiNys Hkkx esa of.kZr xfrfof/k;ksa dh enn yh tk,] rksos n'keyo fcUnq ds ckn ds gj vad dk LFkkuh; eku le>us yxrs gSaA blds ckn os xf.krh; fØ;k,aT;knk csgrj <ax ls dj ikrs gSaA

E9 ^^100 Hkkxksa esa caVs oxZ** dk mi;ksx djds vki fo|kFkhZ dks tksM+ dh {kerk gkfly djus esa dSlsenn dj ldrs gSa\

vkb, vc n'keyo ds ?kVkus ls lacaf/kr leL;kvksa dh ckr djsaA f'k{kdksa dk vuqHko gS fd tc la[;k,a,d ykbu esa fy[kh gksa] rks T;knk xyfr;ka gksrh gSaA blh izdkj ls tc la[;kvksa esa n'keyo ds ckn vadksadh la[;k vyx&vyx gks] rks Hkh cPps T;knk xyrh djrs gSaA

¼d½

1.5 3

3.4

11.9

− ¼[k½

3.4

1.5 3

.8 1

− ¼x½

3.4

1.53

1.93

−

E10 Åij fn, x;s mRrj fdl rdZ ds vk/kkj ij vk, gksaxs\ cPpksa dh le> dks nq:Lr djus ds fy,fdl rjg dk vH;kl o dk;Z t:jh gksxk\

E11 ^D;k 100 fgLlksa esa caVk oxZ* cPpksa dks n'keyo ds ?kVkus ds loky csgrj <ax ls djus esaenn dj ldrk gS\ vius mRrj dk dkj.k Hkh nhft,A

xyfr;ka cPpksa ds lh[kus dk LokHkkfod o vfuok;Z vax gSA xyfr;ksa ls irk pyrk gS fd os fdl rjglksprs o lh[krs gSaA n'keyo ds tksM+us o ?kVkus ls lacaf/kr fofHkUu xyfr;ksa ds fo'ys"k.k ds ckn vki'kk;n lger gksaxs fd bu leL;kvksa dk laca/k ?kVkus dh fØ;k ls u gksdj n'keyo i)fr esa fcUnq dsnksuksa vksj vadksa ds Øe dh le> ls gSA gekjs [;ky ls bldk loksZRre lek/kku rks ;g gksxk fdn'keyo esa LFkkuh; eku dh csgrj le> fodflr dh tk,A

150

xq.kk@Hkkxxq.kk@Hkkxxq.kk@Hkkxxq.kk@Hkkxxq.kk@Hkkx

dqN ekrk&firk ds lkFk ppkZ ds nkSjku ;g ckr lkeus vkbZ fd cPpksa ds fy, xq.kk djuk mruk eqf'dyugha gksrk ftruk fd Hkkx xq.kk djus ds nkSjku FkksM+h lh leL;k ;g vkrh gS fd cPps xq.kk djus dsrFkkdfFkr fu;eksa dks ysdj Hkzfer gks tkrs gSaA nks n'keyo la[;kvksa dk xq.kk djus dk tks fu;eikB~;iqLrdksa esa fn;k x;k gS] og gSA

1- xq.kk Bhd mlh rjg djsa tSls nks iw.kkZad la[;kvksa dk djrs gSaA

2- xq.kuQy esa n'keyo fcUnq bl rjg yxk,a fd xq.kuQy esa n'keyo ds ckn vadksa dh la[;krFkk xqf.kr o xq.kd ¼ewy la[;k,a½ esa n'keyo ds ckn vadksa dh dqy la[;k cjkcj jgsA

bl fu;e dks le>us ls igys cPpksa dks ;g irk gksuk pkfg, fd xqf.kr o xq.kd D;k gksrs gSaA bruhdfBu Hkk"kk ds bLrseky ds ckotwn cPps vDlj xq.kk djus ds ;k vU; fu;e lh[k gh ysrs gSA ijUrqvf/kdrj cPps bUgsa tYnh gh Hkwy Hkh tkrs gSa vkSj fQj os bUgsa xyr <ax ls ykxw djus yxrs gSaA bllanHkZ esa ,d fnypLi okd;kA

mnkgj.k 5 %mnkgj.k 5 %mnkgj.k 5 %mnkgj.k 5 %mnkgj.k 5 % ,d ckj eSaus vius Hkrhts uUnw ls 2-14 esa 10 dk xq.kk djus dks dgk og d{kk 6 esa i<+rkgSA FkksM+h nsj lkspdj mlus dgk ^^D;k -214 gksxk\** fQj rqjUr viuh xyrh lq/kkjrs gq, cksyk ^^ugha]'kk;n n'keyo fcUnq dks nkbZa vksj f[kldkuk iM+sxk] rks 21-4 vk,xkA** ckr ;g gS fd mls fu;e dksysdj vkRefo'okl ugha gSA og bls cxSj le>s ;kn djus dh dksf'k'k djrk gSA eq>s yxk fd dqN mik;djus dh t:jr gSA

ml 'kke eSaus ,d ;kstuk cuk;h fd mls dkSu lh vo/kkj.kk,a o izfØ;k,a le>kÅaxh eSaus mu phtkssa oxfrfof/k;ksa dh Hkh ;kstuk cukbZ tks mu vo/kkj.kkvksa ls igys djuk t:jh gSA vxys fnu geus bl ckjsesa ckrphr 'kq: dh igys eSaus ;g irk fd;k fd mls n'keyo i)fr le> esa vkrh gS ;k ugha mlsn'keyo i)fr esa LFkkuh; eku dks ysdj dksbZ fnDdr u FkhA blds ckn eSa vkxs c<+hA

eSa % eku yks fd ge 0.1 5× djuk pkgrs gSA igys rks ;g crkvks fd 0-1 dk rqe D;k erycle>rs gks\

Hkrhtk % eryc\ fHkUu ds :i esa ;g

1

10

gksxkA

eSa % BhdA rks

0.1 5×

D;k gksxk\

mlus fy[kk

1 55

10 10× =

eSa % bls n'keyo :i esa dSls fy[kksxs\

Hkrhtk % 0-5

eSa % cf<+;kA rks 5

0.1 5 0.510

× = = gqvkA vc crkvks 0.01 5× vkSj

0.001 5×

dk mRrj D;k gksxk\

Hkrhtk %

0.01 5 0.05× =

eSa % dSls fudkyk\

uUnw us fy[kk

1 50.01 5 5 0.05

100 100× = × = =

vkSj

1 50.001 5 5 0.005

1000 1000× = × = =

151

eSa % gka] cgqr cf<+;kA vc ns[krs gSa fd D;k rqe blh rjg ls 0.6 0.3× fudky ldrs gks\

uUnw us fy[kk

6 3 180.6 0.3 0.18

10 10 100× = × = =

vkSj cksyk 'kwU; n'kryo ,d vkBA

eSa % ;kuh 0.6 0.3 0.18× = gqvkA ,d vkSj mnkgj.k ns[ksa &

0.2 0.14×

fdruk gksxk\

uUnw us fy[kk

2 14 280.2 0.14

10 100 1000× = × =

fQj FkksM+k lkspdj fy[kk 0-028 gksxkA

eSa % pyks igys tjk ns[k ysa fd vHkh rd ge yksxksa us D;k&D;k dj fy;k gSA¼eSus lkjs loky ,d&,d djds fy[k fn,½

0.1 5 0.5× =

0.01 5 0.05× =0.001 5 0.005× =0.6 0.3 0.18× =0.2 0.14 0.028× =

eSa % bu lc ij tjk /;ku nksA D;k ^cjkcj* fpUg ds nksuksa rjQ dh la[;kvksa esa n'keyo fcUnqds nkbZa vksj ds vadksa esa dksbZ laca/k fn[krk gS\ igys mnkgj.k dks ns[kksA cjkcj fpUg ds ckbZavksj n'keyo fcUnq ds nkbZa vksj dqy feykdj fdrus vad gSa\

Hkrhtk % ,d gh gSA

eSa % vkSj nkbZa cktw\

Hkrhtk % ,d gh gSA

eSa % vxys loky esa\

Hkrhtk % nkfguh vksj Hkh vad gS vkSj ckbZa vksj Hkh nks gSaA rhljs loky esa nkfguh vksj Hkh rhu gSa] ckbZavksj Hkh rhu gSaA vkSj pkSFks mnkgj.k esa ¼FkksM+k lksprk gS½ 0-6 esa ,d vad gS vkSj 0-3 esa Hkh,d gSA rks dqy 2 gq, vkSj nkfguh rjQ Hkh 2 gSA vkSj vxys loky esa 0-2 esa ,d vksj 0-14 esa nks gSaA rks dqy rhu gq, vkSj nkbZa vksj Hkh rhu gSaA

eSa % rks D;k bu lcesa dksbZ fu;e fn[krk gS\

Hkrhtk % cjkcj fpUg ds nkbZa vkSj ckbZa vksj vadksa dh dqy la[;k cjkcj gSA

eSa % vkSj dqN\

¼og pqi jgk½

eSa % ns[kksA

0.6 0.3×

dks ns[kksA D;k 6] 3 vkSj 18 ds chp dksbZ laca/k gS\

Hkrhtk % gka] 6 xq.kk 3 cjkcj 18 gksrk gSA

eSa % ckdh lokyksa dh la[;kvksa esa Hkh dksbZ laca/k gS D;k\

Hkrhtk % gka] le> x;kA 14 xq.kk 2 ¾ 28 gksxk vkSj

1 5 5× =

gksxkA

eSa % cf<+;k] rks rqeus xq.kk dk fu;e [kqn gh [kkst fy;kA vc rqEgh ;g fu;e crkvksA

Hkrhtk % eku yhft, fd ge 0-7 vkSj 0-6 dk xq.kk djuk pkgrs gSaA rks igys ge 7 vkSj 6 iw.kkZadksa

152

dk xq.kk dj nsaxs vkSj 42 vk tk,xkA vc nksuksa xq.kdksa esa n'keyo ds nkfguh vksj ds vadfxu ysaxsA bl loky esa 2 vad gSaA blfy, xq.kuQy 0-42 gksxkA

eSa % BhdA vc ;fn xq.kk djrs oDr rqEgsa fu;e dks ysdj 'kadk gks] rks rqe la[;kvkas dks fHkUuds :i esa fy[kdj tkap dj ldrs gks%

7 6 420.7 0.6 0.42

10 10 100× = × = =

le> x,\

Hkrhtk % thA

eSa % vc mlh loky dks ysrs gSa tks eSaus rqels dy iwNk FkkA 2.14 10× fdruk gksxk\ rqEgsa dyle> ugha vk jgk Fkk fd ;g 0-214 gksxk ;k 21-4 gksxk\ vc bldh tkap djds ns[k yksA

mlus fy[kk

2142.14 10 10 21.4

100× = × =

Hkrhtk % 21-4 gksxkA

eSa % fu;e ykxw djds ns[kksA

Hkrhtk % 214 10 2140× = A ckbZa gkFk dh la[;kvksa esa n'keyo ds ckn nks vad gSaA blfy, mRrj 21-40 gksxkA

eSa % BhdA vc rqe pDdj esa ugha iM+ksxs] D;ksa\

Åij fn, x, mnkgj.k ls irk pyrk gS fd fdl rjg fo|kFkhZ xq.kk dk fu;e [kqn fodflrdj ldrs gSaA ,slk gksus ij mUgsa ,d ,slh izfØ;k dks ;kn j[kus ij etcwj ugha gksuk iM+sxk]ftls os le>rs ughaA mnkgj.k ls ;g Hkh irk pyrk gS fd fu;e dks ysdj fdlh Hkh Hkzedh fLFkfr esa fo|kFkhZ fHkUu ds rjhds ls vius mRrj dh tkap Hkh dj ldrs gSaA blls muesavkRefo'okl c<+rk gSA

E12 ^^100 fgLlksa esa caVs oxZ dh xfrfof/k ge n'keyo la[;kvksa dh xq.kk fl[kkus ds fy,dSls bLrseky dj ldrs gSa\

vkb, vc n'keyo la[;kvksa ds Hkkx ls tqM+h leL;kvksa ij fopkj djsaA geus ckj&ckj blckr ij tksj fn;k gS fd leL;k dh ewy otg ;g gS fd Hkkx dh izfØ;k esa fufgr cqfu;knhvo/kkj.kkvksa dh le> dk vHkko gSA dqN f'k{kdksa us crk;k fd cPps T;knk xyrh rHkh djrsgSa tc Hkktd n'keyo la[;k gksA vkb, ;g ns[kus dh dksf'k'k djrs gSa fd fHkUu okykrjhdk blesa fdruk ennxkj gks ldrk gSA

mnkgj.k 6 %mnkgj.k 6 %mnkgj.k 6 %mnkgj.k 6 %mnkgj.k 6 % d{kk 5 dh ,d f'k{kd vius fo|kfFkZ;ksa dks ;g le>kus dh dksf'k'k dj jgh Fkh fd n'keyo la[;kls Hkkx dSls djrs gSaA crkSj mnkgj.k mUgksaus cksMZ ij

24 0.4÷

fy[kkA

f'k{kd % xq.kk dh rjg ;gka Hkh ge fHkUu okys rjhds ls vkxs c<+saxsA ;kuh ge n'keyo la[;kvksa dksfHkUu ds :i esa fy[k ysaxs vkSj fQj fHkUu la[;kvksa ds Hkkx dk fu;e yxk,axsA rks crkvksfd 0-4 dks fHkUu ds :i esa dSls fy[ksa\

,d cPpk% 0-4 cjkcj

4

10

gksrk gSA

153

f'k{kd % vc D;k rqe

424

10÷

fudky ldrs gks\

,d Nk= %

424

10÷

;kuh

1024 60

4× =

f'k{kd us iw.kkZad la[;k dks n'keyo la[;k ls Hkkx nsus ds ,d&nks mnkgj.k vkSj djok,A blds cknmUgksaus ;g le>k;k fd ,d n'keyo la[;k dks nwljh la[;k ls Hkkx dSls nsrs gSaA mnkgj.k ds fy,

0.36 0.2÷

fy;kA mUgksaus cPpksa ls dgk fd bUgsa fHkUu la[;k ds :i esa fy[k nsaA blesa cPpksa dks dksbZfnDdr ugha gqbZ

36 2

100 10÷

ijUrq bl pj.k ds ckn cgqr gh FkksM+s cPps lgh&lgh Hkkx dj ik,A

dqN cPpksa us

100 10

36 2÷

dj fn;kA

tks cPps ,d fHkUu la[;k esa nwljh fHkUu la[;k dk Hkkx nsuk le> pqds gSa] mUgsa ;g rjhdk viukus esadksbZ fnDdr ugha vkrhA exj vU; cPpksa ds fy, ;g rjhdk eqf'dy gksrk gSA muds fy, 'kk;n blhrjhds ds leku ,d vU; rjhdk csgrj gksA ;g rjhdk gS]

0.36 0.36 10 3.6

0.2 0.2 10 2

×= =×

pwafd iw.kkZad la[;k ls Hkkx nsus esa dksbZ fnDdr ugha gS] blfy, 'kk;n mUgsa ;g rjhdk vklku yxsA

exj bl rjg ds Hkkx djrs gq, Hkh cPps vDlj xyrh dj cSBrs gSaA os ;g r; ugha dj ikrs fd n'keyofcUnq dgka yxk,aA mnkgj.k ds fy,] tc eSaus NBh d{kk ds ,d cPps dks 54.16 8÷ djus dgk] rks mlusdqN bl rjg fd;k&

.6778 54.16

48

61

56

56

56

0

tkfgj gS fd mlus fu;e dks le>k ugha Fkk vkSj viuk gh fu;e ykxw dj jgh FkhA og ;g Hkwy pqdhFkh fd og 54 ls dqN vf/kd la[;k dks 8 ls Hkkx ns jgh gS] u fd 5412 dks 8 lsA mlus ;g ugha lkspkfd mldk mRrj 7 ds yxHkx vkuk pkfg,A

gekjs fy, cPpksa dks ;g le>kuk cgqr t:jh gS fd os Hkkx esa n'keyo fcUnq dc yxk,¡A ge bl ckrij tksj nsrs gSa fd fcUnq iw.kkZad dks fHkUu okys fgLls ls vyx djus ds fy, gSA bl ckr dks fuEu pj.kksads tfj, ls le>uk Bhd jgsxkA

154

pj.k 1 % igys fn[kk,a fd Hkkx dSls fn;k tk,] tSls fd 4-16 dks 8 lsA bu vadksa dks pquus ds ihNs bjknk;g gS fd 4-16 dk iw.kkZad 4 gS tks 8 ls de gSA ge 4-16 dh txg dksbZ vkSj vad Hkh ys ldrs gSa ftldkiw.kkZad okyk fgLlk 8 ls de gksA

vc 4-16 dks 8 ls Hkkx nsus ds fy, igys gesa 4 dks 8 ls Hkkx nsuk gksxkA ,slk djus ij gesa 1 ls dela[;k feysxh tks fd ,d mfpr fHkUu gSA bl rjg HkkxQy esa dksbZ iw.kkZad ugha gS ¼fp= 3 ns[ksa½A geHkkxQy dks n'keyo fcUnq ls 'kq: djrs gSa ;g fn[kkus ds fy, fd dksbZ iw.kkZad ugha gSA vkSj fHkUu okykfgLlk 'kq: gksrk gSA fQj ge fp= 3 ds vuqlkj izfØ;k tkjh j[krs gSaA

0.528 4.16

40

16

16

0

fp= 3

fVIi.kh % ;gka gesa cPpksa dks ;g le>us esa enn djuh pkfg, fd ;g tkuus dk Hkh ,d rjhdk gS fd

Hkkx lgh gS ;k ugha & ns[ksa fd

.52 8, 4.16×

ds cjkcj gS ;k ughaA

vxyh pj.k esa ge mUgsa

54.16 8÷

tSls loky ns ldrs gSaA

pj.k 2 % /;ku nsa fd igys gesa 54 dks 8 ls Hkkx nsuk gS ¼fp= 4 ns[ksa½ rc 'ks"kQy ds rkSj ij gesa 6 feyrkgSA fQj gesa 6 dks 8 ls Hkkx nsuk gSA bl pj.k ij iw.kkZad okyk fgLlk 8 ls NksVk gSA ;g fLFkfr voLFkk1 tSlh gS vkSj gesa Bhd oSls gh pyuk gksxk ¼ns[ksa fp= 4½A

6.778 54.16

48

61

56

56

56

0

fp= 4

blds ckn vH;kl ds fy, dkQh lkjs loky nsa vkSj gj ckj bl ckr ij tksj nsa fd Hkkx nsus esa tc Hkhog voLFkk vk;s fd iw.kkZad okyk fgLlk Hkktd ls de gksA rks ge HkkxQy esa n'keyo fcUnq yxkrs gSaAbl rjg ds Hkkxksa ls ftuesa la[;k Hkktd ls iwjh rjg foHkkT; gks] ge vxyh voLFkk esa tk ldrs gSaA

pj.k 3 % ,slh la[;kvksa dk Hkkx ftuesa va'k ds nk;ha vksj 'kwU; yxkus iM+sa rkfd og Hkktd ls iwjh rjgfoHkkT; gksA tSls fd 54-12 dks 8 ls Hkkx nsukA

155

vkb, vc ge

3.12 8÷

ds laf'y"V Hkkx dk mnkgj.k ns[krs gSaA

0.398 3.12

24

72

72

0

bl izfØ;k dks le>us ds fy, gesa ;g le>uk t:jh gksxk fd ;gka okLro esa D;k gks jgk gSA

1 13.12 3 1 1 2

10 10= × + × + ×

okLro esa laf'y"V Hkkx dh fØ;k esa dbZ mifØ;k,a 'kkfey gksrh gSA bu mifØ;kvksa dks le>uk Hkkxle>us ds fy, t:jh gSA ;g laHko gS fd ;fn fo|kFkhZ bu mifØ;kvksa ds rdZ dks le>us ds fy, rS;kju gks] rks mifØ;k,a mls Hkzfer Hkh dj ldrh gSaA mnkgj.k ds fy, ;gh ns[ksa fd

3.12 8÷

esa D;k dqNdjuk gksrk gSA

13.12 3 1 1 10 2

100= × + × + ×

30 1 12

10 10 100= + + ×

¼pwafd 3<8 gS blfy, bl jkf'k dks 8 ls Hkkx nsus ls iwoZ gesa 3 ls vxys LFkku ij tkdj 3 dks 30

10

ekuuk gksrk gSA½

3 7 2(8 )

10 10 100= × + +

¼pwafd

31 8 3 7

10 10

× += ½

3 70 28

10 100 100 = × + +

3 728

10 100 = × +

3 98 8

10 100= × + ×

8 0.39= ×

ysfdu geesa ls vf/kdrj yksx cPpksa ls ek= bruh mEehn djrs gSa fd pan pj.k ;kn j[ksa vkSj lokygy dj nsaA bu lkjh mifØ;kvksa dh mis{kk gksrh gSA vki bl ckr ls rks lger gksaxs fd bu mifØ;kvksadks ek= og cPps le> ldrs gSa tks LFkkuh; eku dh /kkj.kk ls HkyhHkkafr ifjfpr gksaAE13) cPpksa esa n'keyo ds xq.kk o Hkkx dh le> csgrj cukus ds fy, dksbZ [ksy rS;kj dhft,A

E14 cPpks esa n'keyo dh fofHkUu fØ;kvksa dh le> ds ewY;kadu ds fy, vki D;k&D;k rjhdsviuk,axs\

156

cPps vius gj vuqHko ls lh[krs gSaA fo'ks"k :i ls rS;kj f'k{k.k lkexzh dh ctk; mudh T;knk #fpjkstejkZ dh phtksa vkSj vkStkjksa esa gksrh gSaA muds nSfud thou esa ,sls i;kZIr volj gksrs gSa tc osn'keyo la[;kvksa dk mi;ksx dj ldrs gSaA n'keyo la[;kvksa dh vo/kkj.kk o gquj fodflr djus esacPpksa ds bu vuqHkoksa dk ykHk mBk;k tkuk pkfg,A

lkjka'klkjka'klkjka'klkjka'klkjka'k

bl ikB esa geus

1- dqN ,slh cqfu;knh leL;kvksa ij ppkZ dh tks cPpksa dks n'keyo ds lkFk vkrh gSaA2- dqN ,sls rjhdksa ij fopkj fd;k ftuds tfj;s cPps la[;kvkas dh n'keyo i)fr dks csgrj le>

ik,aA3- cPpksa dks n'keyo la[;kvksa dh fØ;kvksa ls ifjfpr djkus ds rjhdksa ij xkSj fd;kA

4- fuEufyf[kr ckrksa ij tksj fn;k

• Bksl oLrq@vuqHko vk/kkfjr f'k{k.k

• cPpksa dks fofo/k xfrfof/k;ka nsuk

• mUgsa fu;e jVkus dh ctk; mldk rdZ le>us esa enn djukA

iwjs ikB ds nkSjku geus bl ckr ij tksj fn;k fd ;g fugk;r t:jh gS fd cPps Bhd ls ;g le>sa fdla[;kvksa dh n'keyo i)fr esa D;ksa o dSls fy[kk tkrk gSA ,d ckj;g gks tk, rks vke rkSj ij cPpsdks n'keyo la[;k dh lafØ;kvksa esa dksbZ fnDdr ugha gksrhA

157

txg dh le>txg dh le>txg dh le>txg dh le>txg dh le>

ikB & 11ikB & 11ikB & 11ikB & 11ikB & 11 txg dh le>txg dh le>txg dh le>txg dh le>txg dh le>

cUn vk—fr;k¡ & leery lrg & le vk—fr;k¡ & lefer vk—fr;k¡ & lkjka'kA

ikB & 12ikB & 12ikB & 12ikB & 12ikB & 12 dks.k ekiukdks.k ekiukdks.k ekiukdks.k ekiukdks.k ekiuk

dks.k D;k gksrk gS\ & dks.k ekiuk & lkjka'kA

ikB & 13ikB & 13ikB & 13ikB & 13ikB & 13 ekiu dh 'kq:vkrekiu dh 'kq:vkrekiu dh 'kq:vkrekiu dh 'kq:vkrekiu dh 'kq:vkr

yEckbZ ekiuk& xSj ekud vkSj ekud bdkb;k¡ & ekud bdkb;k¡ & mi&bdkb;k¡ vkSjfefJr bdkb;k¡ & {ks=Qy dk vFkZ D;k gS & {ks=Qy ekiuk & vk;ru ekiuk &èkkfjrk cuke vk;ru & lkjka'kA

;g ckr nksgksa ds ckjs esa dgh tkrh gSA D;k NksVk gS] D;k cM+k gS] ;g loky thus&ejus ds loky lstqM+k gSA [ksr fdruk cM+k gS & bl ij r; gksrk gS fdruh tqrkbZ djuh gksxh] vkSj fdruh mit gksxhAnok dh [kqjkd fdruh ysuh gS& bl ij r; gksrk gS jksx dk byktA lM+d ij cl fdruh nwjh ij gS& bl ij fuHkZj gS fd Hkkxdj lM+d ikj dh tk ldrh gS ;k ugha!

rks cM+s&NksVs] yEcs&ukVs dk eki dSls fd;k tk;sA ekius dk ,d iSekuk gksuk pkfg, tks lcds ekywegks & ugha rks >xM+s gksaxsA ,slk gh gSA yEckbZ dk eki iqjkus fnuksa esa ^vaxqy** vkSj ^gkFk** ls fd;k tkrkFkkA ^rhu vaxqy txg NksM+dj vkjh pykvks*& c<+bZ dgrk FkkA ^N% gkFk diM+k dkQh gksxk* & fdlkulksprk FkkA vaxqy] gkFk] xu] balkuh eki ds iSekus gSaA bUgha ls dke pyrk Fkk] vkSj vkt Hkh pyrk gSAvaxzsth esa ^,d QqV* yEckbZ ,d vaxzst jktk ds iSjksa dk eki gS & vaxzsth esa iSj dks QqV dgk tkrk gSAblh rjg nwjh ekih tkrh Fkh cSyksa ds ,d fnu ds lQj dh nwjh ls & ;gk¡ ls vk;k ^,d dksl*A ;wjksiesa ^,d ehy* vk;k ?kksM+s dh ,d fnu dh ;k=k lsA nsf[k;s] fQj ogh O;kikj ls laca/k! jkLrksa esa iM+ko ;kljk; cSyksa@?kksM+ksa ds ,d fnu ds lQj ds var esa 'kke gksrs gksrs igq¡pus dh txg cuk;s tkrs FksA dghavkSj cuk;s x;s gksrs rks cSy@;k=h jkr esa dgha jkLrs esa vVd tkrsA

;gh ckr gj fdlh rjg ds ekirksy ds iSekus esa ns[kh tk ldrh gSA tc O;kikj iwjh nqfu;k esa QSy x;k]lk/ku cSyksa@?kksM+ksa ls gVdj xkM+h@tgkt gks x;s rks u;s iSekus cus tks nqfu;k esa gj txg ekus tk,¡&ehVj] fdyksxzke vkfnA ;s iwjh nqfu;k ds ekud ekunaM gSaA

tc vki egklkxj esa tgkt esa pys gq, gSa] ;k gokbZ tgkt esa mM+s pys tk jgs gSa] rc vki dSls r;djsaxs fd nq'eu tgkt+] ;k rwQkuh ckny dgk¡ ij ekStwn gSaA lkspdj ns[kus ls ik,¡xs fd vki lwjt dhenn ysaxsA dgsaxs mÙkj esa] nf{k.k esa] iwjc esa] ;k if'pe esaA ysfdu ;g dkQh ugha gksxkA vkSj rks vkSjdHkh lwjt cknyksa ls <dk gksxkA rc\ vki dEikl bLrseky dj ldrs gSa ftlesa pqcd dh lwbZ mÙkjdh vksj b'kkjk djrh jgrh gSA

et+s dh ckr gS fd dEikl Hkh xksy gS] vkSj /kjrh Hkh! ;gha ls lqjkx feyrk gS dks.k dksA iwjh /kjrh xksygS] ?kM+h dh rjg vki dg ldrs gSa fd ik¡p cts dh lwbZa dh fn'kk esa rwQkuh ckny gSA ;k 10 cts dhlwbZa dh fn'kk ls nq'eu tgkt vk jgk gSA blh ?kM+h dks ydhjsa [khapdj &dEikl esa & 3600 esa ck¡V fn;ktkrk gS tks T;knk lgh fn'kk crkrk gSA vkSj yht,] bUgha fMfxz;ksa dh js[kkvksa ds chp ds Qklys ds dgktkrk gS] dks.kA 360 fMfxz;k¡] 360 dks.kA edku] e'khu] lkeku cukus esa dks.kksa dk bLrseky t:jh gSAi`Foh ds dksus&dksus esa dks.k gh gS!

