Varg Aour VargmoolFINAL

ikB&1 oxZ vkSj oxZewy Visual Text Sound

uV[kV%&vjs HkbZ g¡leq[k] g¡leq[k%&gka HkbZ uV[kV uV[kV%&;kn gS u vkt rks vkius eq>s xf.kr dh dqN ubZ fVªDl fl[kkuh gSAg¡leq[k%&vjs gka¡ xf.kr dh fVªDl ? pyks fl[kk nsrs gSa ij blds fy, eq>s rqEgkjs iwoZ Kku dh ijh{kk ysuh gksxhAuV[kV%&fcYdqy ] ys yks ijh{kk eSa rS;kj g¡wAg¡leq[k%& rks tjk esjh ;s igsyh cw>ks&&&&&&&&

dSy Dykl dk scene start

;s gS ,slk prqHkqZt] ftldh Hkqtk,¡ leku] xkSj ls bldks ns[k yks ] fQj nks bldks uke] /;ku ls ns[k yks th] xkSj ls ns[k yks th fn[kus es lqUn&&&&&&&j] 'kDy gS bldh [kkl ] dksa.k gSa blds bDoy] cw>ks vkdj ikl] /;ku ls ns[k yks th] xkSj ls ns[k yks th]

L=1 VARG and VARGMOOL 0 7/10/2008 1

uV[kV%& vjs HkbZ g¡leq[k] rw rks iwjk dfo gks x;k A ij gka bl igsyh es rqe v&&&v&&&&v&&&&&oxZ ds ckjs es gh ckr dj jgsgks u ? g¡leq[k%&Excellent uV[kV] rw ikl gks x;kAvc rqe esjs lkFk bl dSy Dykl es pyks A ;gk¡ rq>s oxZ ds ckjs es dkQh ubZ fVªDl lh[kus dks feysaxhA

Female voice Madam

F crkvks ;s dSlh vkd`fr gS ?

M Madam , ;s ,d oxZ dh vkd`fr gSF ,dne djsDV] osjhxqM] D;k rqe oxZ ds {ks=Qy dk lw= Hkh tkurs gks \

M gka gka ge tkurs gSa oxZ dk {ks=Qy gksrk gS Hkqtk xq.kk Hkqtk A F 'kkck'k ;kfu oxZ dk {ks=Qy gqvk Hkqtk dk oxZA;fn ge oxZ dh Hkqtk dh yEckbZ eku ysa x lseh0 ] rks oxZ dk {ks=Qy gqvk x lseh0 dk


Excellent-vuq vc ;fn ge bls lR;kfir djuk pkgs rks ;s ns[kks ;s xzkQ

isij ysrs gSaA

oxZ vkSj blh izdkj ;fn oxZ dh Hkqtk ,d bdkbZ eku ysa rks bl oxZ dk {ks=Qy gqvk ,d bdkbZ dk oxZA

blh izdkj ;fn ge ekusa fd oxZ dh ,d Hkqtk 2 bdkbZ gS rks oxZ dk {ks=Qy gqvk 2 dh ?kkr 2 vFkkZr~ 2 xq.kk 2 cjkcj 4] bls ge 2 dk oxZ Hkh dgrs gSaA blh izdkj oxZ dh ,d Hkqtk 3 bdkbZ gS rks oxZ dk {ks=Qy gqvk 3 dh ?kkr 2 vFkkZr~ 3 xq.kk 3 cjkcj 9] bls ge 3 dk oxZ Hkh dgrs gSaAle>s dqN !

St -gka Madam bldk vFkZ gqvk fd ]fdlh Hkh la[;k dk oxZ gksrk gS ] ml la[;k dks nksckjk ] mlh la[;k ls xq.kk djukAM- very good vc ;fn ge bls lR;kfir djuk gks rks ;s ns[kks ;s xzkQ isij ysrs gSaA

xzkQ isij ij ;s cukrs gS] ,d bdkbZ dk oxZ ];kfu ,d bdkbZ Hkqtk okyk oxZ blesa vkidks ,d


bdkbZ Hkqtk okys fdrus ckWDl utj vk jgs gSa \

&&&&&&&2&&&&&&&

2 2 2 &&&&&2&&&&&&

M Madam ,d F Good

vc cukrs gSa 2 dk oxZ ;kfu nks bdkbZ Hkqtk okyk oxZ bles rqEgs ,d bdkbZ Hkqtk okys fdrus ckWDl utj vk jgs gSa \

1 2 3 4 5 6 7 8 9

^^ loZlfedk dk [ksy ** (a+b)2 = a2+2ab+ b2

a2 –b2 = (a+b) (a-b)