158

ikB 11ikB 11ikB 11ikB 11ikB 11txg dh le>txg dh le>txg dh le>txg dh le>txg dh le>

ifjp;ifjp;ifjp;ifjp;ifjp;

ge tkurs gS fd fcUnq js[kk] v/kZ js[kk] js[kk[k.M tSlh T;kferh; vo/kkj.kkvksa ls cPpksa dk ifjp; izk;%d{kk 4 esa djk;k tkrk gSA ijUrq ,slk ekuk tkrk gS fd NksVs cPpksa dk vius vkl & ikl ds okrkoj.kls loZizFke lEidZ LFkku lEca/kh vuqHkoksa ds t+fj, gh gksrk gSA blesa n`f"V o Li'kZ dh laosnuk dk fo'ks"k;ksxnku gksrk gSA vkxs pydj Hkk"kk dk fodkl gksrk gS rFkk HkkSfrd i;kZoj.k ds lanHkZ esa gh ;g Hkk"kkvFkZ xzg.k djrh gSA /khjs & /khjs cPps LFkku lEca/kh dqN lgt fopkj fodflr djus yxrs gSa] tSls nwj]ikl] yEck] NksVk] nwjh vkfnA pkgs os ;g u crk ldsa fd buds Bhd & Bhd ek;us D;k gSaA bUgha lgtfopkjksa ij ge T;kferh ds ikBksa dh cqfu;kn j[krs gSaA gelsa ls vf/kdka'k yksx bu fopkjksa vkSj vo/kkj.kkvksa dks fl[kkus ds fy, vkSipkfjd ifjHkk"kkvksa ;k ekSf[kd o.kZu dk lgkjk ysrs gSaA urhtk ;g gksrkgS fd cPps fl[kkbZ xbZ vo/kkj.kkvksa dk ekufld fp= fufeZr ugha dj ikrsA gks ldrk gS fd dksbZ cPphoxZ ;k fdlh vU; cUn vkÑfr dh ifjHkk"kk rks vklkuh ls crk ns exj tc mlls dgk tk, fd dbZlkjh vkÑfr;ksa esa ls og vkÑfr fo'ks"k igpkus rks og u crk ik,A ftl cPph us d{kk esa oxZ vkSj leprqHkZt ds ckjs esa lc dqN lh[kk gS og ;g ugha crk ikrh fd oxZ fdl fdLe dk le prqHkZt gSA vkidksD;k yxrk gS fd cPph dks ,d ,slh vkÑfr dh dYiuk ugha gSA D;k bldk dkj.k ;g ugha gS fd tkspht+ mls le>kbZ xbZ mls ^ns[kus* dk ekSdk dHkh ugha feyk\ pg vius fnekx esa bl vkÑfr dh Nfougha cuk ikrhA fdlh cPph dks d{kk esa nks csyukÑfr;ksa ds vkdkj dh rqyuk djus esa dfBukbZ D;ksa gksrhgS tcfd ?kj ij og cM+h vklkuh ls 1 fdyksxzke 'kDdj j[kus ds fy, cM+k crZu <aw< fudkyrh gS\ D;kvkidks ,slk ugha yxrk fd ge yksx cPpksa dks vo/kkj.kk,a fl[kkus esa bruh tYnckth djrs gSa fd mUgsafdlh pht+ dh vkÑfr o vkdkj dk izR;{k vuqHko nsuk Hkwy tkrs gSa \ ;fn ge cPpksa ls uksV cqd esa oxZf[kapokus ds ctk;] pkj rhfy;ksa ls oxkZdkj cukus dks dgsa] rks D;k blls dqN QdZ iM+sxk\

dgus dh t:jr ugha fd cPpksa dks xfrfof/k;ksa esa etk vkrk gSA mUgsa dqN djuk vPNk yxrk gSA mUgsa[ksydwn esa vkuUn vkrk gSA rks D;ksa u ge muds bl LoHkko dk ykHk mBkrs gq, T;kferh dh dqNvoèkkj.kk,a fl[kkus dk iz;Ru djsa\

bl ikB esa geusa ,slk gh iz;kl fd;k gSA ge cPps dks T;kferh; pht+sa ckjhdh ls ns[kus esa enn djrsgSa rkfd og fofHkUu vkÑfr;ksa o fp=ksa ds xq.k/keZ [kqn gh igpkuus yxsA ;gk¡ geus dksf'k'k dh gS fdgj vo/kkj.kk dks xfrfof/k;ksa ds }kjk le>k;k tk, vkSj bu xfrfof/k;ksa esa iz;ksx dh tkus okyh pht+savklkuh ls miyC/k gksaA bl ikB dk ewy fl)kar ^djds lh[kks* gSA le] lery] vlery] cUn] [kqyh]lefefr vkfn vo/kkj.kkvksa ij ppkZ dh xbZ gSA frdksu] oxZ] vk;r] rFkk vU; fdLe dh pkSdksj vkÑfr;ksao o`Ùk dks le>us ds fy, cPpksa dks bu vkdkjksa dh pht+ksa dks ns[kus vkSj iz;ksx djus dk volj fn;kx;k gSA

;g ikB vU; T;kferh; vo/kkj.kkvksa ds fodkl dh cqfu;kn gSA vr% bldk egRo gSA bl ikB dsvè;;u ls gekjs fo|kfFkZ;ksa dks T;kferh ds ewy rRo izLrqr djus ds fy, xfrfof/k;ksa ij vk/kkfjr f'k{k.kds u;s rjhds [kkstus esa enn feysxh rkfd xf.kr cPpksa ds fy, ,d fnypLi fo"k; cu ldsA

cUn vkÑfr;kacUn vkÑfr;kacUn vkÑfr;kacUn vkÑfr;kacUn vkÑfr;kagj jfookj dh rjg ml fnu tc eSa viuh lgsyh ds ?kj igqaph rks ns[kk fd mldk 9 o"khZ; iq= jke,d fdrkc esa [kks;k gqvk gSA og d{kk 4 dk Nk= gSA fdrkc njvly ,d cky if=dk FkhA og ,dHkwyHkqyS;k igsyh esa ,d ukfodk dks xqIr [ktkus rd igqapkus esa O;Lr FkkA ¼ns[ksa fp= 1½A

159

fp= 1og bl igsyh esa bl dnj [kks;k gqvk Fkk fd mlus eq>s ns[kk gh ughaA vUrr% og ukfod dks mldk jkLrkfn[kkus esa lQy gks x;kA mldh eka js.kq dh f'kdk;r Fkh fd jke ges'kk igsfy;ka lqy>kus esa oDr cckZndjrk gS vkSj ikB~;iqLrd dk ,d 'kCn Hkh ugha i<+rkA dbZ ekrk&firk bl rjg dh f'kdk;r djrs gSaA

eq>s js.kq dks le>kuk iM+k fd cky if=dkvksa dh vf/kdrj igsfy;ka cPpksa dh cgqr ennxkj gksrh gSaA ;sigsfy;ka ,dkxzrk dh dlkSVh gksus ds vykok xf.kr dh dbZ ckrsa lh[kus esa Hkh mudh enn djrh gSaAijUrq js.kq dks fo'okl ugha gqvkA eSaus jke ls ckrphr djus dh BkuhA

mnkgj.k 1 % eSus jke ls iwNk fd D;k mlus d{kk esa cUn o [kqyh vkÑfr;ksa ds ckjs esa lh[kk gSA mlustokc fn;k( Þgka] exj bl igsyh ls eq>s og lc lh[kus esa dSls enn feyrh gS \ß eSaus mldh uksVcqdeaxokbZ ftlesa mlus fy[kk Fkk] Þcan vkÑfr og gksrh gS tks vius izkjfEHkd fcUnq ij lekIr gksrh gS

tcfd [kqyh vkÑfr vkjfEHkd fcUnq ij lekIr ugha gksrhAß mlus cUn vkÑfr n'kkZus ds fy,

vkSj [kqyh vkÑfr n'kkZus ds fy, fp= cuk;k FkkA tc eSaus mlls ,d cUn vkÑfr cukus dks

dgk rks mlus uksVcqd okyh vkÑfr dh gwcgw udy dj nhA tc eSaus lk fp= cukdj iwNk

fd D;k ;g cUn gS] rks og tokc u ns ldkA

E1) D;k vkidks yxrk gS fd jke ^cUnz vkÑfr* dh vo/kkj.kk le> pqdk Fkk\ ,d f'k{kd ds ukrsvki vius Nk=ksa dks ;g vo/kkj.kk dSls fl[kk,axs\ D;k bl laca/k esa dksbZ [ksy ;k xfrfof/k csgrjlkfcr gksxh\ ;fn gka] rks fdlh xfrfof/k dk mnkgj.k nhft,A

bl le; rd iM+kSl ds ?kj esa dkQh 'kksjxqy 'kq: gks x;kA ogka cPps ^ykseM+h vkSj [kjxks'k* dk [ksy[ksy jgs FksA eSaus jke ls [ksy ns[kus dks dgkA cPpksa us ,d nwljs dk gkFk idM+dj ,d cM+k lk xksykcuk fy;k FkkA ;g xksyk ,d fiatM+k FkkA ,d cPpk ykseM+h cudj fiatM+s ds bnZ&fxnZ nkSM+ jgk Fkk vkSj,d vU; cPpk [kjxks'k cuk FkkA og fiatM+s ds vUnj lqjf{kr Fkk ¼fp= 2 ns[ksa½

fp= 2 % ykseM+h vkSj [kjxks'k dk [ksy

160

ykseM+h vUnj ?kqlus dk jkLrk <wa< jgh Fkh exj ?kql ugha ik jgh FkhA jke ls iwNk fd ykseM+h [kjxks'kdks D;ksa ugha idM+ ik jgh gSA mlus dgk fd ykseM+h dks ^vUnj* tkus ds fy, ^jkLrk* ugha fey jgk gSD;ksafd fiatM+k dgha ls Hkh [kqyk ugha gSA

eSa % rks ykseM+h vUnj dSls tk ldrh gS\

jke % tc mlesa vUnj tkus dk dksbZ jkLrk gksA

eSaus mlls dgk fd fiatM+k gj txg ls cUn gS vkSj Q'kZ ij fiatM+s dh dbZ vkÑfr;ksa ds fp= cukdj¼fp= 3½ mlls ;g irk yxkus dks dgk fd muesa dkSu ls fiatM+s cUn gSa vkSj dkSu ls [kqys gSaA

fp= 3

mlus vUnj* tkus ds jkLrs dks /;ku esa j[krs gq, vklkuh ls cUn o [kqyh vkÑfr;ka lgh&lgh crk nhaA

eSaeSaeSaeSaeSa %%%%% vc rqEgkjh ^ukfodk vkSj [kt+kus* okyh igsyh ds ckjs esa crkvksaA HkqyHkqyS;k okyh igsyh!D;k og ,d [kqyh vkÑfr gSa\

jkejkejkejkejke %%%%% ns[kdj crkrk gwaA ckgj ls [k+tkus rd igqapus dk ,d jkLrk rks gSA vki vUnj tkusdk jkLrk [kkst ldrs gSaA rks] ;g [kqyh gSA Bhd gS u \

eSaeSaeSaeSaeSa %%%%% gka] ;g ,d [kqyh vkÑfr gSA ;kfu rqe tks igsyh dj jgs Fks og [kqyh] can vkÑfr dsgh leku gS] tks rqeus d{kk esa lh[kh FkhA

jkejkejkejkejke %%%%% vc eq>s le> esa vk;k fd eSaus uksV cqd esa D;k fy[kk FkkA ;g Hkh le> esa vk;k fdD;ksa can vkÑfr dk vkjEHk fcUnq vkSj vafre fcUnq ,d gh gksrk gSA

E2) D;k vki caUn o [kqyh vkÑfr;ka Åij crk, vuqlkj le>krs jgs gSa\ D;ksa u vki vius ?kj ;kiM+kSl ds fdlh 9 o"khZ; cPps ds lkFk bl rjhds dks vktekdj bldk ifj.kke ns[ksa\

tkfgj gS fd cUn vkÑfr dks ifjHkkf"kr dj fn;k tk, vkSj fQj cPps dh le> dk ewY;kadu dj fy;ktk,A mls bl vo/kkj.kk dk mi;ksx vyx&vyx lanHkZ esa djuk Hkh vkuk pkfg,A blds fy, fofHkUufLFkfr;ksa esa vH;kl t:jh gSA blds fy, cf<+;k rjhdk ;g gks ldrk gS fd fnypLi vkSj pqukSrhiw.kZigsfy;ksa dk bLrseky fd;k tk,A bl dke ds fy, rhfy;ksa] rkj] /kkxs tSlh dqN lkdkj pht+ksa dkbLrseky fd;k tk ldrk gSA ;s xfrfof/k;ka d{kk esa dh tk ldrh gSA ;gka ge vkids fy, ,d ,slhgh xfrfof/k;ksa ns jgs gSaA

mnkgj.k 2 %mnkgj.k 2 %mnkgj.k 2 %mnkgj.k 2 %mnkgj.k 2 % f'kf{kdk chl rhfy;ka ¼[kifPp;ka½ vkSj /kkxs dh ,d xM~Mh ysdj d{kk igqaphA mUgksausd{kk dks pkj Vksfy;ksa esa ckaV fn;kA gj Vksyh dks 5&5 [kifPp;ka nsdj dgk fd os muls ftruh cUn

161

vkÑfr;ka cuk ldsa cuk,aA gj Vksyh us ;g dke [kq'kh&[kq'kh fd;kA mUgksaus viuh ik¡p [kifPp;ksa dksrjg&rjg ls tksM+dj vyx&vyx fMt+kbu cuk,A

f'kf{kdkf'kf{kdkf'kf{kdkf'kf{kdkf'kf{kdk %%%%% ns[kks] rqeus tks fMt+kbu cuk, gSa] os lc ds lc lh/ks dksj okyh cUn vkÑfr;ka gSaAD;k rqe ,slh vkÑfr cuk ldrs gks ftlds dksj lh/ks u gksA

,d fo|kFkhZ,d fo|kFkhZ,d fo|kFkhZ,d fo|kFkhZ,d fo|kFkhZ %%%%% ¼FkksM+k fgpdrs gq,½ eSMe] ;fn vki eq>s FkksM+k /kkxk nsa] rks eSa dksf'k'k dj ldrk gw¡A

f'kf{kdkf'kf{kdkf'kf{kdkf'kf{kdkf'kf{kdk %%%%% Bhd gS! ;gk¡ vkvksA ;s /kkxk yks vkSj dksf'k'k djksA

yM+ds us [kiPph ds fljksa ij /kkxk cka/kdj ,slh vkÑfr cukbZ ftlds dksj lhèksugha FksA

f'kf{kdkf'kf{kdkf'kf{kdkf'kf{kdkf'kf{kdk %%%%% 'kkck'k! ¼mUgksaus ;g vkÑfr d{kk ds lHkh cPpksa dks fn[kkbZA½ ;fn flQZ nks[kifPp;ka gksa vkSj blds vykok dqN u gks] rks D;k cUn vkÑfr cukuk lEHko gS\

cPpksa us [kifPp;ksa dks dbZ rjg ls tek&tekdj ns[kk exj lQy ugha gq,A lc,d lkFk fpYyk iM+sA

cPpscPpscPpscPpscPps %%%%% ugha] eSMeA

f'kf{kdkf'kf{kdkf'kf{kdkf'kf{kdkf'kf{kdk %%%%% D;k bldk eryc ;g gqvk fd cUn vkÑfr ds fy, gesa de ls de rhu[kifPp;ka pkfg, \

cPpscPpscPpscPpscPps %%%%% th gka] eSMeA

cPps izlUu vkSj mRlkfgr ut+j vk jgs FksA os lc /kkxs ls vkSj vkÑfr;ka cukukpkgrs FksA f'kf{kdk us gj Vksyh dks /kkxs dk VqdM+k ns fn;k vkSj vkÑfr;ka cukusdks NksM+ fn;kA

cPpksa dks frdksu] prqHkqZt] iapHkqt] "kV~dks.k] v"VHkqt vkfn ls lHkh ifjfpr djk;k tkuk pkfg, tc oslh/ks dksj okyh cUn vkÑfr;ksa dh vo/kkj.kk ls Hkyh&Hkkafr ifjfpr gks tk,aA dgus dh t:jr ugha fdmDr vkÑfr;ksa ls ifjfpr djkrs oDr muds ukeksa dk cks> mu ij ugha Mkyk tkuk pkfg,A ;g dkelkdkj pht+ksa ds ek/;e ls gh djuk pkfg,A t:jh ugha fd mUgsa gj vkÑfr fl[kkbZ tk,A ge mUgsavyx&vyx ;k ,d leku yEckbZ dh [kifPp;ka] jax&fcjaxh LVªkW] ekfpl dh rhfy;ka rkj ds lh/ks VqdM+soxSjg nsdj dg ldrs gSa fd os muls eupkgh cUn vkÑfr;ka cuk,aA buds fljksa dks xksn ls tksM+k tkldrk gSA [kifPp;ksa dks rks os ,d dkMZcksMZ ij Hkh fpidk ldrs gSaA

E3) vki fuEufyf[kr dks fn[kkus ds fy, fdl izdkj dh xfrfof/k;ka lksp ldrs gSa %

i) fdlh [kqyh vkÑfr@cUn vkÑfr ds lh/ks dksj Hkh gks ldrs gSa] xSj lh/ksHkh ;k fQjnksuksa HkhA

ii) lh/ks dksj okyh [kqyh vkÑfr ds fdrus Hkh dksj gks ldrs gSaA

iii) lh/ks dksj okyh vkÑfr rHkh cUn vkÑfr cu ldrh gS tc mlds de ls de rhu dksjgksaA

iv) fdlh Hkh cUn vkÑfr dk ,d vUnj vkSj ,d ckgj gksrk gS ftUgssa Øe'k% vUrHkkZx ocfgHkkZx dgrs gSaA

dbZ cPps vkSj O;Ld Hkh ;g fuf'pr :i ls r; ugha dj ikrs fd tSlh vkÑfr cUn gS ;k

162

[kqyhA mudk er gksrk gS fd vkÑfr dk ,d fgLlk cUn gS gkykafd vkÑfr cUn ut+j ugha vkrhA ;gh

fLFkfr vkÑfr ds lkFk Hkh gksrh gSA vkids [;ky ls bl xyrQgeh dks nwj djus ds fy, D;k

djuk pkfg, \ vkb, ns[ksa fd d{kk 4 dh ,d f'kf{kdk us bls dSls le>k;kA

fp= 4 % ,d cUn vkÑfr

f'kf{kdk us dkxt+ ij ,d cUn vkÑfr cukbZA mUgksaus fn[kk;k fd bl vkÑfr ds fdlh Hkh fcUnq ls]fdlh Hkh fn'kk esa isafly pykuk 'kq: djsa rks ge vkÑfr ds fdlh Hkh fgLls ij nksckjk pys cxSj okfil'kq:vkrh fcUnq ij igqap tkrs gSaA ;fn fdlh Hkh vkÑfr ds fdlh Hkh fcUnq ls fdlh Hkh fn'kk esa pyrsgq, ;g lEHko gks fd ge vkÑfr ds fdlh Hkh fgLls ij ,d ls vf/kd ckj pys cxSj okfil ewy fcUnq

ij igqap ldsa] rks og cUn vkÑfr gSA ;g le>kus ds ckn mUgksaus ;g vkÑfr cukbZA cPpksa

us ns[kk fd os okfil 'kq:vkrh fcUnq ij ugha igqap ldrsA ;kuh ;g cUn vkÑfr ugha gSA fQj mUgksaus,d vkÑfr cukbZ ¼fp= 4½ ftldh js[kk ,d&nwljs dks dkVrh FkhaA vc mUgksaus cPpksa ls iwNk\ fd D;k;g ,d cUn vkÑfr gS\ mUgksaus cPpksa ls ,d isafly dh enn ls ;g irk djus dks dgk fd D;k os isaflydks vkÑfr ij Qsjrs gq, 'kq:vkrh fcUnq ij igqap ldrs gSaA cPpksa us djds ns[kk fd ;g lEHko gSA ;kuh;g ,d cUn vkÑfr gSA blh rjg mUgksaus 2&3 vkSj vkÑfr;ka cukdj cPpksa ls dgk fd os buesa[kqyh@cUn vkÑfr;ka igpkusaA vUrr% tc f'kf{kdk larq"V gks xbZ] rc mUgksaus cPpksa dks ?kj ij djus dsfy, dqN vkSj loky fn,A

E4) ft;ks cksMZ ydM+h dk ,d vk;krkdkj pkS[kVk gksrk gSA ftl ij cjkcj nwjh ij dhy s a yxhgksrh gSa ¼fp= 5½A ft;ks cksMZ] jcj cSaM ;k /kkxs dk bLrseky djds cPpksa dks [kqyh o cUn vkÑfrfl[kkus ds fy, vki fdl rjg dh xfrfof/k;k¡ vk;ksftr dj ldrs gSa\

ft;ks cksMZ cgqr gh mi;ksxh midj.k gSA bldk] mi;ksx cPpksa dks frdksu] oxZ] vk;r tSlh T;kferh;vkÑfr;ka fn[kkus ds fy, Hkh fd;k tk ldrk gSA oxZ vkSj vk;r ds chp dk vUrj] Hkh ft;ks cksMZ dhenn ls n'kkZ;k tk ldrk gSA ft;ks cksMZ rks t+ehu ij Hkh vklkuh ls cuk;k tk ldrk gSA blds fy,fp= 5 esa fn[kk, vuqlkj t+ehu ij ,d vk;rkdkj {ks= fpfUgr djds mlesa 9 ;k 16 mlls Hkh T;knkcjkcj vkdkj dh Vgfu;ka@[kifPp;ka yxkbZ tk ldrh gSaA

fp= 5 % ft;ks cksMZ

163

jke ds lkFk lEidZ ds nkSjku eq>s ;g le> vk;k fd ikjEifjd d{kk i)fr ls i<+k, tkus ij NksVs cPpsT;kferh dh ewyHkwr vo/kkj.kk,a vke rkSj ij ugha le> ikrs gSaA blds dbZ dkj.k gks ldrs gSaA fd buvo/kkj.kkvksa ds fy, t:jh iwoZ tkudkjh cPpksa ds ikl ugha gksrhA gks ldrk gS fd mUgsa tkus &igpkusiz;ksxksa ds t+fj, ubZ vo/kkj.kkvksa dks le>us dk ekSdk gh ugha feyrkA gks ldrk gS fd f'k{kd ekudjpyrs gksa fd ;s vo/kkj.kk,a cgqr gh vklku gSa rFkk le>kus dh t:jr gh ugha gS D;ksafd cPpksa ds fnekxesa buds vkjs esa lgt fopkj rks gSa gksA dHkh & dHkh ,slk Hkh gksrk gS fd dksbZ vko/kkj.kk cPpksa ds fy,cgqr vewrZ gksrh gSA vkSj f'k{kd bls fl[kkus ds fy, dksbZ ekdwy fof/k dk iz;ksx ugha dj ikrsA leryo vlery leg dh vo/kkj.kk ,slh gh ,d vo/kkj.kk gSA vc ge blh ij ckr djsaxsA

lery lrglery lrglery lrglery lrglery lrg

eS ;g irk yxkuk pkgrh Fkh fd d{kk esa ikjaifjd <ax ls ,slh vo/kkj.kk,a dSls i<+kbZ tkrh gSaA vxysfnu eq>s izkFkfed Ldwy ds f'k{kdksa ds ,d lewg ls ckrphr dk ekSdk feykA ;s yksx xf.kr ds ,dizf'k{k.k dk;ZØe esa Hkkx ys jgs FksA eSaus lkspk fd buds lkFk T;kferh dh ewyHkwr vo/kkj.kk,a fl[kkus dsrjhdksa ij ppkZ dh tk,A izf'k{k.k dk;ZØe esa Hkkx ys jgs vf/kdrj f'k{kd dkQh vuqHkoh Fks vkSj lfØ;fn[krs FksA

f'k{kdksa dks nks Vksfy;ksa esa ckaV fn;k x;k vkSj muls lery o vlery lrgksa dh vo/kkj.kk i<+kus dhfof/k;ksa ij fopkj&foe'kZ djus dks dgk x;kA gj Vksyh ds usrk dks Vksyh }kjk pfpZr fof/k;ksa dk izLrqrhdj.kdjuk FkkA dejk rdZ&fordZ ds 'kksjxqy vkSj tks'k ls Hkj x;kA eSa mUgsa xEHkhjrk ls fopkj &foe'kZ esa Mwckns[k jgh FkhA ,d ?k.Vs ckn os fQj ls bdV~Bs gq,] vius fu"d"kksZa dk izLrqrhdj.k djus dksA

igyh Vksyh dks igys viuk ijpk izLrqr djus dks vkeaf=r fd;k x;kA bl Vksyh ds vuqlkj] NksVs cPpslksprs gSa fd gj fpduh lrg lery lrg gksrh gSA muds fy, rks v.Ms dh lrg] xsan dh lrg ;kfdlh csyukdkj ik= dh lrg] lc likV lrgsa gSaA dbZ cPpksa ds fy, rks lery vkSj vlery lrgdk eryc fpduh o [kqjnjh lrg ls gksrk gSA Vksyh dk er Fkk fd bl leL;k ls fuiVus ds fy, ;gfd;k tk ldrk gS fd cPpksa dh vka[kksa ij iV~Vh cka/kdj mUgsa gkFkksa ls dqN fpduh o dqN [kqjnjh pht+seglwl djus dks nh tk, rkfd os ;g le> ldsa fd lery o vlery lrg dh vo/kkj.kk buls vyxgSA mUgsa ,d v.Ms vkSj ,d vuUukl dh lrg dks Nwdj vUrj eglwl djus nsaA muls bl ckr ij HkhppkZ dh tk ldrh gS fd D;ksa fxVVk dkap ij rks nwj rd yq<+drk gS exj lhesaV ds Q'kZ ij de nwjyq<+drk gSA

lery o vlery lrgksa ds chp Hksn le>kus ds fy, cPpksa dks fdlh est] CySd cksMZ] Q'kZ ;k nhokjdk fujh{k.k djus dks dgk ldrk gSA blds ckn f'k{kd mUgsa crk ldrs gSa fd ;s lHkh likV lrgsa gSvkSj bu ij dksbZ eksM+ ;k ?kqeko ugha gSA bu lrgksa dks lery lrg dgk tkrk gSA fQj mUgsa xsan] v.Ms;k fdlh csyukdkj ik= dh lrg esa ;g fn[kk;k tk ldrk gS fd ;s eqM+h gqbZ ;k oØrk fy, gq, gSaAvr% ;s vlery lrgsa gSaA

E5) D;k vkius dHkh ;g tkapus dh dksf'k'k dh gS fd d{kk 4 ds cPps lery rFkk vlery lrgksads chp Hksn dj ikrs gSa ;k ugha\ bl xfrfof/k dks 9 ;k 10 o"khZ; cPps ds lkFk vktekdj bldhlkFkZdrk dh tkap dhft,A

nwljs ny dk lq>ko Fkk fd f'k{kd cPpksa ls ekfpl] daps] ikals] iksLVdkMZ] Xyksc] xsans tSlh dbZ pht+s ykusdks dg ldrs gSaA f'k{kd d{kk esa vklkuh ls miyC/k dqN pht+sa Hkh tqVk ldrs gSa] tSls iSu] isaflyfdrkc] isafly ckWDl oxSjgA csgrj ;g gksxk fd NksVh&cM+h fpduh&[kqjnjh] lery&vlery gj rjg

164

dh pht+s cPpksa ds lkeus gksaA vc f'k{kd cPpksa ds lkeus bu pht+ksa dks nks lewgksa esa ckaVuk 'kq: djsaAelyu f'k{kd iksLV dkMZ gkFk esa ysdj tkfgj :i ls mldh lrg dks eglwl djs] tcfd cPps mUgsa,slk djrs ns[k ldsaA f'k{kd FkksM+h nsj lkspus dk cgkuk djds iksLVdkMZ dks nkbZaa vksj j[k nsaA bl rjgls os ,dk/k lery pht+sa vkSj mBk, vkSj mUgsa nkbZa vksj j[k nsaA fQj os xsan dks mBkdj mldh lrgdks nksuksa gkFkksa ls eglwl djsa rkfd cPpksa dks ;g ut+j vk tk, fd mldh lrg xksy gS vkSj fQj mlsckbZa cksj j[k nsaA blds ckn f'k{kd cPpksa ls dgsa fd os pht+ksa dks mBk,a vkSj mUgsa lery o vlery¼;k xksyh;½ pht+ksa ds :i esa vyx&vyx djsaA vc os cPpksa ls ;g crkus dks dg ldrs gSa fd mUgksausfdlh pht dks fdlh [kkl lewg esa D;ksa j[kk gSA os mUgsa ;g Hkh fn[kk ldrs gSa fd nksuksa gh lewgksa esacM+h o NksVh] fpduh o [kqjnjh pht+sa gSaA lewghdj.k dk ,dek= vk/kkj lery vkSj vlery lrg gSAbl rjg dh ppkZ ls cPpksa dks ;g le>us esa enn feysxh fd lery lrg D;k gksrh gS rFkk xksykbZokyh lrg D;k gksrh gSA cPpksa dks ,slh pht+ksa dk fujh{k.k djus dks dgk tk ldrk gS ftuesa leryo xksykbZnkj nksuksa rjg dh lrg gksrh gSA <ksyd] rcyk] rsy dk fMCck vkfn pht+ksa esa lery ovlery nksuksa rjg dh lrgsa gksrh gSaA ¼ns[ksa fp= 6½A

fp= 6

E6) d½ ^lery lrg* i<+kus dh ftu nks fof/k;ksa ij geus Åij ppkZ dh] mudh [kkfe;ka gSa\

[k½ lery lrg dh vo/kkj.kk dks lh[kus ds fy, ,d vkSj ,slh xfrfof/k lq>kb, ftls 50cPpksa dh ,d d{kk esa fd;k tk ldsA

^le vkÑfr* vkSj vlekÑfr ,d vkSj ,slk fo"k; gS ftlds ckjs esa vf/kdka'k cPpksa rFkk dqN f'k{kdksa esaHkh xyrQgeh gksrh gSA vkb,] bl vo/kkj.kk dks Li"V djus ds dqN rjhdksa ij fopkj djsaA

le vkÑfr;kale vkÑfr;kale vkÑfr;kale vkÑfr;kale vkÑfr;kadqN f'k{kdksa dk er gS fd ek= cgqHkqt rFkk o`Rr gh le vkÑfr;ka gksrh gSA dqN vU; f'k{kd ekurs gSafd bu vkÑfr;ksa ds esy ls cuh vkÑfr;ka Hkh le gksrh gSA okLro esa 10&11 o"khZ; cPpksa dsk le ovlekÑfr;ksa esa Hksn djus esa dfBukbZ gksrh gSA bl ckr dks ysdj vke rkSj ij nqfo/kk O;Dr dh tkrhgS fd fuEufyf[kr vkÑfr;ka le gSa ;k ugha ¼ns[ksa fp= 7½A

165

fp= 7vkidk bu fp=ksa ds ckjs esa D;k fopkj gS\bu vo/kkj.kkvksa esa n{krk gkfly djuk cPpksa ds fy, lpeqp eqf'dy gksrk gSA cPpksa dks le vkSjvlekÑfr;ksa ds chp varj le>kus ds fy, vki vius iM+ksl ds 10 o"khZ; cPpksa ;k vius Ldwy dh pkSFkhd{kk ds cPpksa ds lkFk ,d xfrfof/k dj ldrs gSaA xfrfof/k 'kq: djus ls igys ;g lqfuf'pr dj ysaAfd cPps frdksu] prqHkqZt rFkk o`Ùk igpkurs gksaA os mudks igpkudj mudk uke Hkh crk ldrs gksaA'kq:vkr vki lery cUn vkÑfr;ksa ls dj ldrs gSaA dqN [kifPp;ka rFkk dkxt ds dVs frdksu]prqHkqZt] o`Ùk rFkk vn~/kZ o`Ùk bdV~Bs dj fyft,A cPpksa dks mudks igpkuus nsa rFkk muds dksjks rFkk dksuksadh la[;k fxu ysus nsaA mUgsa ;g crk;k tk ldrk gS fd ;s le vkÑfr;ka gSaA 'kq:vkr vki lh/ks dksjksaokyh cUn vkÑfr;ksa ls dj ldrs gSaA ckrphr dh 'kq:vkr frdksu ls gks ldrh gSA cPpksa dks fofHkUufrdksuksa ¼fp= 8½ dk fujh{k.k djus dks dgsaA mUgsa ns[kdj os dg ldsa fd ;s lHkh le vkÑfr;ka gSaA,d ckj os le vkÑfr;ksa ls ifjfpr gks tk,a] rks mUgsa fofHkUu izdkj ds prqHkqZt vkSj frdksu fn[kk, tkldrs gSaA blds fy, vyx & vyx yEckbZ dh [kifPp;ka tqVk ldrs gSaA cPpksa ls dgsa fd os fuEukuqlkj[kifPp;ksa ds frdksu cuk,a]

fp= 81½ ftlesa lkjh [kihfPp;ka ,d yEckbZ dh gksa

2½ nks [kifPp;ka ,d gh yEckbZ dh gksa

3½ rhuksa [kifPp;ka vyx & vyx yEckbZ dh gksaA

166

vki mUgsa ;g lq>k ldrs gSa fd oSls rks ;s lkjs frdksu gh gSa exj vkdkjksa dh yEckbZ ds vk/kkj ij budschp Hksn djus ds fy, bUgsa vyx& vyx uke nsuk t:jh gSA vc vki mudk ifjp; leckgq lef}ckgqvkSj fo"keckgq frdksu ls djk ldrs gSaA

vDlj ns[kk x;k gS fd cPpksa ds eu esa dbZ 'kCnksa ds vFkZ dks ysdj xyrQgeh gksrh gSA elyu dbZcPpksa ds fy, frdksu dsoy ogh vkÑfr gS tks leckgq gksA blds vykok dbZ ckj cPps vkÑfr dh fLFkfrdks ysdj Hkh Hkzfer gks tkrs gSaA elyu ;fn fdlh frdksu dh ,d Hkqtk ml dkxt ftl ij oks dkedj jgs gSa ds fupys fdukjs ds lekUrj u gks] rks dbZ erZck os mls frdksu ds :i esa igpku gh ugha ikrs¼fp= 9½A

fp= 9

cPpksa dks ;s vo/kkj.kk,a le>kus ds fy, mUgsa dkQh vH;kl dk ekSdk fn;k tkuk pkfg,A f'k{kd fofHkUuvkdkj dh [kifPp;ksa dk bLrseky djds dbZ rjg ds frdksu cukdj cPpksa ls mUgsa igpkuus dks dgldrs gSaA

blds vykok cPpksa dks ;g ekSdk Hkh feyuk pkfg, ds os f'k{kd }kjk lq>k, x, frdksu dks cukus dsfy, lgh [kifPp;ka pqu ldsaA mUgsa ,sls frdksuksa dks uke nsus esa Hkh leFkZ gks tkuk pkfg, tks Kkr yEckbZdh [kifPp;ka ysdj cPpksa ls iwNsa fd Þbuls eSa fdl fdLe dk frdksu cuk ldrh gwa \ ;k D;k eSa buls,d leckgq frdksu cuk ldrh gw¡ \ ;k D;k eSa buls ,d ledks.k frdksu cuk ikmaxh \ß oxSjgA cPpksadks fofHkUu frdksuksa ls ifjfpr djkrs oDr ,d egRoiw.kZ ckr lqfuf'pr djuk t:jh gSA cPpksa dks ;gvo'; irk gksuk pkfg, fd fdlh Hkh yEckbZ dh rhu [kaifPp;ksa ls frdksu cus ;g t:jh ugha gksrkA ;gvko';d gS fd fdUgha Hkh nks [kifPp;ksa dh yEckbZ dk tksM+ rhljk [kiPph dh yEckbZ ls T;knk gksukpkfg,A ;g vko';drk iwjh gksxh rHkh frdksu cusxkA vkb, ns[ksa fd vki cPps dks ;g le>us esa dSlsenn dj ldrs gSaA

E7) ^fdlh Hkh yEckbZ dh rhu [kifPp;ksa ls frdksu ugha cuk;k tk ldrkA* cPpksa dks ;g vo/kkj.kkle>kus ds fy, ,d xfrfof/k crkb,A

frdksu ls ifjfpr djkus ds ckn vki blh rjg cPpksa dk ifjp; prqHkqZt ls djk ldrs gSaA cPpksa dksfofHkUu fdLe ds prqHkqZtksa dk voyksdu o fo'ys"k.k djus dk volj nsus ds fy, Vksfy;ksa esa ;k fQj iwjhd{kk ds lkFk bdV~Bs xfrfof/k;ka dh tk ldrh gSaA ijUrq T;kferh esa cPpksa dh lksp ds Lrj vyx&vyx gksrs gSaA t:jr bl ckr dh gS fd cPpksa dks cPpksa ds Lrj ij lEcksf/kr fd;k tk,A tjk dYiukdhft, og fLFkfr tcfd cPps rks n Lrj ds gSa vkSj f'k{kd bUgsa n + 2 Lrj ij i<+k jgs gSaA Lrj ds blvarj dh otg ls gksxk ;g fd f'k{kd dh vis{kkvksa vkSj og Lrj ftl ij cPps lh[kus dks rS;kj gSa fdchp [kkbZ jgsxhA urhtk gksxk fd cPps Hkzfer gksaxs vkSj f'k{kd muds ?kfV;k izn'kZu ls grk'k gks tk,axsAvr% f'k{k.k xfrfof/k;ka cPpksa ds Lrj ij gksuh t:jh gSA ;gk¡ ge d{kk 4 ds cPpksa ds fy, ,d xfrfofèklq>k jgs gSaA

167

mnkgj.k 3 %mnkgj.k 3 %mnkgj.k 3 %mnkgj.k 3 %mnkgj.k 3 % 4 vyx & vyx yEckb;ksa dh 50 [kifPp;ka bdV~Bh dj ysaA bUgsa 4 <sfj;ksa esa j[k nsaA gj<sjh esa ,d gh yEckbZ dh [kifPp;ka gksaA cPps vkids funsZ'k ds vuqlkj viuh ilUn dh pkj [kifPp;kamBk ysaA

1½ ,d gh <sjh esa ls ,d gh yEckbZ dh pkj [kifPp;kaA

2½ ,d <sjh esa ls 2 rFkk nwljh <sjh esa ls 2 [kifPp;kaA

3½ ,d <sjh esa ls 3 rFkk nwljh esa ls 1 [kiPphA

4½ izR;sd <sjh esa ls 1 & 1 [kiPphA

vc muls dfg, fd os viuh [kifPp;ksa dks Q'kZ ij ltkdj pkSdksj vkÑfr cuk,aA muds }kjk cukbZxbZ vkÑfr fp= 10 dh fdlh vkÑfr ds leku gks ldrh gSA

fp= 10

cPpksa dks igys bu vkÑfr;ksa dks vPNh rjg ls ns[kus nhft,A fQj muls ;g iwN ldrs gSa fd osvkÑfr;kssa ds dksjksa ds vk/kkj ij muds vUrjksa dks Li"V djsaA ;fn os u dj ik,a rks vki dqN iz'u iwNdj mudh enn dj ldrs gSaA tSls fd izR;sd vkÑfr esa fdrus fdukjs gSa] fdrus Nksj gSa] oxSjgA tSlsfrdksu esa fd;k Fkk mlh izdkj prqHkqZt ds Hkh fofHkUu uke crk, tk ldrs gSa] elyu vk;r] oxZ lekUrjleyEc oxSjgA bl fcUnq ij ppkZ dks dkslsA dh yEckbZ ds vk/kkj ij lhfer j[kk tk ldrk gSAlekUrjiu ;k dks.kksa dh cjkcjh ds vk/kkj dks bl oDr NksM+k tk ldrk gSA ijUrq ,d lko/kkuh t:jcjruh gksxhA dbZ ckj cPps fdlh vkd`fr dks flQZ blfy, oxZ dg vsrs gS D;ksfd og oxZ lh fn[krhgSA ¼fp= 11 d½A blh izdkj ls dbZ erZcksa os ¼fp= 11 [k½ tSlh vkd`fr dks flQZ blfy, oxZ ugha dgrsD;ksafd ;g oxZ tSlh fn[krh ughaA

d [kfp= 11

168

blh izdkj dbZ cPps fp= 12 ¼d½ tSlh vkd`fr dks vk;r ugha ekurs D;ksafd muds fopkj esa vk;r piVk]yEck gksrk gS exj cgqr pkSM+k ugh gksrkA os fp= 12 ¼[k½ dks vk;r ekuus ls bUdkj dj nsrs gS D;ksafd;g ^cgqr iryk*gS ;k D;ksafd os vk;r dks oxZ ls yxHkx nqxqus vkdkj dk ekurs gSA

d [k

fp= 12

blh izdkj ls dbZ cPps xSj &ledks.k lekUrj prqHkqZt ¼fp= 12 d½ dks vk;r ekurs gS vkSj oxZ ¼fp=13 [k½ dks vk;r ugha ekursA

d [kfp= 13-

vki ;g n'kkZ ldrs gSa fd dSls mUgh pkj [kifPp;ksa dks vyx&vyx fLFkfr;ksa esa j[kdj fofHkUu prqHkqZtvkd`fr;ka cukbZ tk ldrh gSA cPpksa dks dkQh vuqHko izkIr djus nsa rkfd os u, fopkjksa ls Hkyh Hkkafrifjfpr gks tk,a fdlh vkd`fr dks fn[kkdj mldk uke crkuk ;k fdlh vkd`fr dh udy mrkj djmls uke nsus ls cPpksa dk 'kCnHk.Mkj fodflr gksxk vkSj mUgs vkd`fr;ksa ds fofHkUu fgLlksa ds chp ijLijns[kus esa enn feysxhA elyu lekUrj prqHkqZt dh vkeus lkeus dh Hkqtkvksa dh yEckbZ cjkcj gksrh gSaAblh izdkj ls leyEc cukus ds fy, nks [kifPp;ksa dks ,d nwljs ds lkeus bl izdkj j[ksa fd gj fcUnqij muds vkil dh nwjh ,d leku gksA cPpksa dks ;g irk djus nsa fd prqHkqZt ds ;s ijLij lenwjLFkdksj gSaA vc igyh nks [kifPp;ksa ds fljksa dks tksM+rh gqbZ nks vkSj [kifPp;k¡ bl rjg j[ksa fd prqHkqZtcu tk, ¼ns[ksa fp= 14½A

fp= 14 % leyEc

169

vc lenwjLFk [kifPp;ksa esa ls fdlh ,d gh fLFkfr cny nsa vkSj cPpksa dks ns[kus nsa fd vc ;g vkÑfrleyEc ugha jghA blh izdkj ls lHkh vkÑfr;ksa dh fo'ks"krkvksa dk ifjp; nhft, rkfd cPps gj vkÑfrvkSj mlds [kkl xq.k dks igpku ldsa tSls fd %

1- pkj fdukjs okyh lHkh vkÑfr;ka prqHkqZt gSaA

2- prqHkqZt dh pkjksa Hkqtk,¡ vyx&vyx yEckbZ dh Hkh gks ldrh gS vkSj leku yEckbZ dh Hkh gks

ldrh gSaA

3- leyEc esa ,d tksM+h Hkqtk,a lenwjLFk gksrh gSaA

4- lekUrj prqHkZt esa vkeus&lkeus dh Hkqtk,a cjkcj yEckbZ dh gksrh gSaA

5- gj lekUrj prqHkqZt leyEc prqHkqZt gksrk gSA

6- gj vk;r lekUrj prqHkqZt Hkh gksrk gSA

7- gj oxZ ,d lekUrj prqHkqZt Hkh gksrk gS vkSj vk;r Hkh gksrk gSA

d{kk esa dqN vklku xfrfof/k;ka Hkh vk;ksftr dh tk ldrh gSaA cPpksa dks 4&5 Vksfy;ksa esa ckaV nhft,A gjVksyh dks [kifPp;ksa ls cuk lekUrj prqHkqZt ns nhft,A cPpksa ls dfg, fd os flQZ dksuksa dks fgyk MqykdjlekUrj prqHkqZt dks vk;r esa cnysaA fQj muls iwfN, fd D;k lekUrj prqHkqZt dks oxZ esa cnyk tk ldrkgS\ D;k oxZ vk;r Hkh gksrk gS\ vkfnA blls mUgsa nksuksa ds chp dk vUrj igpkuus esa enn feysxhA

E8) d{kk esa dh tkus okyh ,d ,slh xfrfof/k lq>kb, ftlesa gj Vksyh dks ;g irk djuk gks fdmUgsa fn, x, prqHkZt ds leku fn[kus okyh dkSu&dkSu lh pht+s d{kk esa ;k muds vkl&iklmiyC/k gSaA

tc ,d ckj cPps oxZ] vk;r] frdksu oxSjg tSlh vk/kkjh; vkÑfr;ksa ls HkyhHkkafr ifjfpr gks tk,¡ vkSj;g le> tk,¡ fd ;s lHkh lh/ks dksjksa okyh le vkÑfr;ka gS] rc mUgsa bu vkÑfr;ka dks tksM+dj ubZvkÑfr;ka cukus dks dgk tk ldrk gSA mudh enn ds fy, fuEufyf[kr xfrfof/k dh tk ldrh gSA

mnkgj.k 5 %mnkgj.k 5 %mnkgj.k 5 %mnkgj.k 5 %mnkgj.k 5 % xÙks] pedhys ;k lk/kkj.k dkxt ds dqN frdksu bdV~Bs dj ysaA cPpksa ls dfg, fd os nksfrdkuksa dks tksM+dj] ubZ&ubZ fMt+kbusa cuk,a] ij /;ku jgs fd frdksu ,d & nwljs dks <¡dsa ughaA mudhfMt+kbu fuEukuqlkj fn[k ldrh gSaA ¼fp= 15½A

fp= 15

170

le vkÑfr;ksa ds esy ls cuh bu vkÑfr;ksa dks uke nsus esa cPpksa dks dfBukbZ gksrh gS D;ksafd ;s fMt+kbusamudh tkuh&igpkuh ugha gksrhA vki mUgsa ;g crk ldrs gSa fd lkjh vkÑfr;ka Hkh le gSaA blds cknmUgsa ekSdk nhft, fd dbZ lkjs frdksu ;k prqHkZtksa dks tksM+&tksM+ dj ubZ&ubZ fMt+kbusa cuk,a ftlesagj fMt+kbu ,d le vkÑfr gksA vki [kqn Hkh dbZ lkjs frdksu&prqHkqZt tksM+dj ,d le vkÑfr cuk,a]tSlh fp=&16 esa fn[kkbZ xbZ gSaA

fp= 16

cPpksa ls dgsa fd os [kifPp;ksa dh enn ls foHkktu js[kk,a [khapdj bu vkÑfr;ksa dks ifjfpr vkÑfr;ksaesa ckaVsA os fxusa fd gj vkÑfr esa ls fdrus frdksu] fdrus prqHkqZt fudyrs gSaA ,slh dbZ vU; vkÑfr;kacukdj cPpksa ls mUgsa ifjfpr vkÑfr;ksa esa ckaVus vkSj dkVus dks dgk tk ldrk gSA dVs gq, VqdM+s dksos fQj ls u, <ax ls tksM+dj ubZ vkÑfr;ka cuk ldrs gSaA ,slh xfrfof/k;ksa ls cPpksa dks ledks.k rFkklekarjrk dh /kkj.kk fodflr djus esa enn feyrh gSA ;s xfrfof/k;ka cPpksa dh LFkku lEca/kh lksp dsfodkl esa Hkh vge Hkwfedk vnk djrh gSaA

E9) vki fdlh 10&11 o"khZ; cPps dks le vkÑfr dh vo/kkj.kk ls dSls ifjfpr djk,axs\ blds fy,vki D;k xfrfof/k djsaxs\

lh/ks dksjksa okyh le vkÑfr;ksa ls ifjp; ds ckn cPpksa ls frdksu&prqHkZqt ds lkFk&lkFk oÙk ;k oÙk dsfgLlksa dks Hkh tksM+dj fMt+kbu cukus dks dgk tk ldrk gSA budks vkil esa tksM+dj os fp= 17 esa fn[kk,vuqlkj vkÑfr;ka Hkh cuk ldrs gSaA cPpksa dks ;g crk;k tk ldrk gS fd ;s lHkh le vkÑfr;ka gSaA

fp= 17

vc rd cPps 'kk;n lkspus yxsaxs fd fQj vlekÑfr;ka dkSu lh gksrh gSaA dqN loky iwNdj vki mUgsa[kqn gh ;g le>us esa enn dj ldrs gSaA muls ;g iwNk tk ldrk gS fd D;k gj fMt+kbu dks frdksu]prqHkZt vkSj o`Ùk ds fgLlksa tSlh ifjfpr vkÑfr;ksa esa ckaVk tk ldrk gS\

E10) vkids vUnkt ls mudk mRrj D;k gksxk\ ;fn os gka dg nsrs gS] rks vki dSls mUgsa le>k,axsfd mudk tokc xyr gS\ dksbZ xfrfof/k lksfp,A

171

xfrfof/k ftlls cPpksa dks ;g le>us esa enn feysxh fd lkjh vkÑfr;ka le ugha gksrhA

mnkgj.k 6 % ,d crZu esa ikuh yhft, vkSj ikuh dks Q'kZ ;k nhokj ij tksj ls Qsafd,A cPpksa dks ikuhls cuk fMt+kbu ns[kus nhft,A mUgsa irk djus nhft, fd D;k os bl fMt+kbu dks [kifPp;ksa dh ennls ifjfpr vkÑfr;ksa esa ckaV ldrs gSa tSlk fd os igys djrs vk, gSaA vkÑfr 'kk;n fp= 18 tSlh fn[ksA

fp= 18cPps ns[ksaxs fd bu vkÑfr ds dksj u rks lh/ks gh gSa vksj u gh o`Ùk ds fgLls gSaA vki dkxt ij L;kghfNM+ddj Hkh fMt+kbu cukdj mUgsa fn[kk ldrs gSa mUgsa ;g le>us dk volj nsa fd ,slh vkÑfr;ksa dksfrdksu] prqHkZt] o`Ùk ds fgLlksa tSlh ifjfpr vkÑfr;ksa esa ugha ckVk tk ldrkA ,slh vkÑfr;ksa le ughagksrh blfy, bUgsa vlekÑfr dgk tkrk gSA vki cPpksa dks vkdk'k esa cknyksa ls cuh fMt+kbu fn[kkdjHkh iwN ldrs gSa fd os le gSa ;k vleA bu vklku xfrfof/k;ksa ls cPpksa dks le o vlekÑfr;ksa esa QdZdjus esa enn feysxhA

E11) 50 cPpksa dh d{kk ds fy, mi;qDr ,d ,slh xfrfof/k eq>kb, ftlls ;g irk yx lds fdcPps le&vlekÑfr dk vUrj le>s gSa ;k ughaA