M- Madam bles gesa ;s] &&;gk¡ &&pkj ckWDl utj vk jgs gSaA F vc ge bl xzkQ isij ij ;fn rhu bdkbZ Hkqtk okyk oxZ cukrs gSa rks &&&&&& ,d bdkbZ Hkqtk okys gesa feyrs gSa&&&&&&&&&&&&&&&&&&& ;s ukS oxZ] vr% lR;kfir gqvk fd fdlh Hkh la[;k dk oxZ dk vFkZ gS mlh la[;k dks fQj ls mlh la[;k ls xq.kk dj nks A vc xq.kk djus esa rks rqe yksx Expert gks gh ! vkvks rqEgsa dqN ,slh fof/k;k¡ fl[kkrh


1 2 3 4

gw¡ ftlls rqEgsa de le; esa ] izR;sd la[;k dk oxZ Kkr gks tk, A blds fy, ge lcls igys [ksyrs gSa] loZlfedk ds dqN [ksy] rks ;kn djks lkroha d{kk esa rqeus i<+k Fkk fd (a+b) dk oxZ cjkcj gksrk gS a dk oxZ tek 2ab tek b dk oxZ

(68)2

(8)2 = 64 4 gkfly 8 102 gkfly 10 (61)2 = 36+ 10 =46 ( 68)2 = 4624

;kfu 152 – 142 = (15-14 (15+14) = (15+14)852 -872= (88-87) (88+87) = (88+87)

;kfu ;fn a,b Øekxr la[;k,¡ gSa rks

rks blh lw= dk iz;ksx djrs gq, vc ge Kkr djrs gSa 68 dk oxZ ] ;gk¡ bdkbZ dk vad gS 8 rks ;gk¡ lcls igys ge djrs gSa] 8 dk oxZ tks vk;k 8 xq.kk 8 cjkcj 64 ]64 dks fy[krs gSa 4 gkfly gqvk 6] vc ] 2 xq.kk 6 xq.kk 8 gqvk 96 ]96 esa tksM+rs gSa 6 rks vk;k 102 ] rks vc 102 dks fy[krs gSa 2 ] gkfly vk;k 10] vc uEcj vk;k 6 dk ] 6 dk oxZ gqvk 6 xq.kk 6 cjkcj 36 blesa tek fd;k gkfly 10 tks vk;k 46 bls fy[krs gSa ;s ;gk¡ ] rks 68 dk oxZ vk;k 4624] blh izdkj ,d vkSj loZlfedk ysrs gSa tks gS a dk oxZ ?kVk b dk oxZ cjkcj gS a+b xq.kk a-b, vc ;fn ge dksbZ nks Øekxr ;a[;k,¡ ysa ekuk 15 dk oxZ ?kVk 14 dk oxZ rks ;s vk;k 15 tek 14 xq.kk 15 ?kVk 14 ]vc 15 tek 14 gqvk 29 rFkk


4624

15 ?kVk 14 gqvk ,d ] vr% 29 xq.kk ,d cjkcj 29] ;kfu ;s vk;k 15 tek 14 ] blh izdkj ;fn uoklh dk oxZ ?kVk 88 dk oxZ djs rks vk;k 89 tek 88] xq.kk uoklh ?kVk 88 tks fd gy djus ij vk;k 177 xq.kk ,d] ;kfu 177 ]blh izdkj 13 dk oxZ ?kVk 12 dk oxZ cjkcj gqvk 13 tek ckjg xq.kk 13 ?kVk 12 tks vk;k 25 tks gqvk 13 vkSj 12 dk ;ksxQy A vFkkZr~ blls ;g fu"d"kZ fudyrk gS fd nks Øekxr la[;kvksa ds oxksZ dk vUrj lnSo Øekxr la[;kvksa ds tksM+ ds cjkcj gksrk gS ;kfu a dk oxZ ?kVk b dk oxZ cjkcj gksrk gS a tek b ds ];fn a cM+k gS b ls rFkk a,b nksuks Øekxr la[;k,¡ gSA

(15)2

F - blh izdkj ,d vkSj etsnkj ckr tjk /;ku nsdj le>ks A ;fn fdlh la[;k ds bdkbZ dk vad ikap gS rks mldk oxZ Hkh ,d Interesting fof/k ls fudysxk ! vkvks 15 dk oxZ djds ns[krs gSaA ns[kks ;gk¡ 5 dk oxZ cjkcj gS 5 xq.kk 5 cjkcj 25 ftls bdkbZ vkSj ngkbZ ds LFkku ij ;s ;gk¡ fy[k nsrs gSaA vkSj ngkbZ dk vad gS ,d] bls djrs gSa blds