,d dkxt dks bl rjg eksfM+, fd mlds vkeus&lkeus ds fljs vkil esa fey tk,aA eksM+ dks vPNs ls ncknhft,A bl eqMs gq, dkxt esa ls ,d VqdM+k bl rjg dkfV, fd eksM+ dh js[kk dk dqN fgLlk mlesa 'kkfeyjgsA ¼fp= 19½ dkVh xbZ vkdfr lefer gksxhA eksM+ dh js[kk bl vkdfr dks nks cjkcj Hkkxksa esa ckaVrh gSrFkk bls ml vkdfr dh lefefr v{k dgrs gSaA lefer v{k fdlh Hkh lery vkdfr dks nks lokZaxleHkkxksa esa ckaVrk gSA ge bUgs lokZaxle blfy, dgrs gSA D;ksafd ;s iwjh rjg ,d:i ugha gksrsA ;s ,d nwljsds izfrfcEc gksrs gSA ,d Hkkx dh ckbZa :ijs[kk nwljs Hkkx dh nkbZa :ijs[kk ls esy [kkrh gSA

fp= 20

cPps ;g ekuus esa 'kk;n FkksMk f>>dsaxs fd ¼d½ vkSj ¼[k½ ;k ¼x½ vkSj ¼?k½ ijLij lokZaxle gSaA v{kjd vkSj b ,d&nwljs ds izfrfcEc gSa exj cPpksa dks rks 'kq: ls lko/kkuh &iwoZd bUgs vyx& vyx ns[kukfl[kk;k tkrk gSA rks izfrfcEc dks dSls ;dhu fnyk,a \ vxys Hkkx esa lefer phtksa ds ckjs esa ppkZ djrsgq, bl loky dk tcko nsus dh dksf'k'k djsaxsA

172

lefer vkd`fr;kalefer vkd`fr;kalefer vkd`fr;kalefer vkd`fr;kalefer vkd`fr;ka

lefer phtsa cpiu ls gh uUgsa fnekxksa dks vkdf"kZr djrh gSA ;fn pht jaxhu gks] rks cM+ksa dks Hkh eksfgrdjrh gSA cPps cgqr de mez esa gh lefefr dh vo/kkj.kk fodflr dj ysrs gS vkSj muds fp=ksa esa bldh>yd ns[kh tk ldrh gSA fdlh cPps }kjk cukbZ xbZ ekuo vkÑfr lefefr iznf'kZr djrh gSa ¼fp= 21½A

fp= 21

cPpksa ds fy, lefefr dk v/;;u cgqr vklku vkSj fnypLi gksrk gS D;ksafd izÑfr esa blds dbZmnkgj.k feyrs gSaA lefer vkÑfr;ksa dk v/;;u djus esa mUgsa lcls T;knk fnDdr og js[kk irk yxkusesa vkrh gS ftlds lkis{k og vkÑfr lefer gSA izkbejh d{kk ds 6&7 o"khZ; cPps dks Hkh lefer fp=cukus esa et+k vkrk gS] gkykafd mls buds xq.k irk ugha gksrsA ;gka eSa ,d xfrfof/k crk jgh gwa tks jkerc dj jgk Fkk] tc eSa mlds ?kj xbZ FkhA

mnkgj.k 7 %mnkgj.k 7 %mnkgj.k 7 %mnkgj.k 7 %mnkgj.k 7 % jke ds ikl ,d L;kgh dh cksry vkSj ,d /kkxk FkkA mlus /kkxs dks L;kgh esa Mqcksdj mlsviuh uksV cqd esa j[k fn;kA fQj mlus uksV cqd dks cUn djds nck fn;kA vc mlus uksV cqd [kksyhvkSj /kkxs dks /khjs&/khjs mBk fy;kA mlus eq>s uksVcqd esa cuk og fMt+kbu fn[kk;kA

jkejkejkejkejke %%%%% ns[kks] nksuksa iUuksa ij dSlk vPNk fMt+kbu cu x;k gSA ,slk fMt+kbu gkFk ls cukukfdruk eqf'dy gksxk uk \ ml fnu vkius dgk Fkk fd eSa ;gka tks dqN djrk gwa og lcLdwy dk gh ikB gksrk gSA vc crkvksa blls eq>s d{kk esa lh[ks ikB esa D;k enn feysxh\

mls mEehn Fkh fd eSa udkjkRed tokc nwaxhA ;g rks tkfgj Fkk fd mlus leferfMt+kbuksa ds ckjs esa dqN ugha i<+k FkkA

eSaeSaeSaeSaeSa %%%%% tokc nsus ls igys eSa rqels ,d loky iwNwaxhA ijUrq esjs dqN dgus ls igys gh jkecksy iM+kA

mlus og if=dk esjh vksj c<+k nhA i`"B [kksyus ij eq>s mlh iUus ij ,d vksj igsyhfn[k xbZA ikl&ikl nks fp= fn, x, Fks ¼ns[ksa fp= 22½A

fp= 22

173

igsyh ;g Fkh fd bu nks fp=ksa esa vkB vUrj <wa<us FksA eSaus jke dk /;ku bl igsyh ij fnyk;kA

jkejkejkejkejke %%%%% eSaus igys gh lkjs vUrj <wa< fy, gSaA

eSaeSaeSaeSaeSa %%%%% cf<+;k! vc t+jk viuh uksVcqd esa cus nks fMt+kbuksa dks ns[kksA tjk ns[kks fd D;k muesarqe dksbZ vUrj <wa< ldrs gksA

mlus nksuksa fp=ksa dks ckjhdh ls ns[kuk 'kq: fd;kA FkksM+h nsj ckn mlus dgk fd ogdksbZ vUrj ugha <wa< ik;kA

eSeSeSeSeS %%%%% rqEgkjk eryc gS fd nksuksa fMt+kbusa gwcgw ,d lh gSa \

jkejkejkejkejke %%%%% gka! ijUrq if=dk ds mu nksuksa fp=ksa tSlh leku ugha gSA eSa crk ugha ldrk fd ,slkD;ksa gSA

eSaus mlls ,d vkbuk ykus dks dgkA og Hkkxdj ys yk;kA

eSaeSaeSaeSaeSa % vc nksuksa iUuksa ds chp vkbus dks [kM+k djds idM+ks ¼;kuh dkx+t ds ry ls yEcor~½Avkbus dk eq¡g fMt+kbu dh rjQ j[kks vkSj ck,a ist dks vkbus esa ns[kksA D;k ;g izfrfcEcnk,a iUus dh fMt+kbu tSlk gS\

mlus izfrfcEc dk v/;;u fd;k ¼ns[ksa fp= 23½A fQj vkbuk gVkdj nk,a iUus dsfMt+kbu dks ns[kkA

fp= 23

jkejkejkejkejke %%%%% ¼eqLdjkrs gq,½ % etsnkj ckr gSA vkbus esa nk,a rjQ dk fMt+kbu ckbZ rjQ ds fMt+kbutSlk fn[krk gSA gS uk] vk.Vh\

blds ckn eSaus mls ,d vkneh dh 'kDy dks iwjk djus dks dgkA eSaus vk/kh 'kDy cuk nh ¼fp= 24½Amlus bls] iwjk djus dh dksf'k'k dh exj ,dne lgh & lgh u cuk ldkA eSaus mlls dgk fd ykbuij vkbuk j[kdj ns[ks fd D;k gksrk gSA mlus ns[kk fd ck;ka Hkkx vkSj mldk izfrfcEc feydj iwjkpsgjk cu x;kA

fp= 24

eSaeSaeSaeSaeSa %%%%% vc rqe le> ldrs gks fd ;fn ge bUlku ds psgjs ds chpksa chp ,d ykbu [khaps rkscka;k Hkkx vkSj nk;ka Hkkx le:i gksrs gSa os ,d] nwljs dk izfrfcEc gSaA ;gh ckr rqEgkjhuksV cqd ds fMt+kbu esa Hkh gSA nk,a iUus dk fmt+kbu] ck,a iUus ds fMt+kbu dk izfrfcEcgS vkSj os le:i gSaA

174

eSaus mlls ckgj pyus dks dgkA eSa mls isM+&ikS/ks fn[kkuk pkgrh FkhA eSaus mlls ,diÙkh rksM+dj mldk fujh{k.k djus dks dgk ¼fp= 25½A

fp= 25

eSeSeSeSeS %%%%% D;k rqe iÙkh ds chpksa chp ,d ul ns[k jgs gks\ D;k ul ds nksuksa vksj iÙkh dk ck;kaHkkx vkSj nk;ka Hkkx le:i gSa\ dSls irk yxkvksxs \mlus ckjhdha ls iÙkh dks ns[kk exj ;g u crk ldk fd nksuksa Hkkx le:i gSa ;k ughaAeSaus mlls iÙkh dks ul ij ls eksM+us dks dgkA mlus oSlk gh fd;kA eSaus iwNk fd ÞD;knksuksa Hkkx esy [kkrs gSa\ß

jkejkejkejkejke %%%%% vPNk! ,sls irk djrs gSa\ gka] nksuksa Hkkx iwjh rjg esy [kkrs gSaA vc eSa le> x;kA

eSaeSaeSaeSaeSa %%%%% ge dgrs gSa fd iÙkh esa chp dh ul ds nksuksa vksj ds Hkkx lefer gSaA rqe vkSj ifÙk;kaysdj Hkh vktek ldrs gks fd D;k muesa Hkh chp dh ul ds nksuksa vksj ds Hkkx lefergSa ;k ughaA

jke us dbZ ifÙk;ka rksM+dj chp ls eksM+dj ns[kkA vf/kdrj ifÙk;k¡ lefer FkhaA dqNugha Hkh FkhaA

jkejkejkejkejke %%%%% ijUrq vk.Vh ;fn ul chpksa&chp u gks] rks ge dSls irk djsaxs fd iÙkh lefer gS ;kugha \

eSaeSaeSaeSaeSa %%%%% bl Qwy dks ns[kks ¼fp= 26 ns[ksa½A D;k rqe dksbZ ,slh js[kk [kkst ldrs gks] ftldsbnZ&fxnZ ;g Qwy lefer gks \ ,d /kkxk ysdj mls Qwy ds Åij j[kks irk yxkvksA

fp= 26'kq: esa og FkksM+k ?kcjk;k exj fQj mlus eq>s ,slh js[kk,a crkbZa ftuds bnZ&fxnZ Qwy lefer FkkA

eSaeSaeSaeSaeSa %%%%% rqEgkjk eryc gS fd fdlh lefer vkÑfr esa ,d ls vf/kd lefefr v{k gks ldrs gSa\

jkejkejkejkejke %%%%% gka ! eq>s iDdk fo'okl gSA

eSaeSaeSaeSaeSa %%%%% 'kkck'kA

blds ckn eSaus ,d iÙkh dks mlds lefefr&v{k ;kuh e/; ul ij eksM+dj mls fn[kk;k fd tc fdlh

175

lefer vkÑfr dks lefefr&v{k ij ls eksM+k tkrk gS rks gesa mlds nksuksa Hkkxksa ds ctk; ,d gh Hkkxut+j vkrk gSA

jke dh fnypLih bruh c<+ xbZ fd og gj Qwy&iÙkh ij /kkxk j[kdj ns[kus yxkA vpkud ,d frryhns[kdj og mNy iM+k vkSj fpYyk;k vk.Vh*A mls lefer pht+ dk ,d cf<+;k mngkj.k fey x;k FkkAijUrq jke dks lcls T;knk gSjkuh rc gqbZ tc eSaus mls crk;k fd tks lekslk ge [kk jgs gSa og Hkhlefer gSA ;g lqudj og FkksM+k pdjk x;kA mlus rhu vyx&vyx fLFkfr;ksa esa /kkxs dks j[kk] eudh eu nksuksa fgLlksa dk v/;;u fd;kA og [kq'k Fkk vkSj vc mldk lansg Hkh nwj gks x;k FkkA

E11) D;k vkidks yxrk gS fd ,slh xfrfof/k;ksa ls cPpksa dks lefer vkÑfr;ksa dh vo/kkj.kk dksle>us esa vklkuh gksrh gS\ D;k fl[kkus dk ;g rjhdk ml ikjEifjd rjhds ls T;knk dkjxjgS ftlesa f'k{kd CySd cksMZ ij pUn lefer vkÑfr;ka cukdj fo|kfFkZ;ksa dks] cxSj fdlh izR;{kvuqHko ds] lefefr ds ckjs esa lc dqN crk nsrs gSa\

E12) de ls de nks ,slh xfrfof/k;k¡ lq>kb, tks vki d{kk esa lefer vkÑfr dh vo/kkj.kk i<+kusds fy, djsaxsA

vkius Hkh /;ku fn;k gksxk fd gekjs vklikl dh dbZ pht+sa o lajpuk,¡ lefer gksrh gSaA ,d ckj cPpklefefr dh vo/kkj.kk dks le> ys rks mls vius vkl ikl lefefr [kkstus ds volj fn, tkus pkfg,AcPps] ifÙk;ksa] Qwyksa] ?kj ds njoktksa] jaxksyh] lkM+h o pknj ds fMt+kbuksa esa lefefr ns[k ldrs gSaA blrjg ls os vius vklikl dh reke pht+ksa esa lefefr [kkst ldrs gSaA fofHkUu le o vlekÑfr;ksa dhlefefr dk iz;ksx djds frdksu] oxZ] vk;r] o`Ùk vkfn tSLh ifjfpr T;kferh; vkÑfr;ksa esa lefefrfn[kkbZ tk ldrh gSA cPps dkxt+ dh vkÑfr dkVdj vkSj mls eksM+dj irk yxk ldrs gSa fd D;k dksbZ,slh ykbu gS ftl ij ls vkÑfr dks eksM+us ,d v/kkZa'k nwljs ls esy [kkrk gSa ,d vkSj et+snkj iz;ksx;g gks ldrk gS fd fdlh vkÑfr dks Vªsflax isij ij mrkjsa vkSj bl dkxt+ ds ihNs dh rjQ fn[kkbZiM+us okyh vkÑfr dh rqyuk ewy vkÑfr ls djsaA ge mudks crk ldrs gSa fd leHkqt frdksu ds rhulefefr&v{k frdksu dks N% cjkcj Hkkxksa esa ckaV nsrs gSaA cPps ;g Hkh ns[k ldrs gSa fd o`Ùk esa rksvufxur lefefr&v{k gksrs gSaA

E13) fuEufyf[kr vo/kkj.kk,a fl[kkus ds fy, vki D;k xfrfof/k lq>k,axs\

¼d½ fdlh vkÑfr esa gj js[kk lefefr&v{k ugha gksrhA

¼[k½ lefefr&v{k ds nksuksa vksj ds laxr fcUnq v{k ls cjkcj nwjh ij gksrs gSaA

¼x½ oxZ esa 4 lefefr&v{k gksrs gSa tcfd vk;r esa flQZ nks gksrs gSaA

¼?k½ rk'k ds iÙkksa ij cus fp= chp esa [khaph xbZ js[kk ij lefer gksrs gSaA

lkjka'klkjka'klkjka'klkjka'klkjka'kbl ikB esa geus fuEufyf[kr fcUnqvksa ij ppkZ dh %1½ tc rd ubZ vo/kkj.kkvksa dk fodkl tkus igpkus vuqHkoksa ds vk/kkj ij u fd;k tk,] rc rd

uUgsa fnekx T;kferh dh ewyHkwr vo/kkj.kkvksa dks vPNh rjg le> ugha ikrsA cPpksa dks [ksydwnesa et+k vkrk gSA mudh bl izÑfr dk ykHk mBkrs gq, geus cUn o [kqyh vkÑfr;ksa dh vo/kkj.kkfl[kkus ds fy, [ksydwn ds rjhdksa dk mi;ksx fd;k gSA [kifPp;ksa] jcM+ cSaM] /kkxs vkfn tSLhlk/kkj.k phtksa ls gks ldus okyh vklku xfrfof/k;ka lq>kbZ gSa ftuls cPpksa dks [kqyh o cUnvkÑfr ds chp varj le>us esa enn fey ldrh gSA

176

2½ dbZ erZck cPps lery@vlery lrgksa dks fpduh@[kqjnjh lrg ekuus dh Hkwy dj cSBrs gSaAmuds fy, v.Ms] xsan ;k csyukdkj crZu dh lrg lery gksrh gSA bl leL;k dks lqy>kusds fy, mUgsa dqN fpduh o [kqjnjh lrg gkFkksa ls eglwl djus dks nh tk ldrh gSaA leryo vlery lrgksa ds chp ds varj dks le>us ds fy, mUgs ekfpl dh fMCch] daps] ikls]iksLVdkMZ] xsansa] Xyksc] fdrkcsa] isafly ckWDl vkfn dk fujh{k.k djus dks dgk tk ldrk gSA

3½ le vkÑfr;ksa dh vo/kkj.kk fodflr djus ds fy, cPpksa dks igys lh/ks dksjksa okyh cUnvkÑfr;ksa ls ifjfpr djk,aA elyu] oxZ] vk;r oxSjgA mUgsa [kifPp;ksa] /kkxs] jcj cSaM vkfn dslkFk xfrfof/k;ka djus nsa vkSj fofHkUu vkÑfr;ka cukus nsaA bl izfØ;k ds nkSjku mUgsa vyx&vyxizdkj ds frdkuksa o prqHkqZtksa ds ukeksa ls ifjfpr djk;k tk ldrk gSA mUgsa lekUrj prqHkqZt] oxZvkSj vk;r ds chp dk lEca/k [kkstus nsaA xksykbZnkj] dksjksa okyh le vkÑfr;ksa rFkk vlekÑfr;ksals Hkh cPpksa dk ifjp; xfrfof/k;ksa ds ek/;e ls djk;k tk ldrk gSA

4½ cPps lefefr dh vo/kkj.kk dkQh NksVh mez esa gh gkfly dj ysrs gSaA ;g ckr muds }kjk cuk,x, fp=ksa esa ns[kh tk ldrh gSA ijUrq dbZ erZck mUgsa lefer T;kferh; vkÑfr;ksa esalefefr&v{k irk djus esa fnDdr gksrh gSA bl ekeys esa mudh enn ds fy, ge mUgsa vklikldh lefer phtksa dk vuqHko ns ldrs gSaA bu pht+ksa esa os vkÑfr ds ry esa ,slh js[kk <wa<s ftlijls eksM+us ij nks v/kkZa'k ,d&nwljs ls esy [kk, vkSj nks dh ctk; ,d gh fgLlk ut+j vk,A mUgsavius vklikl izÑfr esa lefefr [kkstus nhft,A vklku lh xfrfof/k;ksa ds tfj, mUgsa leferpht+ksa dh lHkh fo'ks"krkvksa ls ifjfpr djk;k tk ldrk gSA

177

ikB 12 ikB 12 ikB 12 ikB 12 ikB 12dks.k ekiukdks.k ekiukdks.k ekiukdks.k ekiukdks.k ekiuk

dks.k D;k gksrk gS\dks.k D;k gksrk gS\dks.k D;k gksrk gS\dks.k D;k gksrk gS\dks.k D;k gksrk gS\lcls igys vkb, ge cPpksa esa ^dks.k* dk vglkl fodflr djus ds dqN rjhdksa ij xkSj djsaA ,d ckjd{kk 5 ds ,d f'k{kd us CySd cksMZ ij ,d dks.k cuk;k vkSj dgk fd ;g dks.k dk fp= gSA rRdky,d cPps us loky fd;k] ^dks.k dkSu lk gS lj\ lQsn okyk ;k dkyk okyk\* dkys cksMZ ij lQsn pkWdls cus bl fp= us cPps dks pDdj eas Mky fn;k Fkk fd pkWd ls cuk lQsn fu'kku dks.k gS ;k bl lQsnfu'kku ds vUnj okyk fgLlk dks.k gSA ikjEifjd d{kk fof/k ls i<+k, tkus okys vf/kdka'k cPpksa ds eu esa;g loky iSnk gks ldrk gSA yksxksa dks ;g le>us esa fnDdr D;ksa gksrh gS fd dks.k D;k gksrk gS\ u flQZcPps cfYd dbZ o;Ld Hkh iDds rkSj ij ugha dg ldrs fd dks.k D;k gksrk gSA tc izk;ejh Ldwy ds dqNf'k{kdksa ls iwNk x;k fd fp= 1 esa fdrus dks.k cus gSa rks muds tokc dkQh fnypLi jgs ¼fp= 1½A

fp= 1 esa dqN f'k{kdksa dks 2 dks.k fn[ks] dqN dks 3 rFkk dqN dks 4 dks.k utj vk,A

fp= 1

vkb, bl ckr dk fo'ys"k.k djsa fd ;g xyrQgeh D;ksa iSnk gksrh gSA blds fy, vkb, igys ns[ksa fdesjk ppsjk HkkbZ] tks izk;ejh d{kk esa i<+krk gS viuh d{kk esa ^dks.k* dh vo/kkj.kk dSls crkrk gSA

mnkgj.k 1 % mlds Ldwy esa igyh ckj dks.k ls cPpksa dk lkeuk d{kk 5 esa gksrk gSA f'k{kd lcls igyscPpksa dks ,d ^fdj.k* ds ckjs esa crkrs gSaA vke rkSj ij f'k{kd djrs ;g gSa fd CySd cksMZ ij Ldsy dhenn ls ,d js[kk[k.M [khap nsrs gSa] blds nkfgus fljs ij ,d rhj dk fu'kku cuk nsrs gSa vkSj fQj ck,afljs dks A rFkk nk,a fljs dks B ls vafdr dj nsrs gSaA blds ckn os cPpksa dks crkrs gSa fd bl fp= dks^fdj.k* dgrs gSaA

esjs ppsjs HkkbZ ds eu esa ;g loky vk;k fd ftu cPpksa dk fdj.k ls ifjp; bl rjhds ls djk;k tkrkgS D;k os bl rjg ds lokyksa ds tokc ns ik,axs\

1- dksbZ fdj.k ckbZa ls nkbZa vksj gh D;ksa [khaph tkrh gS\

2- rhj dk fu'kku D;ksa yxkrs gSa\

3- ;fn ckbZa rjQ rhj dk fu'kku yxk nsa] rks D;k gks tk,xk\

4- D;k ge fdj.k dks [kM+s :i esa ugha cuk ldrs\

5- fdruh yEckbZ cukus ds ckn rhj dk fu'kku yxkuk pkfg,A

;kuh bu vo/kkj.kkvksa dks i<+krs oDr gesa ;g /;ku j[kuk gksxk fd cPpk bUgsa fdl rjg xzg.k djsxkAvr% esjs ppsjs HkkbZ us lkspk fd gks ldrk gS fd ,d dYiuk'khy dgkuh ls cPpksa dks ;g vo/kkj.kklh[kus esa enn feysA rks vo/kkj.kkvksa ls ifjfpr djkus ls igys] 'kq:vkr esa os vDlj cPpksa dks fuEuizdkj dh dqN dgkfu;ka lqukrs gSaA

178

,d cgqr ykyph vkSj erych vkneh FkkA og ns'k dk lcls vehj vkneh cuuk pkgrk FkkA og gj fnuHkxoku ls izkFkZuk djrk fd Hkxoku mls lksus vkSj ghjs tokgjkr dk [ktkuk fn[kk nsA Hkxoku us mlslcd fl[kkus dh BkuhA ,d fnu Hkxoku mlds lkeus izdV gksdj dgus yxs] ^eSa rqels izlUu gqvkAeSa rqEgsa /kkxs dh ,d tknqbZ jhy nwaxkA rqe /kkxs dk ,d fljk vius ?kj esa fdlh txg cka/k nsuk vkSj jhygkFk esa ysdj fdlh Hkh fn'kk esa lh/ks py iM+ukA /kkxs dks rkudj j[kukA vxj /kkxk <hyk jgk rks rqEgsadksbZ [ktkuk ugha feysxkA ,d gh fn'kk esa lh/ks pyuk] eqM+uk ughaA rqe nhokjksa] isM+ksa] leUnj] vkx] gjpht dks ikj dj ldksxsA dksbZ pht rqEgsa jksd u ldsxhA tc rqe /kkxs ds nwljs Nksj ij igaqpksxs] rks[ktkuk rqEgkjs dneksa esa gksxkA* ykyph vkneh us oSlk gh fd;kA og cjlksa fnu&jkr pyrk jgkA /kkxsdks rkus j[kkA ijUrq og /kkxs ds nwljs Nksj rd u igqap ldkA ;gh ml /kkxs dk tknw FkkA vHkh Hkh ogmlh fn'kk esa lh/kk py jgk gSA u rks /kkxs dks Nksj vkrk gS] u [ktkukA

fQj og dgkuh dk mi;ksx ;g le>us ds fy, djrk gS fd fdj.k D;k gksrh gSA mlus fp= 2 dh rjgml vkneh dk jkLrk fn[kk;k ¼fp= 2½A bl fp= ls mlus le>k;k fd tgka vkjEHk fcUnq

fp= 2fy[kk gS ogka ls vkneh us pyuk 'kq: fd;k Fkk vkSj og fp= esa n'kkZbZ xbZ fn'kk esa pykA mlus cPpksadks ;kn fnyk;k fd og vkneh 'kq: esa fdlh Hkh fn'kk dks pqu ldrk FkkA ysfdu 'krZ ;g Fkh fd ,dckj fn'kk pqu ysus ds ckn mls yxkrkj mlh fn'kk esa pyuk iM+sxkA ,d fljs ij cus rhj ls blh fn'kkdk irk pyrk gS vkSj ;g Hkh irk pyrk gS fd ml vkneh dh ;k=k [kRe ugha gqbZ gS] og vHkh Hkh pyjgk gSA

,d ckj tc cPps bl fopkj ds vknh gks x,] rc esjs ppsjs HkkbZ us fdj.k dh vkSipkfjd ifjHkk"kk nhvkSj fp= 3 esa fn[kk, vuqlkj fdj.k dk T;kferh; fp= cuk fn;kA

fp= 3

js[kk dh vo/kkj.kk ls ifjfpr djkus ds fy, Hkh mlus cPpksa dks blh rjg dk vuqHko fn;kA mlus cPpksls ,d ,sls tknqbZ lh/ks rus gq, /kkxs dh dYiuk djus dks dgk tks gok esa rSj ldsA tc ge dgsa fd^c<+ks* rks nksuksa fn'kkvksa esa c<+uk 'kq: dj ns vkSj :dus dk uke u ysaA fQj mlus fp= 4 esa fn[kk,vuqlkj fp= cuk;kA

179

fp= 4

fQj mlus lq>ko fn;k fd bl fp= ds xq.kksa dks tkuus ds fy, d{kk esa ckrphr djsaA ge nksuksa rjQ,d&,d rhj dk fu'kku D;ksa yxkrs gSa\ bldh 'kq:vkr dgka gS\ var dgka gS\ ;g fdruh yEch gksldrh gS\ bl rjg ds dbZ loky iwNs tk ldrs gSA blds ckn ge dg ldrs gSa fd fp= 4 esa fn[kkbZxbZ vkÑfr js[kk gSA mlus js[kk o fdj.kksa dks ysdj cPpksa ds lkFk dkQh le; fcrk;k vkSj mUgsaCySdcksMZ ij dkQh vH;kl fn,A

fdj.k vkSj js[kk dks ifjHkkf"kr djus ds ckn mlus dks.k dh vo/kkj.kk 'kq: dhA blds fy, mlus cPpksdks fdj.kksa dk ,d ekWMy fn;kA mlus ftl ekWMy dk bLrseky fd;k og ukfj;y dh ifRr;ksa ls cukFkkA mlus ;g Hkh crk fn;k fd ge rkj ;k jax fcjaxh LVªkW dk mi;ksx Hkh dj ldrs gSaA

iRrh dks fdj.k ds :i esa mi;ksx djus ds fy, mlds MaBy dks dkV ysaxs vkSj ,d fljs ij iRrh dkFkksM+k lk Hkkx jgus nsaxsA bls ,d rhj dh 'kDy ns nsaxsA MaBy vkSj iRrh dqN bl rjg fn[ksaxs ¼mlusfp= 5 tSlh vkÑfr cukbZ½A

fp= 5

ge izR;sd cPps ls ,slh nks fdj.ksa cukus dks dgsaA fQj gj cPpk nksuks fdj.kks dks ,d lkFk bl rjgidM+s fd muds os fljs ,d nwljs dks Nq,a ftu ij fd rhj ugha gSA cPpksa }kjk cukbZ xbZ vkÑfr;ka ,slhfn[ksaxhA

fp= 6

fQj mlus cPpks dks crk;k fd mUgksaus nks fdj.kksa dh enn ls tks vkÑfr;ka cukbZ gSa] ogh dks.k gSaA bldsckn mlus cPpksa ls ckrphr djds dks.k dh vo/kkj.kk muds eu esa cSBk nhA mlus cPpksa ds lkeus blrjg ds loky j[ksa %

1- ,d dks.k cukus ds fy, fdrus rhj yxs\2- fdj.kksa dks dSls j[kk gS rqeus\3- fdj.ksa ,d&nwljs dks dgka Nw jgh gSa\4- vxj fdj.kksa dks ,d&nwljs ds foijhr fn'kk esa j[k nsa rks D;k gksxk\

180

bl txg ij mlus dks.k dh ,d vkSipkfjd ifjHkk"kk ;ksa nsus dh dksf'k'k dh fd tc nks fdj.kksa dk ,dlk>k vafre fcUnq gksrk gS] rc os dks.k cukrh gSaA*

vkSj vkxs c<+us ls igys D;k vki bl mnkgj.k ij fopkj ugha djuk pkgsaxs\ izLrqr gS ,d vH;klA

E 1) mnkgj.k 1 esa crkbZ xbZ f'k{k.k j.kuhfr ds ckjs es vkidh D;k jk; gS\ D;k blls cPpksa dks dks.kdh vo/kkj.kk dh Li"V le> gkfly djus esa enn feyrh gS\ vius mRrj dks dkj.k lfgrle>kb,A

esjh vius ppsjs HkkbZ ls tks ckrphr gqbZ mlh dks tkjh j[krs gSaA mldh ckr /kS;ZiwoZd lquus ds ckn eSausmlls dqN loky fd,] ^D;k dks.k dk eryc le>us ds fy, t:jh gS fd ge fdj.k] js[kk vkfn dhifjHkk"kk ls 'kq:vkr djsa\ D;k rqEgkjs bl rjhds ls cPpksa dks okdbZ viuk ;g lansg nwj djus esa ennfeysxh fd dks.k fdj.kksa }kjk cukbZ xbZ vkÑfr dk lQsn okyk fgLlk gS ;k dkyk okyk\ D;k blls cPpsdks ;g le>us esa enn feysxh fd dks.k njvly nks js[kkvksa ds chp >qdko dk eki gS ;k T;knk Li"V:i esa dgsa rks og ?kw.kZu ¼?kqeko½ dks eki gS\ ge bl eki dk dqN vglkl xfrfof/k vk/kkfjr rjhds lsD;ksa ugha ns ldrs\* mlus ekuk fd cPpksa dks os fnDdrsa vkrh gSa] tks eSaus crkbZaA mldk dguk Fkk fd,slh fnDdrsa tc tc mBsa rc rc Bhd dh tk ldrh gSaA mldk er Fkk fd mlds }kjk viuk;k x;krjhdk ekud rjhdk gS vkSj mlus dHkh vkSj fdlh rjhds ds ckjs esa lkspk gh ughaA

eSaus tc ,d vU; f'k{kd ls bl ckjs esa ppkZ fd rks os Hkh lger Fkh fd dks.k dk ikB :f<+xr <ax lsugha i<+k;k tkuk pkfg,A ;g <ax cPpksa dks cgqr cukoVh yxrk gS vkSj os blls tqM+ ugha ikrsA mUgksauseq>s crk;k fd gesa cPpksa dks ;g fl[kkuk pkfg, fd dks.k ,d fn'kk vkSj nwljh fn'kk ds chp ifjorZudk eki gSA ijUrq vius vuqHko ls mUgsa yxrk gS fd ;g ifjHkk"kk cPpksa ds fy, 'kq:vkr esa FkksM+h T;knkgh eqf'dy gks tk,xhA fygktk mudk lq>ko Fkk fd lgh oDr vkus rd dksbZ ifjHkk"kk nsuh gh ughapkfg,A ge mUgsa lgtrk ls ;g crk ldrs gSa fd tc nks fdj.ksa ,d fcUnq ij feyrh gSa] rks gesa ,ddks.k feyrk gSA vkxs pydj ge mUgsa crk ldrs gSa fd bl dks.k ls gesa nks fn'kkvksa ds chp ds vUrjdk irk pyrk gSA

vkb, vc ge mudh f'k{k.k j.kuhfr dks FkksM+k foLrkj esa ns[ksaA

mnkgj.k 2 % lcls igys mUgksaus cPpksa dks ,d ?kM+h dk xRrs dks ekWMy fn[kk;kA mUgksaus cM+s dkaVs dks2 ds vklikl rFkk NksVs dkaVs dks 10 ds vklikl j[kk rkfd ?kM+h 10%10 fn[kk,A vc mUgksaus vius gkFkcM+s o NksVs dkaVs ij fQjkrs gq, dgk fd ;s nks dkaVs ,d dks.k cukrs gSaA vc mUgksaus ?kM+h ds dkaVksa dhfLFkfr cny nh] gj ckj os le>krh xbZ fd nks dkaVksa ds chp cuk dks.k D;k gSA ¼ns[ksa fp= 7½

fp= 7

181

gj ckj dkaVs dk fp= cukrs oDr mUgksaus rhj dk fpUg cuk;k gkykafd mUgksaus cPpksa dks ;g ugha crk;kfd rhj yxkus dk egRo ;k eryc D;k gSA

blds ckn f'k{kd us nks iSaflyksa dks 45Πds dks.k ij idM+dj iwNk fd D;k ^;gka ,d dks.k cuk gS\* blrjg dh Bksl xfrfof/k;ksa ds tfj,] tks muds lkFk&lkFk cPps Hkh dj jgs Fks] mUgksaus cPpksa dks ;g crkusdh dksf'k'k dh fd ^tc nks fdj.ksa ,d fcUnq ij feyrh gSa] rc gesa ,d dks.k feyrk gSA*

f'k{kd us mUgsa ;g Hkh crk;k fd dks.k cukus okyh nks fdj.kksa dks dks.k dh Hkqtk,a Hkh dgk tkrk gSA

blds ckn f'k{kd us ,d cM+h xRrs okyh fdrkc yhA fp= 8 d dh rjg mldk NksVk fljk mudh rjQj[kdj vkSj mls FkksM+k lk [kksydj cPpksa ls iwNk fd D;k os fdrkc dh nks lkbM ls cuk dks.k ns[k ikjgs gSa\ tc cPps le> x, fd

¼d½ ¼[k½

fp= 8

f'k{kd dk b'kkjk fdl dks.k dh vksj gS rks mUgksaus fdrkc dk FkksM+k vkSj [kksyk ¼fp= 8 [k½A blds vkèkkjij mUgksaus dksf'k'k dh fd cPps ^dks.k* vkSj ^fdrkc fdruh [kqyh gS*] buds chp laca/k ns[k ik,aA ckn esamUgksaus dejs ds dksuksa] rFkk frdksu] vk;r] lekUrj prqHkqZt ds dksuksa ls dks.k dh vo/kkj.kk dks tksM+kA

bl rjg ls f'k{kd us cPpksa dks dks.k dk ,d lgt fopkj fn;kA

ckn esa tc os ewY;kadu dj jgh Fkha fd cPps fdruh gn rd dks.k dh ckr dks le> ik, gSa rks mUgksaus

ns[kk fd vf/kdrj cPps dks.k bl rjg cuk jgs FksA blls mUgsa FkksM+h fpUrk gqbZA mUgksaus r; fd;k

fd os cPpksa ls iwNsaxh fd dks.k vkSj fdu rjhdksa ls cuk;s tk ldrs gSa\ blds fy, mUgksaus dqN cPpksadks CySdcksMZ ij cqyk;k vkSj dgk fd mUgksaus igys tks dks.k cuk, Fks] muls vyx dks.k cuk,aA mUgksaus

cPpksa dks ?kM+h ds dkaVksa dh ;kn fnykbZA /khjs&/khjs cPpksa ds fnekx esa ?kqlk fd vkfn

Hkh dks.k gSaA

cPpksa ls ckrphr djrs gq, mUgsa irk pyk fd dks.k dh vo/kkj.kk dks ysdj dHkh dHkh cPps fcYdqyvyx&vyx fopkj j[krs gSaA mUgsa yxk fd bl vo/kkj.kk dks vPNh rjg le>kus dk lcls cf<+;krjhdk fuEu izdkj dh vo/kkj.kk,a gks ldrh gSaA

f'k{kd us ikap fo|kkfFkZ;ksa dks cqykdj CySdcksMZ ds ikl [kM+k dj fn;kA muesa ls ,d yM+dh ';kek dksCySdcksMZ ds Bhd lkeus [kM+k dj fn;k vkSj cPpksa dks fp= 9 esa fn[kkbZ fLFkfr 1] 2] 3 vkSj 4 esa [kM+kdj fn;kA vc f'k{kd us ';kek ls dgk fd og vius nksuksa gkFkksa dks c<+kdj fLFkfr 1* dh fn'kk esa djsaA

182

fp= 9f'k{kd % vc] ';kek] vius ck,a gkFk dks fLFkj j[kdj nk,a gkFk dks ?kqekdj ^2* dh vksj dj nksA

¼';kek us ,slk gh fd;kA½ vPNk] vc vius nk,a gkFk dks igys okyh fLFkfr esa okil ysvkvks vkSj ?kqekdj fLFkfr ^3* esa ys vkvksA

';kek us ,slk gh fd;kA f'k{kd us blh fØ;k dks fLFkfr ^4* ds fy, nksgjkus dks dgkA

f'k{kd % ';kek] vc crkvks fdl fLFkfr esa rqEgsa viuk gkFk lcls T;knk ?kqekuk iM+k & ^2* dsfy,] ^3* ds fy, ;k fQj ^4* ds fy,A

';kek % ^4* ds fy,A

f'k{kd % Bhd gSA vkSj vc crkvks fd ^2* vkSj ^3* esa ls fdl fLFkfr ds fy, rqEgsa gkFk T;knk?kqekuk iM+kA

';kek rqjUr tokc u ns ikbZA blfy, mlus igys okyh fØ;k dks ,d ckj fQj nksgjk;kvkSj tokc fn;k fd fLFkfr ^2* ds fy, mls viuk gkFk vf/kd ?kqekuk iM+kA

f'k{kd ¼ckdh cPpksa ls iqNrs gq,½ % D;k vki ';kek ls lger gSa\ fLFkfr ^1* ij [kM+kgqvk cPpk % ugha eSMe ^2* ds fy, ugha] ^3* ds fy,A

f'k{kd % D;ksa\

cPpk % ';kek ds gkFkksa dks ?kwers ns[kdj esjs dks ,slk gh yxkA

f'k{kd % pyks! ge ns[krs gSa dkSu lgh gSA

blds fy, f'k{kd us ';kek dks ,d ckj fQj ls ogh fØ;k nksgjkus dks dgkA lkFk ghlkFk oks pkWd ls tehu ij js[kk,a [khaprh jgh ;g fn[kkus ds fy, fd ';kek dk nk,agkFk fdl&fdl fn'kk esa ?kwek ¼fp= 10 nsf[k,½A

fp= 10

183

f'k{kd ¼fp= 10 dh vksj b'kkjk djrs gq,½ % tks js[kk,a eSaus [khaph gS mlesa rqEgsa D;k dksbZ dks.k fn[krkgSA ,d cPpk tehy us ^1* vkSj ^3* ds chp curs gq, dks.k dh vksj b'kkjk fd;kA

f'k{kd % tehy rqEgsa bl dks.k dk dSls irk pyk\

tehy ¼dqN lkspus ds ckn½ % ';kek dk nk;ka gkFk igys ^1* dh vksj eqM+k vkSj ^3* dh vksjA

f'k{kd ¼dks.k dh vksj b'kkjk djrs gq,½ % fcYdqy Bhd] ;s dks.k rc cuk tc ';kek dk gkFk ^1* ls ^3*dh vksj ?kwekA tehy D;k rqEgsa dksbZ vkSj dks.k fn[krk gSA

mlus nks vkSj dks.kksa dh vksj b'kkjk fd;kA

f'k{kd % vc crkvks dkSu lk dks.k vf/kd gS & ^1* vkSj ^2* ds chp ;k fQj ^1* vkSj ^3* ds chp\

t;k ¼nwljh cPph½ % ^1* vkSj ^3* ds chp dk dks.k vf/kd gSA

f'k{kd % lgh gSA bldk eryc gS fd ^1* vkSj ^3* ds chp ds ?kqeko ^1* vkSj ^2* ds chp dk ?kqeko lsT;knk gSA

vc f'k{kd us iwjh d{kk dks 5 Vksfy;ksa esa ckaV fn;kA mlus lHkh Vksfy;ksa ls ';kek vkSj mldh lkfFk;ksa}kjk dh xbZ fØ;k dks nksgjkus dks dgkA bl izdkj mlus lHkh cPpksa dks ;s ,glkl djus dk ekSdk fn;kfd dks.k fdl izdkj ^fn'kk ifjorZu* dks fn[kkrk gSA f'k{kd us le; le; ij d{kk esa blh vo/kkj.kkdks ysdj dqN vkSj Hkh xfrfof/k;ka dha & tc rd mldks ;g rlYyh ugha gks x;h fd cPps ;s le>pqds gSa fd dks.k ^fn'kk esa ?kqeko* dks n'kkZrk gSA

vc vki fuEufyf[kr vH;kl djrs gq, mnkgj.k 1 o 2 esa crkbZ xbZ f'k{k.k j.kuhfr;ksa ij ckjhdh lsxkSj dj ldrs gSaA

E 2) mnkgj.k 1 o 2 esa geus cPpksa dks dks.k dh vo/kkj.kk dk ,d vglkl fodflr djus ds fy,nks vyx&vyx f'k{k.k j.kuhfr;ksa dh ppkZ dh gSA vkidh jk; esa dkSu lh j.kuhfr blvoèkkj.kk dks le>kus esa T;knk dkjxj gksxh\

E3) cPpksa dh dks.k dh vo/kkj.kk dh le> ds ewY;kadu gsrq vki dkSu lh xfrfof/k;ksa@vH;klksa dkmi;ksx djsaxs\

vxj vkius mnkgj.k 1 o 2 ij /;ku ls xkSj fd;k gS] rks vkius ns[kk gksxk fd mnkgj.k 1 esa f'k{kdus vkSipkfjd ifjHkk"kkvksa ij T;knk tksj fn;k gSA f'k{kd us vo/kkj.kk dk laca/k cPps ds jkstejkZ dsvuqHkoksa ls ugha tksM+k gS] gkykafd vo/kkj.kk le>kus ds fy, mUgksaus dqN lkexzh dk mi;ksx vo'; fd;kgSA tSlk fd geus fiNys ikBksa bdkb;ksa esa Hkh dgk Fkk] tc rd ge cPpksa dks fdlh vo/kkj.kk dkvglkl djkus ds fy, ,sls dbZ vuqHko ugha nsrs ftuds tfj, os vo/kkj.kk dks jkstejkZ ds vuqHkoksa lstksM+dj le> ldsa rc rd cPps ml vo/kkj.kk dh idM+ ugha cuk ldrsA dbZ yksxksa dh fpUrk ;g gksrhgS fdlh vo/kkj.kk dh vkSipkfjd ifjHkk"kk fn, cxSj f'k{k.k esa rkfdZd lVhdrk ugha vkrhA mUgsa bl ckrij fopkj djuk pkfg, fd cPps fdl Lrj ij bl rjg dh vewrZrk@rkfdZd lVhdrk dks xzg.k djldrs gSaA nwljk eqn~nk ;g gS fd geesa ls fdrus yksxksa us bl ckjs esa lkspk gS fd D;k ;g okdbZ t:jhgS fd dks.k dh vo/kkj.kk dks i<+kus ls igys ^fdj.k* dh vo/kkj.kk dks i<+k;k tk,A 'kk;n ,slk ugha gSA,slk djus dk ,d dkj.k rks ;g gks ldrk gS fd vki dks.k dks lVhdrk ls ifjHkkf"kr djuk pkgrs gSaAysfdu D;k ;gh gekjk y{; gS\ ;kuh dksbZ Hkh vo/kkj.kk i<+kus ls igys gesa vius ls loky djukpkfg,A ,sls lokyksa ls lh[kus okyksa dks fdlh fu/kkZfjr ikB~;iqLrd esa fn, x, rjhds dh dgha T;knkLokHkkfod :i ls lh[kus esa enn feysxhA

184

T;kfefr ds f'k{k.k esa ,d vkSj [kkeh ns[kus esa vkrh gSA dbZ erZck fdlh ,d js[kkfp= dks mnkgj.k dsrkSj ij ckj&ckj iz;ksx djus ls cPps mls lHkh fLFkfr;ksa ds fy, lgh le> ysrs gSaA eSa ;gka ,d f'k{kddk cgqr gh fnypLi vuqHko vkidks crkuk pkgwaxhA tc Hkh os dks.k dh ckr djrha rks os gj erZck nksfdj.ksa cukrha ftuesa ls ,d {kSfrt gksrh rFkk nkbZa vksj bafxr djrh gksrh FkhA ,d ckj mUgksaus 11 lkyds Nk=ksa dh ledks.k] U;wu dks.k o vf/kddks.k dh le{k dk ewY;kadu djus ds fy, bl rjg ds dqNfp= cuk, ¼ns[ksa fp= 11½A

fp= 11fp= cukus ds ckn mUgksaus cPpksa ls iwNk fd gj vkÑfr esa fn[kk;k x;k dks.k fdl izdkj dk gSA ,dNk= us tokc fn;k fd igys rhu dks.k rks U;wu (acute)] le (right) o vf/kd dks.k gSa rFkk pkSFkkokyk ys¶V ¼ck;ka½ dks.k gSA ;g xyrQgeh blfy, iSnk gqbZ D;ksafd tc Hkh ge ledks.k (rightangle) dh ckr djrs gSa rks bldk fp= L ,sls cukrs gSa] dHkh Hkh ;k ugha cukrsA blls irk pyrkgS fd tc Hkh ge fp= dh enn ls dksbZ vo/kkj.kk le>k,a] rks ge t:j ;g Hkh lkQ&lkQ crk,a fdml fp= dks dbZ rjg ls cuk;k tk ldrk gSA cPpksa esa fnypLih iSnk djus ds fy, dYiuk'khy f'k{kdcgqr dqN dj ldrk gSA og Ldwy esa xf.kr Dyc ;k xf.kr iz;ksx'kkyk 'kq: dj ldrk gSA vki cPpksals isM+ksa dh Vgfu;ka vkfn ,slh phtsa bdV~Bh djus dks dg ldrs gSa tks U;wu] le ;k vf/kd dks.k ls esy[kkrs gksaA bl rjg bdV~Bh dh xbZ phtksa dk ,d ,Ykce cu ldrk gSA vki bls izÑfr esa xf.kr* tSlkdksbZ uke ns ldrs gSaA

,d vU; leL;k ;g ns[kh xbZ gS fd cPpksa ds fnekx esa i<+kbZ xbZ vo/kkj.kk dh rLohj ugha cu ikrhAelyu vxj fdlh 12 lky dh cPph ls iwNk tk, fd U;wu dks.k D;k gksrk gS* rks og vklkuh ls vkidkscrk nsxh fd 90 va'k ls de ds dks.k dks U;wu dks.k dgrs gSaA* ysfdu vxj mlls 130Πdk dks.k [khapusdks dgk tk, rks og 50Πdk dks.k cuk nsxhA rks leL;k dgka gS\ vkb, ns[krs gSaA ;g rks tkfgj gS fdmlds fnekx esa ;g rLohj ekStwn ugha gS fd 130Πdk dks.k dSlk fn[krk gSA ;kuh og ;g ugha tkurhfd 130Πdk dks.k vf/kd dks.k gksrk gS vkSj vf/kd dks.k dSlk fn[kuk pkfg,A T;kfefr esa iq[rk vk/kkjcukus ds fy, T;kfefr; vo/kkj.kkvksa dh ekufld rLohj gksuk fugk;r gh t:jh gSA bls dSls fodflrfd;k tk,\ bls fodflr djus dk md mEnk rjhdk ;g gS fd bu vo/kkj.kkvksa dks xfrfof/k ds tfj,i<+k;k tk,A ysfdu /;ku j[ksa fd blds fy, ,d xfrfof/k dkQh ugha gksxhA gesa dbZ rjg dh xfrfof/k;ka vktekuh gksaxhA rks loky ;g gS fd fdl rjg dh xfrfof/k;ks ls cPpksa dks dks.k dh ekufld rLohjcukus esa enn feysxh\ ge pkgsaxs fd vxys vH;kl esa vki bl ckjs esa dksf'k'k djsaA

E4) cPpksa dks fofHkUu fdLe ds dks.kksa dh ekufld rLohj cukus esa enn ds fy, xfrfof/k;ka lq>kb,A

cPpksa dks dks.k ukius esa vkus okyh fnDdrsaA

dks.k ukiukdks.k ukiukdks.k ukiukdks.k ukiukdks.k ukiuk

cPpksa ds ekrk firk vkSj f'k{kdksa ls ckrphr ds nkSjku geus ns[kk fd vf/kdrj cPps dks.k ukius ds

185

lokyksa esa xyfr;ka djrs gSA bl Hkkx esa ge dks.k ukius esa cPpksa dks vkus okyh dqN fnDdrksa dh ppkZdjsaxsA blds ckn ge dqN ,sls rjhdksa ij fopkj djsaxs ftuls cPpksa dks lgh rjhds ls dks.k ukius esa ennfeysA

tc eSaus dqN f'k{kdksa ls dks.k ukius esa cPpksa dh fnDdrksa ds ckjs esa ckrphr dh rks mUgksaus crk;k fd;g leL;k,a eq[;r% ukius ds midj.k ;kuh pkans dks xyr <ax ls bLrseky djus dh otg ls iSnk gksrhgSA cPpksa dks nks fLFkfr;ksa esa pkans ds mi;ksx esa fnDdr gksrh gS %i) tc ,d gh 'kh"kZ ij ,d ls vf/kd dks.k gksa ¼nsf[k, fp= 12 d½Aii) tc dksbZ Hkh fdj.k {kSfrt u gks ¼fp= 12 [k½A

¼[k½ ¼d½

fp= 12tc eSaus f'k{kdksa ls iwNk fd pkans dk bLrseky djrs gq, ,slh xyfr;ka D;ksa gksrh gSa] rks mUgksausvyx&vyx otgsa crkbZA buesa ls dqN bl rjg dh Fkha %

1- cPpksa dks U;wu o vf/kd dks.k dh le> ugha gksrhA

2- dks.k ukirs oDr cPps pkans dh 'kwU; fpUg okyh vk/kkj js[kk dh ctk; pkans ds ,d fdukjs dksns[krs gSaA

3- pkans ij ,d gh dks.k ij nks&nks vad gksrs gSaA cPps xyr vad i<+ ysrs gSaA

4- os dks.k ds 'kh"kZ dks pkans ds e/; fcUnq ij ugha j[krsA

5- /kkrq ds dqN vikjn'khZ pkanksa esa] os ftl dks.k dks uki jgs gSa ogh fNi tkrk gSA

vkxs c<+us ls igys ge pkgsaxs fd vki ,d vH;kl dj MkysaA

E5) vkids eqrkfcd dks.k ukiuk 'kq: djus ls igys cPps dks D;k dqN vk tkuk pkfg,\

E6) fdlh 10 ;k 11 lky dh cPph dks pkans ls dks.k ukius dks dfg,A og ;g dke djrs gq, fdlfdLe dh xyfr;ka djrh gSa\

vxj vki pkans ls dks.k ukius dh fnDdrksa ij xkSj djsa rks vki ekusaxs fd bu fnDdrksa dh otg ;ggks ldrh gS fd cPps okLro esa pkans ij fy[ks vadksa dk vFkZ ugha le>rsA ;s ;g ekurs gSa fd ;s vaddkxt ij fu'kku yxkus ds fy, ladsr ek= gSaA os budk laca/k fdlh [kkl dks.k ds fp= ls ugha tksM+ikrsA mUgsa ;g Hkh irk ugha gksrk fd bl va'k dk eryc D;k gksrk gSA vkerkSj ij d{kk esa gksrk D;kgS fd ge ges'kk bl va'k ds laca/k dks lsaVhehVj@ehVj dh bdkbZ ls tksM+ nsrs gSa] tks njvly nwjh ukiusdh bdkb;ka gSaA ysfdu ,slk djrs oDr geesa ls fdrus yksx ;g ns[kus dh tger mBkrs gSa fd dks.kekiu vkSj nwjh ekiu esa D;k lekurk,a gSa vkSj fdu ek;uksa esa ;s fHkUu gSa\ ;gka ge ftl ckr ij tksjnsuk pkgrs gSa og ;g gS fd fdlh Hkh ekiu ds fy, ,d 'kq:vkrh fcUnq gksrk gS vkSj ,d vafre fcUnqrFkk dks.k ekiu vkSj nwjh ekiu esa ;g lk>k ckr gSA tSls lsaVhehVj] ehVj nwjh ukius dh bdkb;ka gSa]