25

2 25

a2 –b2 = (a+b)

vxys ;kfu Next vad ls xq.kk ;kfu ,d xq.kk nks tks vk;k 2 ] rks 2 fy[krs gSa lkS ds LFkku ij ;s ;gk¡ ;kfu 15 dk oxZ gqvk nks lkS 25

(65)2 = 25 42 25

(165)2 = 272 25

blh izdkj 65 dk oxZ gqvk] ;s ;gk¡ 5 dk oxZ 25] vkSj ;s ngkbZ dk vad gSa 6 ftldk Next vad gS 7 A vc 6 xq.kk 7 cjkcj ] ;s 42 vk;k ;gk¡ rks 65 dk oxZ gks x;k 4 gtkj 2 nks iPphlA gks x;k u >ViVA bl fof/k ls rqe cM+h ls cM+h la[;k ftldk bdkbZ dk vad 5 gks rks oxZ rqe vklkuh ls Kkr dj ldrs gksAM vPNk esMe ;fn eq>s 165 dk oxZ djuk gks rks 5 dk oxZ gqvk 25 tks vk;k ;s ;gk¡ ] rFkk 16 dks djrs gSa Next Number ls xq.kk rks vk;k 16 xq.kk 17 rks vk;k 2 lkS 72] rks 165 dk oxZ gqvk lÙkkbZl gtkj nks lkS iPphlvjs ! okg ;s rks esjs fy;s Hkh cgqr vklku gks x;kA Madam D;k bl rjg dh Tricks ] ,slh la[;kvksa ds fy, Hkh gS] ftlds ngkbZ dk vad 5 gks A F fcYdqy gS csVk]


51

01 56 36

;fn ngkbZ dk vad 5 gks rks Hkh ,slh la[;k dk oxZ Kkr djus dj rjhdk Hkh cgqr ljy gS A tSls ekuk la[;k gS 51] D;ksfd bdkbZ dk vad gS ,d] vkSj ,d dk oxZ cjkcj gqvk cjkcj ,d] rks ;s ,d dks fy[krs gS nks vadks ds :i es bdkbZ vkSj ngkbZ ds LFkku ij ] ;s ;gk¡ vk;k thjks ,d vc vkrh gS ckjh] ngkbZ dh la[;k dh] tks gS ik¡p] ik¡p dk oxZ gqvk ik¡p xq.kk ik¡p cjkcj 25 vc blesa tksM+rs gSa bdkbZ dh la[;k ] rks 25+1 gqvk 26 tks vk;k ;s ;gk¡ fy[krs gSa] bl izdkj 51 dk oxZ gqvk 2601 vc fQj ls Kkr djrs gSa 56 dk oxZ ] rks D;ksafd bdkbZ dh la[;k 6 gS vr% 6 dk oxZ ;kfu 36 vk;k ;s bdkbZ vkSj ngkbZ ds LFkku ij fy[krs gSaAvkSj ngkbZ dh la[;k gS ik¡p vkSj ik¡p dk oxZ dk oxZ gqvk 25] vc bles tek fd;k bdkbZ dh la[;k 6 dks ] tks vk;k 31] rks 31 fy[krs gSa ;s ;gk¡ rks 56 dk oxZ gqvk 3136 ] rks gks xbZ u gekjh x.kuk ,dne easy !


31

26

01

M gka Madam, easy Hkh gks xbZ vkSj etsnkj Hkh gks xbZA

(11)2 = 121Fvkvks vc ,d tks vU; :fpdj x.kuk lh[krs gSa ftlesa fQj ls la[;k dk oxZ ] {k.k Hkj esa Kkr gks tk,xkA vc ge iqujko`fÙk okys vadks ds oxZ djrs gSaA ns[kks ;gk¡ la[;k 11 es ,d gh vad dh iqujko`fÙk gks jgh gS rks blesa /;ku nsa fd ,d fdruh ckj nksgjk;k x;k] &&&&&&& ,dne Bhd &&&&& nks ckj nksgjk;k x;k gS vRk% 11 ds oxZ esa lcls igys fy[ksaxs ,d fQj 2 ¼2 rd gh fy[ksaxs D;ksafd ,d dks nks ckj gh nksgjk;k x;k gS½ vc bls ?kVrs Øe esa fy[krs gSa rks vc fQj ls vkrk gS ,d ] rks X;kjg dk oxZ gqvk ,d lkS bDdhlA blh izdkj 111 es ,d vk jgk gS rhu ckj vr%igys fy[krs gSa1]2]3 vc ?kVrs Øe es fy[krs gSa 2]1 ;kfu 111 dk oxZ gqvk 12321] blh izdkj ;fn gesa ¼111111½2 ¼,d yk[k x;kjg gtkj ,d lkS X;kjg dk oxZ djuk gks rks ge fQj ls ns[ksaxs fd ,d fdruh ckj vk;k gS \ 6 ckj ! gS u A rks igys