186

mlh rjg va'k dks.k ekius dh bdkbZ gSA f'k{kkfon~ gSUl ÝkmMsUFky ds vuqlkj dks.k gh ,dek= ,slhpht gS ftldh ,d dqnjrh bdkbZ ¼,d iwjk pDdj½ gSA vc] vkids ikl nwjh ¼yEckbZ½ ds nks eki gksa]rks vki mUgsa tksM+ ldrs gSa vkSj xq.kk dj ldrs gSaA dks.k dks ysdj D;k gksrk gSa\ D;k yEckbZ ds ekiksadh rjg ge dks.k ds ekiksa dks Hkh tksM+&xq.kk dj ldrs gSa\ cPpksa dks ,sls lokyksa ij fopkj djus dkekSdk fn;k tkuk pkfg,A ijUrq mlls igys t:jh gksxk fd ge mUgsa dks.kh; ekiu dh bdkbZ dkvglkl nsaA vkb, d{kk 5 dh ,d f'k{kd ls lqurs gSa fd os cPpksa dks dks.kh; ekiu dh bdkbZ le>usesa enn nsus gsrq vkerkSj ij D;k djrh gSa\

mnkgj.k 3 % eSa lcls igys dks.kksa dk ,d laxzg rS;kj dj ysrh gwa % blds fy, eSa xRrs ij vyx&vyxO;kl ds xksys cuk ysrh gwa vkSj mUgsa O;kl [khap&[khapdj [kaMksa esa ckaV nsrh gwa] tSlk fd fp= 13 d] [kvkSj x esa fn[kk;k gSA

¼d½ ¼[k½ ¼x½fp= 13

vki ns[k ldrs gSa fd o`Rr I dks 15&15Πds [kaMksa esa] o`Rr II dks 45&45Πds [kaMksa esa rFkk o`Rr III dks90&90Πds [kaMksa esa ckaVk x;k gSA vc ge gj o`Rr esa ls dqN [kaM dkV ldrs gSaA

fp= 14

vc ge cPpksa ls dg ldrs gSa fd os dks.k ds lkbt ds vuqlkj bu [kaMksa ds lewg cuk,aA ge 90Œ okys[kaMksa dks ledks.k ¼cPps ledks.k ls ifjfpr gh gSa½] 45Œ okys [kaMksa dks ykydks.k rFkk 15Œ dks.k okys [kaMksadks Hkwjkdks.k dg ldrs gSaA ¼ns[ksa fp= 14½A

vc ge cPpksa ls dg ldrs gSa fd os [kaMksa dks ,d&nwljs ds Åij j[kdj dks.kksa dh ijLij rqyuk djsaAos ;g crk ik,axs fd ledks.k ykydks.k ls cM+k gS vkSj ykydks.k Hkwjsdks.k ls cM+k gSA vc ge Hkwjkdks.kdks dks.k dh bdkbZ eku ysrs gSaA vc ge Hkwjkdks.kksa dks fp= 15 d esa fn[kk, vuqlkj ykydks.k ds Åij,d&nwljs ls lVkdj j[k ldrs gSa] tSlk fd fp= 15 [k esa fn[kk;k x;k gSA

¼d½ ¼[k½fp= 15

187

blls cPpksa dks ;g le>us esa enn feysxh fd rhu Hkwjsdks.k ,d ykydks.k curk gSA ;kuh ge dg ldrsgSa fd ,d ykydks.k rhu dks.k bdkb;ksa ls curk gSA blh izdkj ls cPps ;g Hkh ns[k ldrs gSa fd 6Hkwjsdks.k feydj 1 ledks.k ds cjkcj gksrs gSaA ;kuh 1 ledks.k 6 dks.k bdkbZ ds cjkcj gSaA vc ge mulsdg ldrs gSa fd frdksu tSlh dqN ifjfpr vkÑfr;ksa esa dks.kksa dks ukisaA os ns[ksaxs fd bldk gj dks.k4 bdkbZ gSA bl rjg dh xfrfof/k ls cPpksa dks ;g le>us esa enn feysxh fd ekiu dh bdkbZ gksrhdSlh gSA blds ckn ge mUgsa dks.k dh loZekU; bdkbZ ;kuh 1 va'k ds ckjs esa crk ldrs gSaA vki mUgsacrk ldrs gSa fd 1 va'k cgqr gh NksVk [kaM gksrk gSA Hkwjs dks.k dks 15 Hkkxksa esa ckaVus ij 1 va'k izkIrgksrk gSA bls le>us ds fy, FkksM+h dYiuk dh t:jr gksrh gSA vkxs pydj tc os pkans dk mi;ksxdjsaxs] rks os ns[k ik,axs fd ledks.k 90Œ dk gksrk gS D;ksafd ;g 1&1 va'k n'kkZus okys 90 [kaMksa ds cjkcjgksrk gSA

mijksDr mnkgj.k ls Li"V gksrk gS fd ekiu 'kq: djus ls igys t:jh gS fd cPpksa dks bdkbZ dk HkkugksA yEckbZ] {ks=Qy vkSj vk;ru ds ekiu dh gh rjg dks.k ukius dh izfØ;k esa Hkh pkj vkSj ewyHkwrxf.krh; fopkj 'kkfey gksrs gSaA ;s gSa %

1- rqyuk & cPps ifjek.k ds fygkt ls nks dks.kksa dh rqyuk dj ik,aA

2- laØkedrk % ;fn A, B, C rhu dks.k gSa vkSj A>B o B>C rks A>CA

3- laj{k.k % cPpksa dks ;g ns[k ikuk pkfg, fd dks.k ds ekiu esa dkSu lh phtsa izHkkodkjh ugha gSAleyu vkSj ,d gh dks.k n'kkZrs gSaA

4- bdkbZ dh le> % tSlk fd mnkgj.k 4 esa crk;k x;k] bdkbZ dk fopkj igys xSjekud bdkb;ksads ek/;e ls fn;k tk ldrk gSA blds ckn ^va'k* crk;k tk ldrk gSA

bldk eryc ;g gS fd ekiu midj.k dk mi;ksx djus ls igys cPpksa dks bu pkj igyqvksa dh le>gksuh pkfg,A

E7) dksbZ ,slk [ksy lq>kb, ftlls vki cPpksa dks ekiu dh fdlh bdkbZ ds ifjek.k ls ifjfpr djkldsaA

mnkgj.k 5 % mlus ns[kk fd dks.k ukius oDr mlds vf/kdrj Nk= ;g r; ugha dj ikrs fd pkans ijvafdr nks esa ls fdl vad dks ysaA dks.k ukius esa ;g ,d izeq[k leL;k vkrh FkhA vr% mlus lkspk fd'kk;n ,slk pkank Nk=ksa ds fy, T;knk vklku gksxk ftl ij ,d fpUg ij ,d gh vad fy[kk gksA mlusl[r ikjn'khZ lkexzh ls ,d ,slk pkank cuk fy;k ¼;g inkFkZ oSlk gh Fkk tSlk iSfdax oxSjg esa bLrsekygksrk gS½] tSlk fd fp= 16 esa fn[kk;k x;k gSA

fp= 16

188

mlus lkspk fd blh d{kk ds vxys cSp ds fy, og bl pkans dk bLrseky djsxkA blh chp mlds iM+kslhdk 11 lky dk cPpk dks.k ukius esa dksbZ fnDdr ysdj mlds ikl vk;kA mlus viuk pkank bl yM+dsij vktek;kA 'kk;n vkidh ;g tkuus esa fnypLih gks fd mlus pkans dk bLrseky dSls fd;k vkSj blij Nk= us D;k fd;k vkb, mlh dh tqckuh lqurs gSaA

^chtw uke dk ;g yM+dk esjs ikl viuh uksVcqd vkSj dEikl ckWDl (Geometry box) ysdj vk;kAmls dks.k ukius esa enn pkfg, FkhA mlus eq>s crk;k fd mls le> ugha vk jgk Fkk fd pkans ij fy[ksvadksa dh nks drkjksa esa ls fdls ysuk pkfg,A igys rks eSaus ;g irk yxk;k fd og ;g vPNh rjg le>kgS ;k ugha fd dks.k D;k gksrk gSA irk pyk fd dks.k dh vo/kkj.kk dks ysdj mlds eu esa dbZxyrQgfe;ka gSaA fygktk eSaus igys bu xyrQgfe;ksa dks nwj fd;kA blds ckn eSaus mls fdlh js[kk[k.Mdh yEckbZ ukius dk rjhdk ;kn fnyk;kA

eSa % rqe dSls irk djksxs fd eSa rqels fdruk vf/kd yEck gwa\

mlus eq>s nhokj ls lVkdj [kM+k fd;k vkSj nhokj ij ,d fu'kku yxk;k tks esjk dnfn[kkrk FkkA fQj og [kqn nhokj ls lVdj [kM+k gks x;k vkSj eq>ls fu'kku yxokfy;kA nksuksa fu'kku ikl&ikl FksA vc mlus nksuksa fu'kkuksa ls 'kq: djds ,d&,d ljyjs[kk Q'kZ ij [khaph vkSj budh yEckbZ ,d lsaVhehVj iSekus ls ukihA fQj mlus nksuksaekiksa ds vUrj dh x.kuk dhA

eSa % cgqr vPNsA ;kuh ge nks Åapkb;ksa dk varj fudkydj t:jh ÅapkbZ irk dj ldrs gSaAvc eku yks gesa nks dks.kksa dh rqyuk djuh gS] rks og dSls djsa\ gesa mu nksuksa dks.kksa dksukiuk iM+sxkA ;g ,d ;a= gS ftls eSa dks.k ekius ds fy, bLrseky d:axkA ¼eSaus mlspkank fn[kk;kA mlus ns[kdj 'kwU; va'k] 10 va'k] 20 va'k] rFkk 180 va'k ds fu'kkuksa ijfy[ks vad i<+ MkysA½

eSa % va'k dk eryc D;k gksrk gS\ va'k ls gesa D;k irk pyrk gS\

chtw % tc Hkh ge dks.k fy[krs gSa rks gesa mlds Åij Œ fy[kuk gksrk gSA ,sls ---------- ¼mlus pkansdh vksj b'kkjk fd;k½A

eSa % ij D;k rqEgsa irk gS fd ,slk D;ksa fy[krs gSa\

chtw % ughaA

eSa % tc ge yEckbZ dk uki fy[krs gSa rks ge lasVhehVj ;k ehVj esa fy[krs gSaA tc ge otudk uki fy[krs gSa rks xzke] fdyksxzke] oSxjg esa fy[krs gSaA lsaVhehVj] ehVj] fdyksxzkeoSxjg 'kCnksa dk D;k vFkZ gS\ ;s D;k gSa\

chtw % ;s ekiu dh bdkb;ka gSaA

eSa % cf<+;kA blh rjg va'k dks.k ukius dh bdkbZ gSA ¼eSaus bl ppkZ dks ;gha NksM+ fn;kAT;knk foLrkj esa ugha x;k D;ksafd eq>s yxk fd 'kk;n og bl oDr bruk lc ughale> ik,xkA½ pyks vc ns[krs gSa fd bl dks.k dks dSls ukisa\ ¼mlus fp= 17 tSlk dks.kuksVcqd esa cuk;kA½

fp= 17

189

bl dks.k dks ukius ds fy, pkans dks bl rjg j[krs gSa fd pkans dk e/; fcUnq Bhd ml txg jgs tgkanksuksa js[kk,a feyrh gSaA bl txg dks dks.k dk 'kh"kZ dgrs gSaA ¼mlus pkans dks ogka j[kdj dgk½ fQj ;gns[krs gSa fd pkank nksuksa fdj.kksa dks <ad ysaA vc nksuksa fdj.kksa ds Åij iM+us okys vadksa dks fy[k ysrs gSaAvklkuh ls djus ds fy, eSa bu fdj.kksa dks R

1 vkSj R

2 uke ns nsrk gwaA

chtw % R1 fdj.k 30ΠvkSj 40Πds chp gS rFkk R

2 fdj.k 170ΠvkSj 180Πds chp gSA

eSa % ¼ R1 dh vksj b'kkjk djds½ ;g fdj.k 30Œ ds T;knk djhc gS vkSj nwljh fdj.k 180Œ ds

T;knk djhc gSA bls ge ;ksa fy[k ldrs gSa ¼eSaus bls bl rjg fy[kk %½

R1 ij jhfMax ¾ yxHkx 30Œ

R2 ij jhfMax ¾ yxHkx 180Œ

nksuksa jhfMax dk varj ¾ 180Œ & 30Œ ¾ 150Œ

eSa % vc D;ksa u bl pkans dks bl rjQ ?kqekdj ns[ksa ¼mlus fn'kk gkFk ls crkbZ½A ysfdu e/; fcUnq viuh txg ls ugha fgyuk pkfg,A eSaus mlls ,slk djok;kA vc crkvks D;kjhfMax vkbZ\

mlus crk;k fd R1 ij jhfMax 20 vkSj 10 ds chp gS tcfd R

2 ij jhfMax 170 vkSj 160

ds chp gSA eSaus mls crk;k fd tc jhfMax nks dks.kksa ds chp gks rks ge mu nksuksa ds chpdh jhfMax fy[k ysrs gSaA ;kuh eSaus mlls fy[kok;k %

R1 ij jhfMax ¾ yxHkx 15Œ

R2 ij jhfMax ¾ yxHkx 165Œ

varj ¾ 165Œ & 15Œ ¾ 150Œ

chtw % mRrj ogh vk;kA

eSa % blls irk pyrk gS fd vxj rqe pkans ds e/; fcUnq dks 'kh"kZ ls u gVkvks vkSj fQj pkgspkans dks fdlh Hkh fLFkfr esa j[kks] nks jhfMax ds varj ls rqEgsa dks.k dk uki fey tk,xkA

chtw % lpeqp\ ,d ckj fQj djds ns[krk gwaA ¼mlus djds ns[kk vkSj mls ;dhu gks x;kA½

blds ckn eSaus mls 60Œ] 30Œ] 40Œ] 90Œ oxSjg ds dks.k fn[kk, vkSj pkans ls ukius dksdgkA fQj eSaus fp= 18 d esa n'kkZ, vuqlkj ,d dks.k OAB [khapk vkSj dgk fd vxjOB ?kM+h ls okeorhZ (anti clockwise) fn'kk esa ?kwes vkSj fp= 18 ¼[k½ dh rjg gks tk,]rks ;g u;k dks.k fdruk gksxk\ mlus pkans ls ukik vkSj crk;k fd u;k dks.k 90Œ gSA eSausfQj dgk fd vc vxj OB ?kM+h ls mYVh fn'kk esa vkSj ?kwedj fp= 18 ¼x½ dh rjg gkstk, rks rqEgsa fdrus dk dks.k feysxk\ mlus ik;k fd ;g dks.k 180Œ gSA blds ckn eSaus90Œ ds vk/kkj ij ledks.k] U;wu dks.k vkSj vf/kd dks.k 'kCnksa ls mldk ifjp; djk;kAvkf[kj esa eSaus mls ;g crk;k fd vius dEikl ckWDl ds pkans dk bLrseky dSls djsaA eSaus,slh dksbZ 'krZ ugha yxkbZ fd de ls de ,d fdj.k fu'kku ij gksuh gh pkfg,A

fp= 18

190

eSaus mlls ;g iDdk ns[k ysus dks t:j dgk fd pkans dk e/; fcUnq dks.k 'kh"kZ ij gksA

igys rks eSaus mls ;g le>k;k fd pkans dk e/; fcUnq dgka gSA eSaus mlls dgk fd bl ij O vafdr dj ysaA

esjs [;ky esa cPpksa dks ;g tkuuk pkfg, fd e/;fcUnq dgka gS vkSj bls <wa<uk D;ksa t:jh gSA ,slkblfy, D;ksafd eSaus ,sls pkans ns[ks gSa ftu ij O lkQ&lkQ vafdr ugha gksrkA ,slk gksus ij Hkh cPpksa dkspkans dk lgh&lgh bLrseky dj ikuk pkfg,A

fQj eSaus mlls pkans ds e/; fcUnq dks Bhd dks.k ds 'kh"kZ ij tekus dks dgk vkSj ;g iDdk djus dksdgk fd nksuksa fdj.ksa pkans ls <ad tk,aA fQj eSaus mlls dgk fd vc igys okys pkans dh rjg gh jhfMaxysA eSaus mls crk;k fd jhfMax ysrs oDr vadksa dh ,d gh drkj dks ns[ksaA ;kuh ;k rks nksuksa jhfMax Åijhvad dh gksa ;k nksuksa jhfMax fupys vad dh gksaA fQj eSa mls dks.k ukirs gq, ns[krk jgkA og gj erZckÅij okys fpUg dks ns[krk FkkA vr% eSaus mlls uhps fu'kkuksa dk mi;ksx djds ns[kus dks dgk fd D;keki esa dksbZ varj vkrk gSA bl rjg ds dqN vkSj vH;kl ds ckn og c[kwch pkans dk mi;ksx djus yxkA

E8) E6 ds vius mRrj dks nsf[k,A D;k mnkgj.k 4 esa crkbZ xbZ f'k{k.k j.kuhfr ls mu xyfr;ksa dkslgh fd;k tk ldsxk tks vkius ik;h Fkha\ vxj ugha rks D;ksa\

E9) dkxt eksM+dj 45 dk dks.k dSls cuk,axs\

,d ckr ;g /;ku j[kuh pkfg, fd fdlh cPps dks flQZ bruk crkus ls dke ugha pyrh fd fdlh pht dksdSls ukisaA t:jr bl ckr dh gksrh gS fd vki mls rjg&rjg dh phtsa ns vkSj mUgsa bLrseky djds ekiudh viuh fnDdrksa dks lqy>kus dh dksf'k'k djus nsaA f'k{kd dks rks loky iwNus okys dh Hkwfedk fuHkkuh pkfg,A

voLFkk 1 % js[kh; ekiu ls tqM+s loky rks gy dj ikrs gSa vkSj dks.kh; ekiu ds loky gy djus dsfy, dqN v/kdpjh /kkj.kkvksa dk lgkjk ysrs gSa] tcfd /kkj.kkvksa dk lgh mi;ksx irk ugha gksrkA

voLFkk 2 % lgh rjhdk bLrseky djds js[kh; o dks.kh; nksuksa rjQ ds ekiu okys lokyksa dks lqy>kldrs gSaA uhps nh gqbZ ckrksa ls f'k{kd dks ;g tkuus esa enn feysxh fd cPps D;k dj jgs gSa vkSj D;klksp jgs gSaA

1- cPpksa dks ekiu dh xfrfof/k;ksa esa 'kkfey djsaA

2- ,d&,d cPps dks vkSj cPpksa ds NksVs&NksVs lewgksa dk voyksdu djsa vkSj muls ckrphr djrsgq, mudh xfrfof/k;ksa esa 'kkfey gksaA

3- nks&nks cPpksa dks ,dlkFk dke djus nsaA vxj dksbZ Nk= fdlh 'kkjhfjd fnDdr dh otg ls dksbZxfrfof/k ugha dj ikrk rks mldk lkFkh mls xfrfof/k le>k ldsxk ;k djds fn[kk ldsxkA

4- xyrQgfe;ksa dks lef>,A

5- leL;kvksa dks lqy>kus ds fy, QkWyks&vi xfrfof/k;ka crkb,A

vUr esa ge ,d ckj fQj bl ckr ij tksj nsuk pkgsaxs fd cPpksa dks dks.k ukiuk fl[kkus ls igys vki;g tkap t:j ysa fd og dks.k dh vo/kkj.kk le>rs gSa ;k ughaA fiNys Hkkx esa geus ,slh dqNxfrfofèk;ka nh gSa ftuls cPpksa dks ;g vo/kkj.kk fodflr djus esa enn feysxhA

lkjka'klkjka'klkjka'klkjka'klkjka'k

bl bdkbZ esa geus bu ckrksa ij ppkZ dh %

1- cPpksa dks dks.k dk eryc le>kus ds dqN rjhdsA

2- dks.kksa dks mudh lkbt ds vk/kkj ij oxhZÑr djus esa cPpksa dh enn dSls djsaA

3- pkans ls dks.k ukius esa cPpksa dks vkus okyh dqN fnDdrsa vkSj bu fnDdrksa dks lqy>kus ds dqN mik;A

191

ikB 13ikB 13ikB 13ikB 13ikB 13ekiu dh 'kq:vkrekiu dh 'kq:vkrekiu dh 'kq:vkrekiu dh 'kq:vkrekiu dh 'kq:vkr

ifjp;ifjp;ifjp;ifjp;ifjp;ekiu ,d ,slk gquj gS tks gj O;fDr ds thou esa t:jh gSA geesa ls gj O;fDr dks dqN&u&dqN ukiukgh iM+rk gSA gesa dq,a ls ikuh [khapus ds fy, jLlh ds uki dh t:jr iM+ ldrh gS] f[kM+dh&njoktksads fy, insZ ds diM+s dh yEckbZ crkuh gksrh gS] gekjs Hkkoh edku ds csM:e dk lkbt r; djuk iM++ldrk gS] oxSjgA bu lHkh ekeyksa esa ukius dh ckr vk tkrh gSA njvly ekiu dk vFkZ gksrk gS fdfdlh pht ds lkbt dks ek=kRed :i esa irk@O;Dr djukA tc ek= xq.kkRed fooj.k ls dke u pysrks ge fdlh pht dh yEckbZ] {ks=Qy ;k vk;ru n'kkZus ds fy, mls ,d la[;k ns nsrs gSaA cPpksa dksekiu dh dbZ iz.kkfy;ka lh[kuh iM+rh gSaA buesa ls yEckbZ] {ks=Qy] dks.k vkSj vk;ru izkjafHkd Ldwy dsxf.kr esa 'kkfey gSaA

yEckbZ ekiukyEckbZ ekiukyEckbZ ekiukyEckbZ ekiukyEckbZ ekiuk

ekiu esa vuqeku dh Hkwfedk egRoiw.kZ gksrh gSA vuqeku og izfØ;k gS ftlds fy,] cxSj fdlh midj.kvFkok dkxt&isafly ij ifjdyu fd,] ,d lfUudV mRrj gkfly fd;k tkrk gSA blds tfj, ukidh =qfV;ksa dks igpkudj nwj Hkh fd;k tk ldrk gS c'krsZ fd cPps ds ikl bruk vuqeku gquj gks fdog bl iz'u dk mRrj [kkst ys fd ^D;k esjk mRrj mfpr yxrk gS\* vuqeku ,d rjg ls ekiu gh gStks fnekxh <ax ls fd;k tkrk gS fdlh tkuh&igpkuh ekud ;k xSj&ekud bdkbZ ds lanHkZ esaA

fdlh pht dks ukius ls igys cPpksa dks mldh yEckbZ dk vuqeku yxkus ds fy, izksRlkfgr fd;k tkukpkfg,A rHkh rks os ekiu esa izkIr la[;k dk vFkZ ns[k ik,axsA ;fn dksbZ cPph xyrh ls ehVj Ldsy dksmYVk idM+dj fMCcs dh yEckbZ ukius yxs tks 37 lseh- Åaph gS] rks gksxk ;g fd og 60 lseh- dk vadi<+dj vkxs fxuus yxsxh] bdlB] cklB] frjlB] oxSjgA exj ;fn mlus ukius ls igys vuqekuyxk;k gS fd fMCck yxHkx 40 lseh- Å¡pk gS] rks og 'kk;n vius ekiu dh tkap djds viuh xyrhidM+ ysxhA

fdlh Hkh pht dks nks rjg ls ukik tk ldrk gS % 1- xSj&ekud bdkbZ] 2- ekud bdkbZ ds mi;ksx lsAigys ukius dh xSj&ekud bdkb;ksa dh ckr djrs gSaA

xSj&ekud bdkb;kaxSj&ekud bdkb;kaxSj&ekud bdkb;kaxSj&ekud bdkb;kaxSj&ekud bdkb;ka

vkius ns[kk gksxk fd ge ges'kk ekiu dh ekud bdkb;ksa dk bLrseky ugha djrsA ekud bdkb;ksa dkmi;ksx djuk&u&djuk bl ckr ij fuHkZj gS fd ml dk;Z&fo'ks"k esa fdruh lVhdrk dh t:jr gSAelyu vius ykWu ds fy, [kkn ge eqV~Bh ls ukidj larq"V gks tkrs gSaA blh izdkj ls ?kj ds dbZdkedkt esa ge fcRrs vkSj dne dk bLrseky dj ysrs gSaA

ijUrq ge 11&12 lky ds cPpksa dks yEckbZ ukius dh xSj&ekud bdkb;ksa dh ckr dSls le>k,a\ gemuds lkeus okLrfod thou dh dksbZ ,slh fLFkfr j[k ldrs gSa] tgka ekiu dh t:jr iM+sA elyufdlh dq,a ls ikuh [khapus ds fy, jLlh dh yEckbZ irk djus dh ckr gks ldrh gSA cPpksa ls iwfN, fd;fn iqjkuh detksj jLlh dh txg ubZ jLlh ykuh gks rks os D;k djsaxs\ os jLlh dk lgh lkbt dSlsirk djsaxs\ gks ldrk gS fd vkidks fuEufyf[kr esa ls dksbZ mRrj feys %

1- eSa iqjkuh jLlh ysdj nqdku ij tkÅaxh vkSj mruh gh yEckbZ dh nwljh jLlh ys vkÅ¡xhA

192

2- eSa iqjkuh jLlh ds cjkcj ,d /kkxk dkV ywaxk vkSj /kkxs dks ysdj nqdku tkÅaxkA

3- eSa ,d M.Mh ls jLlh dks uki ywaxh vkSj irk dj ywaxh fd jLlh ^fdruh M.Mh* yEckbZ dh gSfQj M.Mh ysdj nqdku ij tkÅaxhA

4- eSa jLlh dks vius dne ls ukidj irk yxkÅaxk fd jLlh fdrus dne yEch gSA

5- eSa nqdkunkj ls ,d jLlh ys vkÅaxhA ;fn ;g ikuh rd ugha igqaph rks tkdj nwljh FkksM+h yEchokyh ys vkÅaxhA

6- irk ugha] dSls djsaxsA

mRrj 2] 3 o 4 ls irk pyrk gS fd cPps ekiu dh HkkSfrd bdkb;ksa dk bLrseky vo'; djrs gSa exjmUgsa irk ugha gksrk gS fd os ,slk dj jgs gSaA mUgsa fofHkUu HkkSfrd bdkb;ksa dk bLrseky djus dk vH;klnsus dh t:jr gSA vki ;g fn[kk ldrs gSa fd ,d fuf'pr lkbt dh M.Mh ls yEckbZ dSls ukisaA gjsdls dfg, fd og vius vklikl dh phtksa dh yEckbZ fuEukuqlkj fy[ksa %

1- csap & 4 M.Mh

2- cjkenk & 40 M.Mh A

mijksDr rhuksa ekeyksa esa M.Mh ,d bdkbZ dk dke dj jgh gSA ,slh bdkb;ka HkkSfrd bdkb;ka gSa D;ksafd bUgsans[kk] Nqvk o fxuk tk ldrk gSA cPpksa dks fofHkUu HkkSfrd bdkb;ksa ls phtksa dh yEckbZ ukius dk vH;klfn;k tkuk pkfg,A ;s HkkSfrd bdkb;ka ekfpl dh fMCch] isafly] M.Mh] Øs;kWu vkfn gks ldrh gSA

vki ,slh xSj&ekud bdkb;ka Hkh crk ldrs gSa tks izR;sd cPps dh futh gksrh gSa] tSls fcRrk] dneoxSjgA vki mUgsa fcRrs] dne] gkFk vkfn ls ukiuk Hkh fl[kk ldrs gSa ¼ns[ksa fp= 4½A cPpksa dks bubdkb;ksa ds bLrseky dk vH;kl fn;k tkuk pkfg,A vki mUgsa fn[kkdj le>k ldrs gSa fd fcRrs ;k iSjdks ftl pht dh yEckbZ ukiuh gks] ml ij fdl rjg ,d&ds&ckn ,d lVkdj j[krs gSa ¼,d&nwljsij p<+k, cxSj½ vkSj fxurs tkrs gSaA

fp= 13-1

193

'kq:vkr esa xSj ekud bdkb;ksa ls ukius esa cPpksa dks fdl rjg dh enn feyrh gS\

bu xSj ekud bdkb;ksa ls ukius dk vH;kl cPpksa ds fy, dbZ rjg ls ennxkj gksrk gSA

(i) bdkbZ esa ukius dh ckr ls cPpksa dk ifjp; lh/ks gh jgLe; lsaVhehVj tSlh pht+ ds t+fj, ugksdj] tkuh&igpkuh pht+ksa ds ek/;e ls gksrk gSA bl rjg ls os ekiu ds ,d u, vuqHko dslkFk&lkFk ,d loZFkk ubZ 'kCnkoyh ds cks> ls cp tkrs gSaA

(ii) NksVs cPpksa ds fy, ekiu ds 'kq:vkrh dk;Z ds fygkt+ ls xSj ekud bdkb;ka T+;knk mi;qDrlkbt dh gksrh gSaA lsVhehVj cgqr NksVk gS vkSj gks ldrk gS fd est+ ukirs oDr ;k vius nksLrdk dn ukirs oDr muds fygkt+ ls lsaVhehVjksa dh la[;k cgqr T;knk gks tk, vkSj blh dkeds fy, ehVj Li"V :i ls cgqr cM+h bdkbZ gSA

(iii) xSj&ekud bdkb;ksa ls ukius ds vuqHko ls cPpksa dks ;g xqatkb'k Hkh utj vk,xh fd tc ekudiSekuk u gks ;k vuqi;qDr gks] rc fdlh [kkl dke ds fy, iSekus cuk, Hkh tk ldrs gSaA

(iv) xSj ekud bdkbZ ds bLrskey ds t+fj, cPps ekud bdkbZ dh t+:jr dks eglwl dj ik,axsAelyu tc os ;g ns[ksaxs fd os ukirs gSa rks dejk 20 dne yEck gksrk gS vkSj tc f'k{kd ukirsgSa rks mlh dejs dh yEckbZ 10 dne jg tkrh gSA

E5½ bu xSj&ekud fof/k;ksa ds vk/kkj ij vki ekud bdkb;ksa dk fopkj dSls izLrqr djsaxs\ vkicPpksa dks dSls ;dhu fnyk,axs fd yEckbZ ukius esa xSj ekud bdkb;ka vi;kZIr gSa\

;fn lkjs cPps dbZ pht+ksa dh yEckbZ fcÙks@dne ls ukisa rks 'kk;n mUgsa bl fu"d"kZ ij igqapus esa ennfeysxh fd ,d gh pht+ dks vyx&vyx O;fDr ukis rks ;s bdkb;ka vyx&vyx yEckbZ crkrh gSaAbldks ns[krs gq, ekiu dh ekud bdkb;ksa dk mi;ksx t:jh gks tkrk gSA

ekud bdkb;kaekud bdkb;kaekud bdkb;kaekud bdkb;kaekud bdkb;ka

d{kk esa ekud bdkbZ rHkh crkbZ tkuh pkfg, tc [kqn cPps ,slh fdlh bdkbZ dh t:jr eglwl djusyxsaA ;fn igys >Vds esa gh f'k{kd CySdcksMZ ij ,d js[kk [k.M [khapdj mldh yEckbZ Ldsy ls ukinsa rks cPps ;g le> gh ugha ikrs fd lsaVhehVj dks ekud bdkbZ D;ksa dgrs gSaA bl lanHkZ esa eSa vkidksog rjhdk crkuk pkgwaxh tks esjh ,d nksLr viuh d{kk esa viukrh gSA og izk;ejh Ldwy f'kf{kdk gSA

mnkgj.k 5%mnkgj.k 5%mnkgj.k 5%mnkgj.k 5%mnkgj.k 5% f'kf{kdk us dqN cPpksa dks ,d&,d djds viuh est ds ikl cqykdj muls est dh yEckbZfcRrksa ls ukidj fy[kus dks dgkA fQj mUgksaus gj cPps ls mldk mRrj iwNkA

eksgu % eSMe] yackbZ 6 fcRrk gSA

jkuh % ugha eSMe] yEckbZ rks 7 fcRrk gSA

jfo % th gka eSMe] 7 fcRkk gSA

jhrk % eSMe] eksgu lgh dg jgk gSA yEckbZ 6 fcRrk gSA

bl rjg mUgksaus 2&3 vkSj cPpksa ls iwNkA muds mRrj Hkh 6&7 fcRrk FksA

f'kf{kdk % Bhd gSA vc eSa ukirh gwaA vjs] ;g rks 5 fcRrk gh fudyhA

jkuh % eSMe] gekjs uki vyx&vyx D;ksa vk jgs gSa\

f'kf{kdk % D;k dksbZ jkuh ds loky dk tokc ns ldrk gSA

eksgu % eSMe] uki vyx&vyx blfy, gks ldrs gSa D;ksafd esjk gkFk jkuh ls cM+k gS vkSj

194

vkidk gkFk eq>ls cM+k gSA

f'kf{kdk % lgh ckr gSA ge lcds fcRrs dh yEckbZ vyx&vyx gSA blfy, vyx&vyx mRrjvk jgs gSaA pyks ,d dke djrs gSaA esjs ikl ;g ,d M.Mh gSA blls est dh yEckbZukirs gSaA

fQj f'kf{kdk us dqN vU; cPpksa dks cqyk;k ftUgsa igyh ckj ekSdk ugha feyk FkkAmuls est dh yEckbZ M.Mh dh enn ls ukius dks dgkA izR;sd cPps us yEckbZ ukidj4 M.Mh crkbZA

f'kf{kdk % D;k rqe lc lger gks fd est dh yEckbZ 4 M.Mh gS\

lc cPps % th eSMeA

f'kf{kdk % bl le; D;k eSa bl M.Mh dks ukius dh ekud bdkbZ eku ldrh gwa\

lc cPps % th eSMeA

f'kf{kdk dkQh [kq'k Fkh fd cPps ukius esa ekud bdkbZ dh t:jr dks le> x, gSaA fQj mlus mudk/;ku diM+s ds O;kikjh dh vksj fnyk;k rks diM+k ukirk gSA fQj mlus cPpksa ls dgk fd mUgksaus ns[kkgksxk fd diM+k ukius ds fy, og ,d NM+ dk bLrseky djrk gSA bl NM+ dks ehVj Ldsy dgrs gSaAbl NM+ dk bLrseky lc txg yEckbZ ukius ds fy, fd;k tkrk gSA blfy, bls nqfu;k Hkj ds lcyksx viukrs gSaA blfy, ;g yEckbZ ukius dh ,d ekud yEckbZ gSA

E 10 yEckbZ ukius dh ,d bdkbZ ds :i esa vki feyhehVj ls cPpksa dk ifjp; dSls djk,axs\

vius cuk, Ldsy vkSj ehVj Ldsy ds lkFk dkQh vuqHko ds ckn cPpksa dks lkekU; 15 ls-eh-okyh Ldsy ls ifjfpr djk;k tk ldrk gSA bl ij fu'kku yxs gksrs gSa rFkk ;s fu'kku ls-eh-ds gksrs gSaA Ldsy ls ifjfpr djk;k tk ldrk gSA bl ij fu'kku yxs gksrs gSa rFkk ;s fu'kkuls-eh- ds gksrs gSaA cPpksa dk izk;% ukirs oD+r Ldsy dks lgh j[kus esa fnDdr gksrh gSA ck+kj esafeyus okyh dbZ Ldsyksa esa fu'kku ,dne fljs ls yxs gksrs gSa A

d{kk esa ekud bdkbZ rHkh crkbZ tkuh pkfg, tc [kqn cPps ,slh fdlh bdkbZ dh t:jr eglwl djusyxsaA ;fn igys >Vds esa gh f'k{kd CySdcksMZ ij ,d js[kk [k.M

mi&bdkb;ka vkSj fefJr bdkb;kami&bdkb;ka vkSj fefJr bdkb;kami&bdkb;ka vkSj fefJr bdkb;kami&bdkb;ka vkSj fefJr bdkb;kami&bdkb;ka vkSj fefJr bdkb;ka

cPps ds eu esa ;g loky vkuk LokHkkfod gS fd ;fn mlds ikl flQZ ,d ehVj dh Ldsy gks] rks ,slhyEckbZ dks dSls ukisaxs tks ,d ehVj ls de gks ;k ,d ehVj ls FkksM+h T;knk gksA

bl ekeys esa Hkh cPpksa ds lkeus okLrfod thou dh dksbZ ,slh fLFkfr j[kuh gksxh tgka mUgsa ,slh NksVhbdkbZ dh t:jr eglwl gksA 10&11 o"kZ dh gj cPph ls viuh ÅapkbZ ukius dks dgk tk ldrk gSAog ns[ksxh fd og 1 ehVj ls T;knk yEch gS exj 2 ehVj ls deA ijUrq fdruh T;knk ;k fdruh de\og rks cl bruk tkurh gS fd mldh ÅapkbZ 1 ehVj ls FkksM+h T;knk gSA

bl ekSds ij cPpksa ds lkeus nthZ dk Qhrk j[kk tk ldrk gS ftls cksypky esa baph Vsi dgrs gSaA mulsiwfN, fd mUgksaus ,slh pht dgha ns[kh gS D;k vkSj ;g fdl dke vkrh gS\ muds lkFk ckrphr dhft,rkfd os [kqn gh fuEukafdr rF; ns[k ldsa %

1- Vsi ,d ehVj ls T;knk yEch gSA

195

2- bl ij 1] 2] 3] ---------------] 180 ds fu'kku yxs gSaA

3- Vsi ds fu'kku lsaVhehVj esa gSaA

4- ehVj Ldsy dh yEckbZ 100 lasVhehVj gSA

5- 100 lsaVhehVj dk 1 ehVj gksrk gSA

6- Vsi dks mi;ksx ls fdlh Hkh pht dh yEckbZ ukih tk ldrh gS] pkgs og yEckbZ 1 ehVj ls degks ;k 1 ehVj ls T;knk gksA

,slh NksVh bdkb;ksa dh t:jr dks Li"V djus ds fy, :i, vkSj iSls dk mnkgj.k fn;k tk ldrk gSA;g tkapus ds fy, fd cPps ehVj vkSj lsaVhehVj dk vkilh lEca/k le> x, gSa] mUgsa dbZ lkjs ekSf[kdloky Hkh fn, tk ldrs gSaA tSls&

1- ,d NM+ ehVj Ldsy ls 20 ls-eh- NksVh gSA bldh yEckbZ fdruh gS\

2- deht+ dk ,d diM+k ehVj Ldsy ls 30 ls-eh- T;knk gSA ;g fdruk yEck gS\

3- 1 ehVj 10 ls-eh- T;knk yEck gS ;k 110 ls-eh-\

4- fuEufyf[kr phtksa esa ls dkSulh pht+sa 1 ls-eh- ls de yEckbZ dh gksxh\

1- ekfpl dh rhyh 2- thjk

3- VqFk cz'k 4- rqEgkjs ckr dh eksVkbZ

E10) yEckbZ ukius dh ,d bdkbZ ds :i esa vki feyhehVj ls cPpksa dk ifjp; dSls djk,axs\ yEckbZ ukius dh ,d bdkbZ ds :i esa vki feyhehVj ls cPpksa dk ifjp; dSls djk,axs\ yEckbZ ukius dh ,d bdkbZ ds :i esa vki feyhehVj ls cPpksa dk ifjp; dSls djk,axs\ yEckbZ ukius dh ,d bdkbZ ds :i esa vki feyhehVj ls cPpksa dk ifjp; dSls djk,axs\ yEckbZ ukius dh ,d bdkbZ ds :i esa vki feyhehVj ls cPpksa dk ifjp; dSls djk,axs\

vius cuk, Ldsy vkSj ehVj Ldsy ds lkFk dkQh vuqHko ds ckn cPpksa dks lkekU; 15 ls-eh- okyh Ldsyls ifjfpr djk;k tk ldrk gSA bl ij fu'kku yxs gksrs gSa rFkk ;s fu'kku ls-eh- ds gksrs gSaA cPpksa dksizk;% ukirs oDr Ldsy dks lgh j[kus esa fnDdr gksrh gSaA cktkj esa feyus okyh dbZ Ldsyksa esa fu'kku,dne fljs ls yxs gksrs gSa ¼ns[ksa fp= 8 d½ ijUrq dqN Ldsyksa esa nksuksa fljksa ls FkksM+h txg NksM+dj fu'kkuyxs gksrs gSa ¼ns[ksa fp= 8 [k½A

fp= 8 ¼d½

fp= 8 ¼[k½

bu Ldsyksa dk mi;ksx djrs oDr cPps vDlj tks xyfr;ka djrs gSa] os gSa]

• os uikbZ 'kwU; ls 'kq: djus dh lko/kkuh ugha cjrrsA

196

• os Ldsy ds ,d fljs dks pht+ ds fljs dh lh/k esa j[k ysrs gSaA ,slk djrs gq, os ;g /;ku ugha

j[krs fd Ldsy ij 'kwU; dk fu'kku dgka gS ¼ns[ksa fp= 9 d½A os rc Hkh ,slk gh djrs gSa tcLdsy dk fljk VwV QwV x;k gks vkSj 'kwU; ut+j gh ugha vkrkA bldh otg ls tks mRrj vkrkgS og okLrfod yEckbZ ls de gksrk gSA

fp- 9 ¼d½

• dbZ cPps js[kk[k.M ds fljs dks Ldsy ij yxs A* ds fu'kku dh lh/k esa j[krs gSa ¼fp= 9 [k½ ijUrq

uki ysrs gq, bl ckr dk /;ku ugha j[krs fd ;fn og 'kwU; ds vykok fdlh Hkh fu'kku ls ukiuk'kq: djrs gSa rks bl ckr dk /;ku j[krs gq, gh mUgsa viuk uki fy[kuk pkfg,A urhtk ;g gksrkgS fd mudk ifj.kke okLrfod yEckbZ ls 1 ls-eh- ;k mlls Hkh T;knk vkrk gSA Ldsy dkslgh&lgh j[kus ds fy, dqN iwoZ gquj t+:jh gSA vius f'k{kd ;k fdlh vkSj dks ukirs ns[kusls cPpksa dks ukius dk vuqHko ugha feyrkA mUgsa ;g vuqHko [kqn djds gh gkfly djuk gksxkAijUrq dqN Hkh ukiuk 'kq: djus ls igys t+:jh gksxk fd mUgsa Ldsy bLrseky djus dk lghrjhd+k fl[kk;k tk,A fl[kkrs oD+r muds }kjk vkerkSj ls dh tkus okyh xyfr;ksa dks en~nsut+j j[kuk gksxkA

• yEckbZ ukius ds fy, fdlh Hkh Ldsy dk lgh mi;ksx djus esa vki cPpksa dh enn dSls djsaxs\

igys vki mUgsa ;g fn[kk ldrs gSa fd 3 ls-eh-] 4 ls-eh-] 5 ls-eh- ;k fQj 10 ls-eh- oxSjg dhpht+ksa@js[kk[k.Mksa dh yEckbZ dSls ukih tkrh gSA blds fy, vki lkjh miyC/k Ldsyksa dk bLrseky djldrs gSaA vki mUgsa fn[kk ldrs gSa fd Ldsy dks fdlh Hkh fLFkfr esa j[ksa] js[kk[k.M dh yEckbZ 6 ls-eh-gS] rks 6 ls-eh- gh jgsxhA blds ckn mUgsa vuqeku yxkus nsa fd dksbZ pht+@js[kk[kaM 4 ls-eh- o 5 ls-eh-ds chp dh yEckbZ dh gSA rc vki mUgsa fn[kkb, fd bls dSls ukisaxsA vki mUgsa fn[kkb, fd fdlhjs[kk[k.M elyu 43 ls-eh- yEckbZ ds fdlh js[kk[k.M dks ukirs oDr Ldsy dks dSls i<+k tkrk gSAfofHkUu fLFkfr;ksa esa Ldsy j[kdj ;g ckr Li"V dhft, ¼ns[ksa fp= 10 d] [k] x½A

fp= 10 ¼d½

fp= 10 ¼[k½

fp= 10 ¼x½

197

'kq:vkr esa cPpksa dks dksbZ Hkh pht ukius dks dgk tk ldrk gS ;k ,d fuf'pr yEckbZ dh dkxt dhifV~V;ka ;k /kkxs ds VqdM+s dkVus dks dgk tk ldrk gSA gj cPpk viuh iV~Vh ;k /kkxs dh rqyuk viuslkFkh dh iV~Vh ;k /kkxs ls djds irk djs fd D;k mlus yEckbZ lgh ukih Fkh ;k ughaA vki Hkh mudhifV~V;ksa dh tkap dj ldrs gSaA tc vki cPpksa ds izn'kZu ls larq"V gks tk,a] rks muls ,d fuf'pryEckbZ dh js[kk cukus ;k Ldsy ls fdlh js[kk[k.M dh yEckbZ ukius dks dg ldrs gSaAE11) vki viuh d{kk esa bl ckr dk ewY;kadu dSls djsaxs fd cPpksa us yEckbZ ukius dh n{krk gkflydj yh gS\ekiu ds mi;qDr lk/ku ¼midj.k½ dk pquko Hkh ,d ,slk gquj gS tks cPps dks gkfly djuk gksxkA mlsfn, x, dk;Z dks lEiUu djus ds fy, miyC/k lk/kuksa esa ls lcls mi;qDr lk/ku dk pquko djuk vkukpkfg,A bl lanHkZ esa fuEufyf[kr xfrfof/k ennxkj gks ldrh gSA

mnkgj.k 8 %mnkgj.k 8 %mnkgj.k 8 %mnkgj.k 8 %mnkgj.k 8 % cPpksas dks ,d baph Vsi] ,d ehVj Ldsy] ,d 30 ls-eh- Ldy] vkSj 15 lsaVhehVj dh Ldsyns nhft,A mUgsa Vksfy;ksa esa ppkZ djds irk yxkus nhft, fd D;ksa buesa ls dqN lk/ku izkIr djus okyhdqN yEckb;ksa dks ukius ds fy, mi;qDr ugha gksrsA ¼elyu 15 ls-eh- okyh Ldsy cjkenk ukius ds fy,Bhd ugha gSA½ os fdlh dkih] csap] isafly] viuh Åaxyh] cjkens ;k fdlh pkSdksj [kEHks ds vklikl dhyEckbZ ukisaA cPpksa dks r; djus nhft, fd dkSu lh yEckbZ ukius ds fy, dkSu&lh Ldsy mi;qDr jgsxhvkSj D;ksa\

mnkgj.k 9 %mnkgj.k 9 %mnkgj.k 9 %mnkgj.k 9 %mnkgj.k 9 % cPpksa dks leku pkSM+kbZ dh exj 1 ls-eh- ls 10 ls-eh- yEckbZ dh vyx&vyx dkxt+ dhifV~V;ka cukus dks dfg,A os gj iV~Vh ij mldh yEckbZ Hkh fy[ksa ¼nsf[k, fp= 11½A

fp= 11muls 10 ls-eh-] 20 ls-eh-] 30 ls-eh- ¼;kuh yEckbZ 10 ls-eh- dh xq.kt½ dh dkxt dh 10 ifV~V;ka cuokb,Avc vki cM+h yEckbZ okyh dqN ifV~V;ksa dks Q'kZ ij fcNk nsa vkSj cPpksa ls dgsa fd os bUgsa NksVh okyhifV~V;ksa ls <adsA <adus dk dke bl rjg ls djsa rkfd NksVh ifV~V;ksa de ls de yxsa ¼nsf[k, fp- 12½A

¼fp= 12½ekiu ds fy, mi;qDr lk/ku ds p;u ls ,d Qk;nk ;g Hkh gksrk gS fd ekiu esa gksus okyh =qfV;ka degks tkrh gSaA ijUrq ,d ckr tks gesa ;kn j[kuh pkfg, og ;g gS fd dksbZ Hkh ekiu ,dne lgh ugha

198

gksrkA ekiu dk csgrj midj.k T;knk csgrj lfUudVu nsxkA ,d midj.k gesa crkrk gS fd dksbZyEckbZ 43 vkSj 44 ls-eh- ds chp gS tcfd dksbZ vU; midj.k gesa crk ldrk gS fd ogh yEckbZ 43-3 vkSj43-4 ls-eh- ds chp gSA

xyr uki feyus ;k ekiu esa =qfV gksus ds dbZ dkj.k gks ldrs gSaA ;gka ge dqN dkj.k ns jgs gSaA

1- fuekZ.k ds le; ekiu ;a= esa jg xbZ dks [kkehA

2- fpfUgr djrs le; ekiu ;a= esa jg xbZ dksbZ [kkehA

3- ekiu ;a= dk mi;ksx djus okys O;fDr }kjk uki dk lfUudVu vius <ax ls fd;k tkukA

4- uki i<+us esa xyrhA

5- ukirs oDr ;a= dks j[kus esa xyrhA

6- ,d gh ;a= ls ,d gh pht ds nks O;fDr ukisa rks Hkh uki vyx&vyx vk ldrs gSaA

E 12) D;k vki crk ldrs gSa fd ;s =qfV;ka dSls gksrh gSa\ buls fuiVus ds fy, vki D;k mik;lq>k,axs\ yEckbZ ukius ds fy, vki fdl rjg dh Ldsy bLrseky djuk pkgksxs\

lkbt ds vU; ukiksa ds nkSjku vkus okyh fnDdrsaaA

{ks=Qy dk vFkZ D;k gS\{ks=Qy dk vFkZ D;k gS\{ks=Qy dk vFkZ D;k gS\{ks=Qy dk vFkZ D;k gS\{ks=Qy dk vFkZ D;k gS\

,d fnu eSa viuh cgu ds ?kj xbZ FkhA esjk HkkUtk jfo cjkens esa dkxt ds nks VqdM+s gkFk esa fy, cSBkFkkA og d{kk 6 esa i<+rk gSA og FkksM+k ijs'kku utj vk jgk FkkA iwNus ij mlus crk;k fd mldhf'kf{kdk us mls dkxt ds nks VqdM+s fn, gSa & ,d vk;rkdkj gS vkSj ,d oxkZdkjA mls ;g irk djukgS fd buesa ls T;knk cM+k dkSu lk gS ¼ns[ksa fp= 13½A

jfo us crk;k] d{kk esa gekjh Vhpj us gesa ,slh gh vyx&vyx vkÑfr dh ifV~V;ka fn[kkbZ Fkha vkSj dqNfp= CySdcksMZ ij Hkh cuk, FksA mUgksaus dksbZ lw= Hkh le>k;k Fkk vkSj og dHkh vk;r dks cM+k crkrhFkha rks dHkh oxZ dksA ijUrq eq>s dqN le> ugha vk;kA* eSaus jfo dh enn djus dh lksph vkSj eSafuEukuqlkj vkxs c<+hA

mnkgj.k 10%mnkgj.k 10%mnkgj.k 10%mnkgj.k 10%mnkgj.k 10% eSaus mls dkxt ds nks VqdM+s fn[kk,A buesa ls ,d Li"V :i ls nwljs ls cM+k FkkA

eSa % FkksM+h nsj ds fy, rqe vius dkxtksa dks Hkwy tkvks vkSj crkvks fd bu nksuksa dkxtksa esals dkSu lk NksVk gSA

jfo dks NksVk okyk dkxt igpkuus esa nsj ugha yxhA

eSa % rqe dSls dg ldrs gks fd ;g NksVk gS\

jfo us QkSju nksuksa dkxt fy, vkSj ,d ds Åij nwljk j[k fn;kA

jfo % ns[kks ;g okyk cM+s okys dkxt ds Åij j[kus ij iwjk vkjke ls vk tkrk gSA rks ;glkbt esa NksVk gqvk uA

eSa % lkbt esa NksVk! lkbt ls rqEgkjk D;k eryc gS\

jfo % ¼FkksM+k lkspus ds ckn½ % lkbt dk eryc ------- vka -------- irk ughaA

eSa % pyks eSa rqEgsa le>krh gwaA

eSaus dkxt ds nksuksa VqdM+ksa dks ,d dkxt ij j[kdj iasfly ls mudh :ijs[kk cuk nhA¼ns[ksa fp= 14½A eSaus FkksM+h nsj mlls ckrphr dh] mlls dqN loky fd, vkSj mlls ;gdgyok fy;k fd ;s nksuksa can lery vkÑfr;ka gSaA