fy[krs gS ,d ls N% rd ;s ,sls 123456 vkSj fQj ?kVrs Øe esa fy[krs gSa ;s ,sls 54321 rks bl la[;k dk oxZ gqvk 123456 54321 ;kfu vc rqe bl izdkj vad ,d ls cuh l[;kvksa dk oxZ Hkh tYnh ls fudky ldrs gks AtSls 11 dk oxZ cjkcj gS 121] 111 dk oxZ cjkcj gS] ckjg gtkj rhu lkS 21

(111111)2 = 1234564321 (11)2 = 121 (111)2 = 12321(1111)2 = 1234321(11111)2 =123454321(111111)2 = 123456543211+2+1---------- = 4 = (2)2

1+2+3+2+1---- = 9 = (3)2

1+2+3+4+3+2+1---=16 (4)2

1+2+3+4+5+4+3+2+1=25(5)2

1+2+3+4+5+6+5+4+3+2+1 -----= 36 (6)2

F vjs ;s &&&&&&&&rks &&&&&& cgqr cf<+;k &&&&&&&& isVuZ curk tk jgk gSA ;gka 11 dk oxZ gqvk 1]2]1 rks 1111 dk oxZ gqvk 1]2]3]4]3]2]1+ M vjs okg ! blesa rks dkQh et+k vk jgk gSAMadam

;gk¡ ns[kks ge ;fn ge bu la[;kvksa dks tksM+rs pys tk,¡ rks ,d tek nks tek 1 cjkcj gqvk pkj ] tks gqvk nks dk oxZ ] vc ge ;fn] 1 tek nks tek rhu tek nks tek 1 tksM+s rks feyrk gS 9 tks cjkcj gqvk 3 dk oxZ] vc 1 tek nks tek rhu tek pkj tek rhu tek nks tek 1 cjkcj gqvk 16 tks vk;k 4 dk oxZ vkxs rd ,sls gh tksM+rs tk,a rks ;s vk;k 49 tks gqvk 7 dk


oxZ ] vkSj vk;k 64 tks gqvk 8 dk oxZA rks bl izdkj x.kuk djrs tkvksxs rks xf.kr ds tknqbZ jax es Mwc tkvksxs M vkt rks vkius gesa oxZ ds cgqr lkjs xq.k fn[kk fn, A

001 1000-999 =1 998 001 999-1 = 998

(8)2 =? 64 10-8 = (2)2 = 4 8-2 = 6

999, 1000 ls 1 de gSA (1)2 = 1 = 001 999-1 = 998 (999)2

vkvks vc ge oxZ djus dh ,d vkSj ubZ Trick lh[krs gS ;s mu la[;kvksa ds fy, mfpr gS] tks 10]100]1000]10000 vkfn ds Nearest ; ;kfu djhc gSA

tSls 8 dk oxZ ] pwafd 8 vkSj 10 dk vUrj 2 gS vr% 2 dk oxZ gqvk 2 dh ?kkr 2 cjkcj 4 tks vk;k ;s bdkbZ LFkku ij vkSj vc bl vUrj dks 8 es ls ?kVkrs gSaA] rks vk;k 8 ?kVk 2 cjkcj 6 bl 6 dks fy[kks ] ;s ngkbZ LFkku ij ]rks 8 dk oxZ gqvk ;s pkSlB vkSj vc 999 dk oxZ djs A D;ksafd 999 vkSj ,d gtkj dk vUrj ,d gS vkSj 1 dk oxZ gqvk ,d]


2

= 9,98 , 001

rks ;s ,d fy[kk ;s b/kj ijUrq la[;k ,d dks gesa lsdM+k ngkbZ vkSj bdkbZ ds LFkku ij ;kfu rhu vadks eas ,sls fy[kuk gS D;ksafd ]999 la[;k Hkh rhu vadks dh la[;k gS A

vc 999 es ls ?kVkrs gSa bl vUrj ;kfu ,d dks ] rks vk;k 998] tks fy[krs gSa] ;s ;gk¡ A rks 999 dk oxZ gqvk 9 yk[k 98 gtkj ,d ]rks vkt rqeus fdruh lkjh Trick lh[k yhM gka esMe vc rks ge dqN &dqN vadks ds tknwxj cu x,] gSa uAF ¼galdj½ gks Bhd dgk A

1=1

22 = 4 32 = 9

42 = 16 52 = 25 62 = 36 72 = 49 82 = 64 92 = 81 102 = 10

vc rqe rqe Loa; Hkh blh izdkj dh Calculation dk vH;kl djuk vkSj Hkwyuk ughaA vkvks vc eSa rqEgs iw.kZ oxZ la[;kvksa ds dqN vkSj rF;ksa ls ifjfpr djkrh gw¡A 1 iw.kZ oxZ la[;k ges'kk 0]1]4]5]6 ;k 9 ij lekIr gksrh gSA vFkkZr~ & iw.kZ oxZ la[;k dHkh Hkh 2]3]7]8 ij lekIr ugha gksxh A


2 vkSj ,d ckr vkSj fQj ls ;kn fnykrh gw¡ fd nks Øekxr la[;kvksa ds oxksZ dk vUrj ] muds ;ksx ds cjkcj vkrk gS

oxZ vkSj oxZewy Hkwfedk iw.kZ oxZ

fØ;kdyki vHkkT;xq.ku[kaM fof/k

fo"ke la[;k dk oxZ 12 = 1 32 = 9 52 = 25 72 = 49 92 = 81

la[;k& 1,3,5,7,9

3 la[;k vkSj mlds oxZ dk vkys[k djus ij ge ikrs gSa fd tc la[;k c<+rh gS rks mldk oxZ cgqr vf/kd c<+ tkrk gS

4 ;fn fdlh la[;k es bdkbZ dk vad 1]4]5]6]9;k 0 es ls gS rks ;g vko';d ugh fd og iw.kZ oxZ gksxh tSls 111 ] 124] 215]136]159]1000 iw.kZ oxZ ugh gS A5 vc dqN le vkSj fo"ke la[;kvksa ds oxZ djds ns[krs gS ;s ,sls &&&&&&&vr% le la[;k dk oxZ le la[;k gS rFkk fo"ke la[;k dk oxZ fo"ke la[;k gSA6 vc /;ku ls ns[kus ij ge ;g Hkh ikrs gSa fd 1 dk oxZ igyh fo"ke la[;k gSA nks dk oxZ igyh 2 fo"ke la[;kvksa dk tksM+ gSArhu dk oxZ igyh 3 fo"ke la[;kvksa dk


la[;k dk oxZ& 1,9,25,49,81

le la[;kvksa dk oxZ 22 = 4 42 = 16 62 = 36 82 = 64 102 = 100

la[;k& 2,4,6,8,10

la[;k dk oxZ& 4,16,36,64,100

tksM+ gSA pkj dk oxZ igyh 4 fo"ke la[;kvksa dk tksM+ gSA N dk oxZ igyh N fo"ke la[;kvksa dk tksM+ gSA7 la[;k esa vafre LFkku ij vxj le la[;k es 0 gksaxs rks Hkh ] la[;k dk ] iw.kZ oxZ la[;k ] gksuk fuf'pr ugh gS tSls 500]1000] vkfnAiw.kZ oxZ ds dqN vU; xq.k rqe vHkh vkSj------- tkuksxs A ij igys rqe eq>s ikbFkkxksjl izes; ds ckjs esa dqN crkvks \M ese]ikbFkkxksjl izes; ds vuqlkj ledks.k f=Hkqt es d.kZ dk oxZ lnSo 'ks"k nks Hkqtkvksa ds oxksaZ ds ;ksxQy ds cjkcj gksrk gSA F 'kkck'k ] vc ;fn d.kZ dh eki gS C rFkk vU; nks Hkqtkvks dh eki gS a rFkk b rks ikbFkkxksjl izes; ds vuqlkj a dk oxZ tek b dk oxZ cjkcj gS c dk oxZ Rkks blh izdkj ds vU; f=d Hkh ge vklkuh ls fudky ldrs gSaA


M oks dSls ese \F blds fy, ,d lw= ;kn dj yks

2p ] p dk oxZ ?kVk 1 ] p dk oxZ tek ,d ];g fdlh Hkh la[;k p ¼> 1½ ds fy, lR; gS] vc ;fn p dk eku gqvk 3 rks ikbFkkxksfj;u f=d gqqbZnks xq.kk 3 ] rhu dk oxZ ?kVk ,d ] rhu dk oxZ tek ,d tks vk;k 6]8 rFkk 10 ;kfu bl eki dh Hkqtk ls cuk f=Hkqt ,d ledks.k f=Hkqt gksxkA ijUrq /;ku jgs ;g lw= fdlh Hkh ,d ls cM+h la[;k ds fy, gh lR; gSA

M vc tjk fQj ls bl Triangular Number ij Hkh /;ku nksA blesa fdrus o`Ùk gSaA F ,d M vkSj blesa fdrus o`Ùk gSa \ F rhu M blesa