199

fp= 13-3

eSaeSaeSaeSaeSa %%%%% ns[kks bu vkd`fr;ksa dk QSyko gh budk lkbt+ gSA ;s dkxt+ ij ftruh QSyh gqbZ gSa ;kuhbu vkd`fr;ksa ds vUnj ftruk dkxt+ ;k ry gS ogh budk lkbt+ gSA D;k vc rqe crkldrs gks fd bu vkd`fr;ksa dk {ks=Qy D;k gS\

jfojfojfojfojfo %%%%% vka----- esjs [;ky ls lkbt+ vkSj {ks=Qy ,d gh ckr gSA

eSaeSaeSaeSaeSa %%%%% 'kkck'k! bldk {ks=Qy ogh gS tks bldk QSyko ;k lkbt+ gSA

blds ckn eSaus mls blh rjg dh vkSj vkd`fr;ka fn[kkbZ ¼ns[ksa fp= 15½A exj bl ckj eSaus viuh'kCnkoyh cny nhA eSaus mlls iwNk] ^^gjsd tksM+h esa fdl vkd`fr dk {ks=Qy T;knk gS\

fp= 15

bl izfØ;k esa eSaus vkd`fr;ksa ds lkbt+@{ks=Qy ls lEcfU/kr lkjh 'kCnkoyh dks nksgjk fn;kA tSls fd]

(i) bl tksM+h esa dkSu lh vkd`fr cM+h gS\

(ii) fdldk lkbt+ T+;knk cM+k gS\

(iii) dkSu lh vkd`fr dkxt ds T;knk cM+s fgLls dks <ads ;k ?ksjs gq, gS\

(iv) fdldk QSyko T;knk gS\

(v) fdldk {ks=Qy T;knk gS\

jfo dks gj ckj lgh mRrj nsus esa dksbZ fnDdr ugha gqbZA fQj eSaus mlls 100 #i, ds uksV vkSj 20 #i,ds uksV ds lkbt dh rqyuk djus dks dgkA blh izdkj ls nks ,d tSlh vlekd`fr;ksa vkSj nks ,d tSlhfn[kus okyh ifÙk;ksa ds lkbt dh rqyuk Hkh djokbZ ¼fp= 16½A

200

fp= 16

eSa ns[krh jgh fd mlus igys nks uksVksa dks ,d&nwljs ij j[kk] fQj nksuksa vkd`fr;ksa dks ,d&nwljs ijj[kk vkSj fQj nksuksa ifRr;ksa dks ,d&nwljs ij j[k dj ns[kkA mls ;g r; djus esa dksbZ fnDdr ughagqbZ fd dkSu lh pht+ cM+h gSA

vc eSaus r; fd;k fd mldks fn, x, oxkZdkj vkSj vk;rkdkj dkxtksa ij ykSVuk pkfg,A ftudks ysdjog ijs'kku gks jgk Fkk ¼ns[ksa fp= 13½A jfo us dkxt ds mu nksuksa VqdM+ksa dks ns[kkA mlus ,d dks nwljsij j[kdj ns[kk exj fQj Hkh ijs'kku gh FkkA og r; ugha dj ik jgk Fkk fd dkSu lk cM+k gSA mldhenn djus ds edln ls eSaus lkspk fd mlds ikl tks rjg&rjg ds fp=ksa dk laxzg gS] D;ksa u mudkbLrseky fd;k tk,\

eSaus mlls dgk fd ml laxzg esa ls dqN ,sls vk;rkdkj ;k oxkZdkj fp= ys ys] tks ,d gh lkbt+ ds gksaAjfo us ;g dke QkSju dj fy;kA vc eSaus mlds nksuksa dkxt+ ds VqdM+ksa dks Q'kZ ij j[k fn;k vkSj muij ;s fp= ,d&,d djds tekuk 'kq: fd;kA eSaus lko/kkuh ;g j[kh fd nks fp=ksa ds chp esa dksbZ [kkyhtxg u jgs] vkSj u gh ;s ,d&nwljs ij p<+s gksa ¼ns[ksa fp= 17½A jfo us Hkh bl dke esa esjh enn dhA

fp= 17og eqLdjk jgk Fkk vkSj dkQh jksekafpr FkkA ,slk yx jgk Fkk fd og ml ckr dks le> pqdk Fkk] tkseSa mls crkus dh dksf'k'k dj jgh FkhA blls igys fd eSa mlls dksbZ loky iwNwa] og ph[k iM+kA

jfo % vk.Vh] ;s nksuksa dkxt cjkcj lkbt ds gSaA

eSa % rqEgsa dSls irk pyk\

jfo % eSaus nksuksa dkxtksa ij fcNs ¼tes½ fp= fxu fy, gSaA ;s cjkcj gSaA

eSa % 'kkck'k! ;kuh ge dg ldrs gSa fd bu nksuksa dkxtksa dk {ks=Qy cjkcj gSA

blls ge ;g fu"d"kZ fudky ldrs gSa fd nks fcUnq] lery vkd`fr;ksa ds lkbt+@{ks=Qy dh rqyukdjus ds fy, ge mUgsa ,d gh lkbt+ dh NksVh bdkb;ksa ls Hkj nsaA /;ku ;g j[kuk iM+sxk fd buds chp

201

dksbZ txg u NwVs vkSj ;s ,d&nwljs ij u p<+saA rc ftl vkd`fr ds vUnj T;knk bdkb;ka Hkjh gksaxh]og vkd`fr cM+h gSA vke rkSj ij ge NksVh bdkb;ka oxkZdkj ysrs gSa] tSls ;gka geus rqEgkjs ekfpl dhfMfCc;ksa okys fp= fy,A ,slk blfy, djrs gSa D;ksa lk/kkj.k rkSj ij gekjk okLrk ftu vkdfr;ksa ls iM+rkgS muds vUnj ds ryh dks bu oxks± ls Hkjk tk ldrk gSA ;kuh os oxZ {ks=Qy ukius dh bdkbZ cu tkrsgSaA ijUrq fdlh txg dks Hkjus ds fy, ge ftl Hkh fdlh vkdfr dk mi;ksx djsaxs] ogh ekiu dk lk/ku cu tk,xhA tSls rqe fdlh cM+s frdksu dks NksVs&NksVs frdksuksa ls Hkj ldrs gksA bl ekeys esa rqEgkjhekiu dh bdkbZ ;s NksVs&NksVs frdksu cu tk,axsA jfo [kq'k FkkA mls ;g xfrfof/k djus esa et+k vk;k FkkA

;g xfrfof/k dkQh vklkuh ls dh tk ldrh gS vkSj blls cPps dks ;g le>us esa enn feyrh gS fdfdlh vkd`fr esa ftrus T;knk NksVs VqdM+s lekrs gSa] mldk {ks=Qy mruk gh T;knk gksrk gSA mUgsa ;gHkh le>us esa enn feyrh gS fd ;fn vki fdlh lery vkd`fr ds vkdkj dks cny nsa] rks Hkh mldk{ks=Qy ogh jgrk gSA ,d cjkcj la[;k esa ,d gh lkbt+ ds VqdM+ksa ls vkneh] vkSjr] fpfM+;k] i'kq vkfndh vkd`fr;ka cukbZ tk ldrh gSaA blls cPpksa dks ;g le>us esa enn feysxh fd vkd`fr;ka vyx&vyxgksus ij Hkh {ks=Qy cjkcj gks ldrk gSA

E13) f'kf{kdk }kjk fn, x, nks dkxtksa esa ls dkSu lk cM+k gS] ;g irk yxkus esa jfo dh enn ds fy,vki D;k rjhdk viukrs\

E14) ,d ,slh xfrfof/k vk;ksftr dhft, ftlls cPpksa dks ;g le>us esa enn feys fd vyx&vyxvkd`fr;ksa dk {ks=Qy cjkcj Hkh gks ldrk gSA

tc cPps ;g le> tk,axs fd fdlh Hkh lery vkd`fr dk QSyko gh mldk {ks=Qy gksrk gS vkSj osnks le vkd`fr;ksa dh rqyuk mu ij dksbZ tkuh&igpkuh NksVh bdkbZ fcNkdj djus yxsaxs rks tYnh ghmUgsa Hkh le> vk tk,xk fd lery vkd`fr;ksa dks Hkjus ds fy, tc ge vyx&vyx NksVh bdkb;ksadk bLrseky djrs gSa rks gesa mlh fglkc ls vyx&vyx {ks=Qy feyrk gSA rc os LokHkkfod :i ls;g loky djsaxs fd ftl rjg ge isafly] est] dejs vkfn dh yEckbZ dks O;Dr djrs gSa] oSls {ks=Qydks dsls O;Dr djsa\ bl oDr mudk ifjp; {ks=Qy ukius dh bdkbZ ls djk;k tkuk pkfg,A vkb, ns[ksafd og rjhdk tks vf/kdrj Ldwyksa esa viuk;k tkrk gS ls bls djus ij D;k fnDdrs lkeus vkrh gSa vkSjblesa lq/kkj ykus ds dqN lq>koksa ij Hkh ge xkSj djsaxsA

tc cPps ;g le> tk,axs fd fdlh Hkh lery vkÑfr dk QSyko gh mldk {ks=Qy gksrk gS vkSj osnks le vkÑfr;ksa dh rqyuk mu ij dksbZ tkuh&igpkuh NksVh bdkbZ fcNkdj djus yxsaxs rks tYnh ghmUgsa Hkh le> vk tk,xk fd lery vkÑfr;ksa dks Hkjus ds fy, tc ge vyx&vyx NksVh bdkb;ksadk bLrseky djrs gSa rks gesa mlh fglkc ls vyx&vyx {ks=Qy feyrk gSA rc os LokHkkfod :i ls;g loky djsaxs fd ftl rjg ge isafly] est] dejs vkfn dh yEckbZ dks O;Dr djrs gSa] oSls {ks=Qydks dSls O;Dr djsa\ bl oDr mudk ifjp; {ks=Qy ukius dh bdkbZ ls djk;k tkuk pkfg,A vkb, ns[ksafd og rjhdk tks vf/kdrj Ldwyksa esa viuk;k tkrk gS ls bls djus ij D;k fnDdrsa lkeus vkrh gSa vkSjblesa lq/kkj ykus ds dqN lq>koksa ij Hkh ge xkSj djsaxsA

{ks=Qy ukiuk{ks=Qy ukiuk{ks=Qy ukiuk{ks=Qy ukiuk{ks=Qy ukiukvf/kdka'k cPps dkQh e'khuh <ax ls lw= dk bLrseky djds {ks=Qy dk ifjdyu djrs gSaA ,slk djrsgq, os ;g ugha le> ikrs fd os D;k dj jgs gSaA urhtk ;g gksrk gS fd okLrfod ifjfLFkfr esa tgka mUgsaifjfefr fudkyuh gksrh gS] os {ks=Qy fudky cSBrs gSaA ;gka ge ,d xfrfof/k lq>k jgs gSa ftlls cPpksadks ;g le>us esa enn feysxh fd fdlh vk;r dk {ks=Qy yEckbZ × pkSM+kbZ D;ksa gksrk gS rFkk bls oxZ

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lasVhehVj vkfn esa O;Dr D;ksa djrs gSaA ijUrq mlls igys D;ksa u vki ,d vH;kl dj Mkysa\

mnkgj.k 11 % ,d f'kf{kdk 1 lseh- lkbt ds jax&fcjaxh dkMZcksMZ ds VqdM+s ysdj d{kk esa igqaphA mUgksausd{kk dks pkj Vksfy;ksa esa ckaV fn;k vkSj mUgsa cjkcj&cjkcj la[;k esa dkMZ cksMZ ds VqdM+s ns fn,A fQjmUgksaus gj Vksyh ls dgk fd viuh ilUn ds VqdM+s eupkgh la[;k esa yxkdj fofHkUu fMtkbu cuk,aAdqN le; ckn mUgksaus Vksfy;ksa ls muds }kjk cuk, x, fMtkbuksa dks ysdj loky iwNuk 'kq: fd;kA

f'kf{kdk % ¼igyh Vksyh ls½ fMtkbu cukus ds fy, rqeus fdrus oxksZa dk mi;ksx fd;k\

igyh Vksyh % eSMe 16

f'kf{kdk % ¼nwljh Vksyh ls½ rqEgkjs fMtkbu dk lkbt ,d oxZ dk fdrus xquk gS\

nwljh Vksyh % ¼FkksM+k lkspus ds ckn½ eSMe 12 xquk gSA

f'kf{kdk % ¼rhljh Vksyh ls½ rqEgkjs fMtkbu dk {ks=Qy fdrus oxZ gS\

rhljh Vksyh % 20 oxZ gSA

f'kf{kdk % ¼pkSFkh Vksyh ls½ rqEgkjh vkÑfr dk {ks=Qy fdruk gS\

pkSFkh Vksyh % eSMe gekjh vkÑfr dk {ks=Qy 20 oxksZa ds cjkcj gSA

f'kf{kdk % Bhd gSA vc gj Vksyh ;g dkxt ys ys vkSj bl ckj bl dkxt dk lkbt flQZ,d oxZ dk bLrseky djds ukiksA

f'kf{kdk us gj Vksyh dks cjkcj&cjkcj lkbt dk ,d&,d vk;rkdkj dkxt nsfn;kA

jkuh % ijUrq eSMe] ge flQZ ,d oxZ ls bldk {ks=Qy dSls ukisaxs\

f'kf{kdk % D;k dksbZ bl loky dk tokc ns ldrk gS\

jke % th eSMe] eq>s ;kn gS ftl rjg geus iSjksa ls dejs dh yEckbZ ukih FkhA ge gj ckjQ'kZ ij iSj j[kdj mlds lkbt dk fu'kku Q'kZ ij yxk nsrs FksA eq>s yxrk gS fdmlh rjg ge dkxt ij oxZ ds lkbt ds fu'kku yxk ldrs gSaA

f'kf{kdk % lgh crk;kA rks D;k vc rqe ;g dke dj ldrs gks\

lkjs cPps % th eSMeA

gj Vksyh us dkxt ij oxZ ds lkbt ds fu'kku yxk fy,] tSlk fd fp= 18 esa fn[kk;k x;k gSA

lHkh Vksfy;ksa us iwjs dkxt dks cjkcj lkbtksa ds oxksZa esa ckaVus ds ckn oxksaZ dh la[;k fxu yhA f'kf{kdkus gj Vksyh ls ckrphr djds irk yxk fy;k fd lHkh us lgh fd;k FkkA lHkh Vksfy;ksa dk mRrj Hkh ,dgh Fkk ;kuh 24 oxZA blds ckn mUgksaus Vksfy;ksa ls dgk fd os dkMZcksMZ ds NksVss oxZ dh Hkqtkvksa dksukidj mldk {ks=Qy irk djsaA lcus irk fd;k fd ;g oxZ pkjksa fdukjksa ij 1 lseh- yEck gSA fQjf'kf{kdk us mUgsa crk;k fd ;g oxZ ,d [kkl lkbt dk gSA pwafd bldh pkjksa Hkqtk,a 1 lseh- yEckbZ dhgS] blfy, bls ,d ^lsaVhehVj oxZ* dgrs gSaA rks {ks=Qy dks ^24 oxZ* dgus ds ctk; ge dgrs gSa fd;g ^24 lsaVhehVj oxZ* gSA {ks=Qy dks ^lsaVhehVj oxZ* ds :i esa O;Dr fd;k tkrk gSA lasVhehVj oxZ{ks=Qy ukius dh bdkbZ gSA**

vk;ru ukiukvk;ru ukiukvk;ru ukiukvk;ru ukiukvk;ru ukiuk

vk;ru 3&foeh; QSyko dk uki gSA fMCcs] uksVcqd] cUn ihik] vkyekjh] bZaV] iRFkj tSlh 3&foeh; canphtsa ftruh ?ksjrh gSa og mudk vk;ru gksrk gSA vk;ru ;kuh bu phtksa }kjk ?ksjh xbZ txgA cPpksa dks

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?ksjh xbZ txg dk vglkl nsus ds fy, dqN iRFkj] bZaVsa] yksgs ds VqdM+s] oxSjg bdV~Bs dj ysaA IykfLVd dh,d ckYVh esa ikuh Hkj yhft,A gj pht dks ,d /kkxs ls cka/kdj mUgsa ,d&,d djds ikuh esa Mqckb,Ansf[k, fd D;k gj ckj ikuh dk ry ,d cjkcj gh c<+rk gSA cPpksa ls fuEu iz'uksa ij ppkZ dhft,A

Û ry vyx&vyx D;ksa c<+rk gS\

Û ikuh dk ry lcls Åapk dc mBk\

Û ,slk D;ksa gksrk gS\

Û MqckbZ xbZ pht ds lkbt vkSj ikuh ds ry ds chp D;k laca/k gksrk gS\ oxSjgA

,d ckj cPpksa dks ?ksjs x, vk;ru dk vglkl gks tk,] rks os nks phtksa ds vk;ru dh rqyuk dj ldrsgSaA nks vle phtksa ds vk;ru dh rqyuk fuEufyf[kr xfrfof/k }kjk dh tk ldrh gSA

mnkgj.k 12 % nks iRFkj yhft,] ftuds vk;ru dh rqyuk djuh gS vkSj dkap dk ,d vk;rkdkj crZuys yhft,A dkap ds crZu esa 3@4 ikuh Hkj nhft,A bl ij fp= 21 esa fn[kk, vuqlkj xzkQ isij dh,d iV~Vh fpidk nhft,A

fp= 21

lcls igys xzkQ isij dh iV~Vh ds }kjk [kkus fxudj ikuh dk ry i<+ yhft,A vc iRFkjksa dks ,d&,d/kkxs ls cka/k yhft,A fp= 22 esa fn[kk, vuqlkj ,d iRFkj dks ikuh esa Mqckb, vkSj ikuh ds ry esa gq,ifjorZu dks uksV dhft,A blh izdkj ls nwljs iRFkj dks ikuh Mqckdj ikuh ds ry dks i<+ ysaA

fp= 22

ppkZ dhft, fd ikuh dk ry dc T;knk p<+k\ D;ksa\ dkSu lk iRFkj T;knk txg ?ksjrk gS\ fdldkvk;ru T;knk gS\ oxSjgA

dHkh&dHkh nks phtksa ds vk;ru dh rqyuk ns[kdj Hkh dh tk ldrh gsA blds fy, nks phtksa }kjk ?ksjhxbZ txg dh rqyuk dh tkrh gSA vki bl rjg ds loky iwN ldrs gSa fd est dh njkt esa dkSu lhpht T;knk txg ?ksjrh gS & ekfpl ;k lkcqu dh fMfc;k\ dkSu lh pht cM+h gS\ fdldk vk;ruT;knk gS\ oxSjgA

204

mijksDr xfrfof/k;ksa ls cPpksa dks ;g le>us esa enn feysxh fd

1- le&vle gj pht dk lkbt gksrk gSA

2- cM+h phtsa T;knk txg ?ksjrh gSaA

3- cM+h phtsa ikuh dh lrg dks T;knk Åij mBkrh gSaA

4- ftl pht dk lkbt T;knk gks] mldk vk;ru Hkh T;knk gksrk gSA

?ksjs x, vk;ru dh vo/kkj.kk lh[krs gq, cPpksa dks inkFkZ dh ek=k ds laj{k.k dk Hkh vglkl jgukpkfg,A dksbZ cPph bl ckr dks fdruh gn rd le>rh gS] bldk vkdyu djus ds fy, fuEufyf[krxfrfof/k ij xkSj dhft,A eSaus ;g xfrfof/k utnhd ds ,d Ldwy esa ns[kh FkhA

?kukHk dk vk;ru ¾ yEckbZ × pkSM+kbZ × ÅapkbZ vkSj

?ku dk vk;ru ¾ ¼yEckbZ½3 gksrk gSA

/kkfjrk cuke vk;ru/kkfjrk cuke vk;ru/kkfjrk cuke vk;ru/kkfjrk cuke vk;ru/kkfjrk cuke vk;rufdlh ik= dh /kkfjrk dk vFkZ gS fd mlesa fdruk rjy inkFkZ ;k jsr ;k ued Hkjk tk ldrk gSA pwafdrjg inkFkZ ;k jsr ;k ued dk vkdkj ml ik= ds vuqlkj ftlesa os j[ks x, gSa] cnyrk jgrk gS blfy,cPpksa dks Bksl inkFkksZa ds laj{k.k ds eqdkcys rjg inkFkksZa dk laj{k.k le>us esa T;knk fnDdr gksrh gSAbldk vkdyu djus ds fy, cPps dks nks ,d tSls fxykl X vkSj Y fn[kkb,A nksuksa esa cjkcj ek=kesa ikuh Hkh Hkjdj fn[kkb, ¼fp= 26 nsf[k,½A

fp= 26vc Y fxykl ds ikuh dks cPps ds lkeus gh ,d vU; vkdkj ds crZu Z esa Mky nhft,A vc mllsiwfN, fd D;k X vkSj Z esa cjkcj ikuh gSA ;fn og bl loky dk lgh mRrj ugha ns ikrk rks bldkeryc ;g gS fd vHkh mlus bl vo/kkj.kk dks xzg.k ugha fd;k gSA ,sls ekeys esa mldh enn djus dkrjhdk ;g gS fd ikuh dks ¼cxSj Nydk,½ okfil Y fxykl esa Mkydj mls fn[kk;k tk,AcPpksa dks vyx&vyx vkdkj ds crZuksa dh /kkfjrk dh rqyuk djus dk gquj Hkh gkfly djuk pkfg,AmUgsa ;g crkus esa fnDdr ugha gksuh pkfg, fd ,d ex esa ,d di ls T;knk ikuh vkrk gS vkSj ,d txesa ex ls T;knk ¼fp= 27 ns[ksa½A

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fp= 27,d di esa ikuh Hkjdj mls ,d [kkyh ex esa Mkyus ls] ;k ,d ex dks ikuh ls Hkjdj mls ,d tx esamM+syus dh fØ;k ds }kjk cPpksa dks ;g r; dj ikus esa enn feysxhA vki cPpksa ls ;g Hkh dg ldrs gSafd fofHkUu crZuksa dh /kkfjrkvksa ds ckjs esa vius fu"d"kksZa dks fp=ksa ds :i esa fjdkMZ djsa ¼fp= 28 ns[ksa½A blfp= dks ns[kdj vki crk ldrs gSa fd tx esa ex ls T;knk pht lek,xh vkSj dsryh esa lcls T;knkA

fp= 28bl ekeys esa di /kkfjrk ukius dh HkkSfrd bdkbZ ekuh tk,xhA rc vki /kkfjrk dh ckr bl HkkSfrdbdkbZ ds lanHkZ esa dj ldrs gSaA elyu ex dh /kkfjrk nks di gS] tx dh /kkfjrk 5 di gS vkSj dsryhdh /kkfjrk 6 di gSApEep] tx] ÝwVh ds fMCcs oxSjg dbZ phtsa yh tk ldrh gSaA buesa ls fdlh Hkh pht dks /kkfjrk ukiusdh HkkSfrd bdkbZ ds :i esa bLrseky fd;k tk ldrk gSA

lkjka'klkjka'klkjka'klkjka'klkjka'kbl bdkbZ esa geus fuEufyf[kr fcUnqvksa ij ppkZ dh %

1- vius vklikl dh fofHkUu 3&foeh; phtksa ds lkFk cPpksa dks cpiu esa gq, vuqHkoksa dk mi;ksxmUgsa lkbt dk ,d vglkl nsus ds fy, fd;k tk ldrk gSA

2- yEckbZ] {ks=Qy o vk;ru ukius dh t:jr dks mHkkjk x;k gSA

3- 'kq:vkr esa cPpksa dks ekiu dh HkkSfrd bdkb;ksa ds mi;ksx dk izf'k{k.k fn;k tk ldrk gSA fcÙkk]dne] gkFk] iSj oxZjg dk bLrseky yEckbZ ukius ds fy, fd;k tk ldrk gSA {ks=Qy ukius dsfy, dkMZcksMZ ds VqdM+ksa rFkk vk;ru ukius ds fy, ydM+h ds xqVdksa ;k ekfpl dh okyhfMfCc;ksa dk mi;ksx fd;k tk ldrk gSA bu xSj&ekud bdkb;ksa ds bLrseky ds vuqHko ls cPpksadks ;g Li"V gks tk,xk fd fofHkUu O;fDr;ksa }kjk bu bdkb;ksa dk mi;ksx fd;k tk, rks fdlhpht dh yEckbZ@{ks=Qy@vk;ru dk uki vyx&vyx vk ldrk gSA uki esa xSj&ekudbdkbZ ds cnyrs lkbt ds vuqlkj uki esa Hkh cnyko vk tkrk gSA fygktk os ekiu esa ,dekud bdkbZ dh t:jr eglwl djsaxsA

206

4- yEckbZ ukius ds :f<+xr midj.kksa dk mi;ksx 'kq: djus ls igys t:jh gS fd cPps ukih tkusokyh yEckbZ dk vuqeku yxk ik,a rkfd ekiu midj.k ds mi;ksx esa gqbZ fdlh cM+h xyrh dksvkSj mlds dkj.k izkIr uki esa gqbZ xyrh dks vklkuh ls idM+k tk ldsA

5- gj cPps dks Ldsy ;k Vsi ls ukius dk gquj gkfly djuk pkfg,A flQZ nwljksa dks ukirk gqvkns[kus ls ;g gquj gkfly djus esa dksbZ enn ugha feyrhA

6- cPpksa dks ;g le>uk pkfg, fd dksbZ Hkh uki ,dne lgh ugha gksrkA lkjs uki lfUudV gksrsgSaA mUgsa izkIr uki esa xyrh gksus ds fofHkUu dkj.k irk gksus pkfg, rkfd os ukirs oDr bulscp ldsa vkSj ;FkklEHko loksZÙke ifj.kke izkIr dj ldsaA

7- tSls yEckbZ jS[kh; pht dk lkbt crkrh gS] mlh rjg {ks=Qy fdlh lery vkd`fr ¼nks foeh;vkd`fr½ dk lkbt crkrk gSA fdlh lery vkd`fr dk lkbt@{ks=Qy mldk QSyko* gSA ,slhdbZ xfrfof/k;ksa dh ppkZ dh xbZ gS ftuls cPps xSj&ekud o ekud nksuksa rjg dh bdkb;ksa esa{ks=Qy fudky ldrs gSaA bu xfrfof/k;ksa ls cPpksa dks ;g Hkh le>us esa enn feyrh gS fdvyx&vyx vkd`fr;ksa dk {ks=Qy leku Hkh gks ldrk gS vkSj mUgsa fdlh vk;r vFkok oxZ ds{ks=Qy dk lw= [kqnc[kqn izkIr djus esa Hkh enn feyrh gSA

8- cPpksa dks vk;ru dk laj{k.k] nks phtksa ds vk;ru dh rqyuk rFkk HkkSfrd bdkbZ o ekudbdkb;ksa ds :i esa vk;ru ukiuk lh[kus esa enn nsus ds fy, fofHkUu xfrfof/k;ksa dh ppkZ dhxbZ gSA

9- cPpksa dks 3&foeh; phtksa ds vk;ru o /kfjrk ds chp vUrj le>kus ds rjhdksa dh ppkZ Hkh dhxbZ gSA