F N% M vc ;gk¡ fdrus o`Ùk gSa \ F ;gk¡-----------------dqy X;kjg M vkSj ;gk¡ F ;gk¡ dqy 18

F vc tjk fdUgh Hkh nks Triangular Number dks tksM+ksA /;ku nks ----------;s uEcj Øe ls gh gksus pkfg,A cksyks &cksyks A dksbZ nks la[;k,¡ cksyks] Øe ls yxh gqbZ ;s &&&&&&&&&&&3 vkSj 6&&&&&&&&&&&& F gka ,dne Bhd ] vc bUgsa tksM+ks M Å Å &&&&&& 3 vkSj 6 ;kfu tksM+ gqvk 9] F tks gS oxZ &&&&&&&&&fdldk cksyks &&&&&& fdldk


M rhu dk F vc dksbZ vkSj Øe ls yxh la[;k ds tksM+s dks] tksM+ksA Å&&&&&&;s tksM+rs gSa 10 vkSj 15 dks ] tks vk;k 25

M ,d ne Bhd vkSj 25 ] oxZ gS M & 5 dk F & Correct---------

bl rjg rqe vU; Triangular Number ds lkFk ;s Game

[ksy ldrs gksA

F vc tjk crkvks 1]2]3]4]5]6]7]8 dk 1]4]9]16]25]36]64 ls D;k lEcU/k gS \ M v&&&v ]lEcU/k rks ;gh gS fd ;s la[;k,a] bu izkd`r ;a[;kvksa dk oxZ gSA

ijUrq ese] oxZ Kkr djus ds fy, rks ge la[;k dks


mlh la[;k ls xq.kk dj nsrs gSA ijUrq oxZewy Kkr djus ds fy, ge D;k djsaxs \

F ns[kks dqN la[;kvksa ds oxZewy rks ge ekSf[kd Kkr dj ldrs gSa ijUrq lHkh la[;kvks ds lkFk rks ekSf[kd oxZewy Kkr djuk eqf'dy gS vr% ,slh la[;kvks ds oxZewy Kkr djus ds fy, ge la[;kvksa ds vHkkT; xq.ku[kaM Kkr djsaxs ! vc rqEgsa vHkkT; xq.ku[kaM Kkr djuk rks /;ku gS u] dgh Hkwys rks ugh vkvks bls fQj ls rks nksgjk ys A

2 324

2 162

3 81

3 27

3 9

3 3 1

vc 324 dk oxZewy Kkr djuk gks rks lcls igys 324 ds vHkkT; xq.ku[kaM Kkr djsaxs tks gqvk ;s &&&&&bl izdkj

324 = 22 X 32 X 32 rks 324 cjkcj gqvk 2 dk oxZ xq.kk 3 dk oxZ


xq.kk 3 dk oxZ vc oxZewy Kkr djus ds fy, ge gj tksM+s es ls ,d pqurs gSaA M- ;kfu 2 fr;k 6 vkSj 6 fr;k vBkjg

F- gk¡ rks 324 dk oxZewy gqvk vBkjg blh izdkj ;fn ge 7056 dk oxZewy Kkr djuk pkgrs gSa rks Hkh gesa blh izdkj vHkkT; xq.ku[kaM Kkr djus gksxsa tjk rqe djds fn[kkvks \

7056 = 2 X 2 X 2 X 2 X 3 X 3 X 7 X 7

= 2 4X 3 2 X 7 2

iwtk esMe & 7056 dk vHkkT; xq.ku[kaM &&&&&&;s ,sls &&&&&Kkr djsa rks vk;k

;kfu 2 dh ?kkr pkj xq.kk 3 dh ?kkr 2 xq.kk 7 dh ?kkr nksA

2 7056

2 3528

2 1764

2 882

3 441

3 147

7 49

;kn j[kks lcls ogys %& fdlh la[;k dk oxZewy Kkr djus ds fy, mlds vHkkT; xq.ku[kaM Kkr djrs gSa


7 7

1

fQj leku xq.ku[kaMks ds tksM+s cukrs gSA fQj izR;sd tksM+s es ls ,d pqurs gSaA vkSj vc budk xq.kuQy gh] ml la[;k dk oxZewy gSA rks bl izdkj 7056 dk oxZewy gqvk 84

= = 84

viwokZ& ,d ckr iwNuh gS ese] D;k vHkkT; xq.ku[kaM Kkr djds ge lHkh la[;kvksa ds oxZewy Kkr dj ldrs gS \ujs'k& gka esMe] eq>s Hkh ;g iwNuk Fkk \

F ns[kks cPpks tc fdlh la[;k ds] vHkkT; xq.ku[kaMks ds iwjs tksM+s ugh curs] rc og la[;k iw.kZ oxZ ugh gksrh


2 1800

2 900

3 450

3 150

2 50

5 25 5 5 1

tSls ;fn ge 1800 dk oxZewy Kkr djuk pkgs rks lcls igys ge 1800 dk vHkkT; xq.ku[kaM djrs gSa %& ;gk¡ 1800 ds vHkkT; xq.ku[kaMks es crkvks fdldk tksM+k ugha cu jgk \

M- esMe ;gk¡ 2 dk tksM+k ugh cu jgk gSA ;kfu 1800 ds vHkkT; xq.ku[kaM djus ij iwjs&tksM+s ugh cu jgs blfy, la[;k 1800 iw.kZ oxZ la[;k ugh gS

1800 = 2 x 2 x 2 x 3 x 3 x 5 x 5 F ,dne BhdA 1800 iw.kZ oxZ ugha gSA vkSj 1800 dk oxZewy ge bl rjhds ls ekywe ugh dj ldrs A;gk¡ laVh ] rqe ;g rks crkvks fd 1800 dks iw.kZ oxZ cukus dk dksbZ vkbfM;k gS] rqEgkjs fnekx es \laVh % v&&v esMe ;fn la[;k] nks] vkSj gksrh rks ;s tksM+s] iwjs gks tkrs A esMe%& ;kfu vxj ge 1800 dks nks ls xq.kk dj nsa rks&&;s tks gesa feyrh gS la[;k 3600 ] ;g iw.kZ oxZ gksxhA


vkSj gk¡ blds lkFk &lkFk ;fn ge bl vdsys nks dks ;gk¡ ls gVk nsa] rks Hkh 1800 iw.kZ oxZ gksxh A ;kfu

vxj ge 1800 dks nks ls Hkkx dj nsa ] rks Hkh gesa iw.kZ oxZ izkIr gks tk,xk

vr% la[;k = 3600 ,d iw.kZ oxZ la[;k gS ftldk oxZewy 60 gS rFkk la[;k 1800 2 = 900 ,d iw.kZ oxZ la[;k gS ftldk oxZewy 30 gSA

pyks egs'k vH;kl ds fy, ,d ,slk gh iz'u] gy djrs gSaAekuk eq>s ;s vius Ldwy ds bl cxhps esa 1225 isM+ bl izdkj yxkus gS fd gj iafDr esa mrus gh isM+ gks ftruh dqy iafDr;ka gS iafDr;ksa dh la[;k ge fdl izdkj Kkr djsxs\ --- rqe dqN crkvksxh viwokZ ] ;s ge dSls djsxs\

Ekkuk iafDr;ksa dh la[;k = x,d iafDr esa isM+ks

viwokZ %& D;ksfd ;gkWa gesa iz'u esa fn;k x;k gS fd iafDr es isM+ksa dh la[;k cjkcj gSa iafDr;ksa dh la[;k


dh la[;k =iafDr;ksa dh la[;k = xdqy isMks dh la[;k = iafDr;ksa dh la[;k xq.kk ,d iafDr esa isM+ks dh la[;k

Madam :-

gka ,dne Bhd] rks dqy isM+ksa dh la[;k fdruh gqbZ\

tksfd cjkcj gqvk x xq.kk vFkkZr x dk oxZ = 1225

;k

vr% ckx es 35 iafDr;ka gksaxh vkSj gj iafDr;ksa es 35 isM+ gksaxsA

viwokZ& Madam ;s please vki crk nks u \ Madam - ekuk iafDr;ksa dh la[;k cjkcj gS x , ,d iafDr es isM+ksa dh la[;k = iafDr;ksa dh la[;k = x vr% dqy isM+ksa dh la[;k = iafDr;ksa dh la[;k xq.kk ,d iafDr esa isM+ks dh la[;k tks gqvk x

xq.kk x

laVh ;kfu fd x dk oxZ cjkcj gqvk 1225 ds] gS uMadam,


F very good vkSj x cjkcj gqvk oxZewy 1225 ds vc fQj] 1225 dk oxZewy Kkr djus ds fy, blds vHkkT;xq.ku[k.M Kkr djus gksxsaA

5 1225

5 245 7 49

7 7

1

tks fd vk;k ;ss& & & & 1225 = 5 dk oxZ xq.k 7 dk oxZ ;kfu x cjkcj oxZewy 5 dk oxZ xq.kk 7 dk oxZ vFkkZr x cjkcj 5 xq.kk 7 cjkcj 35vr% ckx esa 35 iafDr;kWa gksxh vkSj gj iafDr esa 35 isM+ gksxsa rks vHkkT; xq.ku[k.Ma Kkr djds ge fdlh Hkh la[;k dk oxZewy Kkr dj ldrs gSaA ijrq cM++h & cM+h la[;k ds vHkkT; xq.ku[k.M Kkr djus es ges vf/kd le; yxrk gSaA vkvks rks blds fy, vc eSa rqEgas ,d ,slh fof/k fl[kkrh gwa ftles vHkkT; xq.ku[k.M Kkr fd, fcuk] la[;k dk oxZewy Hkkx & fof/k ls ge Kkr dj ldrs gSaAMadam tjk crkvks rks ,d vad okys iw.kZ oxZ tSls 1]4 vkSj 9 ds oxZewy esa fdrus vad gksrs gSa \St ,d vad okyh la[;k


,d dk oxZewy gqvk ,d pkj dk oxZewy gqvk nks ukS dk oxZewy gqvk rhu

vr% oxZewy esa gS dsoy ,d vad Madam vkSj nks vad okys iw.k oxZ tSls 16]25]36]49]64 vkSj 81 esa fdrus vad gksrs gSa \ St ----- mlesa gksrs gS Madam

M ---- ns[kks eSa crkrh gw¡ oxZewy 36 cjkcj gS 6 ds oxZewy 49 cjkcj gS 7 ds oxZewy 64 cjkcj gS 8 dsoxZewy 81 cjkcj gS 9 ds

;kfu nks vad okys iw.kZ oxZ es ,d vad gksrk gS vc ;fn ge rhu vad okyh la[;k tSls 100] 121] 144] 169] 196 225] 961 ds oxZewy Kkr djsa rks ikrs gSa fd buds oxZewy es nks vad gksaxs vkSj ;fn pkj vadks okyh la[;k tSlas


1024]1089 ;k 9801 dk oxZewy djsa rks ikrs gSa fd buds oxZewy esa Hkh nks vad gksxsa A

blh izdkj ik¡p vkSj 6 vad okys iw.kZ oxZ ysdj &&&&ge ;s bl izdkj tk¡prs gSa rks ikrs gSa fd buds oxZewy esa vadks dh la[;k gS rhu rks bl fØ;kdyki }kjk ;gh fu"d"kZ fudyrk gS (ii)fd ;fn iw.kZ oxZ esa vadks dh la[;k le gS tSls 2] 4] 6&&&&&&vkfn rks ml la[;k ds oxZewy esa vadks dh la[;k vk/kh ;kfu 1]2]3&&&&vkfn gksxh A (ii ;fn iw.kZ oxZ esa vadks dh la[;k fo"ke gS tSls 1]3]5&&&& vkfn rks ml la[;k ds oxZewy es vadks dh la[;k ] iw.kZ oxZ ds vadks dh la[;k es ,d tksM+dj vk/kh gksxh tSls 1 tek 1 cVk 2] 3 tek ,d cVk 2] 5 tek 1 cVk nks ;k 1]2]3 vkfn gksxh A


26

2 676 4

46 276 276

X

bl fØ;kdyki dks djus ds ckn vki fdlh Hkh nh xbZ iw.kZ oxZ okyh la[;k dks ns[kdj mlds oxZewy ds vadks dh la[;k crk ldrs gSaAekuk gesa 676 dk oxZewy Kkr djuk gS rks 676 ds oxZewy es nks vad gksaxs \ ;g ge QkSju crk ldrs gSa ] vc 20 dk oxZ gS 400 rFkk 30 dk oxZ gS 900 ;kfu 676 bu nksuksa ds chp es dgha gS rks ;gh irk yxkus ds fy, lcls igys ¼1½ 676 ds vadks ds nks tksM+s cukrs gSa ;s ,sls && && /;ku j[ksa fd tksM+s cukrs le; ges'kk nkbZa vksj ls ckbZa vksj pyrs gSa] ¼2½ vc igys&tksM+s esa ,d gh vad jg x;k gSA vc ,slh cM+h ls cM+h la[;k crkb;s ftldk oxZ 6 ;k 6 ls FkksM+k de gSA og la[;k 2 gSA (iii) vr% 2 dks 2 ls xq.kk dj 6 ds uhps ;s mÙkj fy[krs gSaA(iv) ?kVkus ij o vxyk tksM+k mrkjus ij la[;k cuh 276 (v) igyh pquh la[;k dks nqxquk dj ngkbZ ds LFkku ij fy[krs gSaA


IV vc ,d ,slh la[;k bdkbZ ds LFkku ds fy, pqurs gSa ftllss xq.kk djus ij mÙkj 276 ls vf/kd u gks vkSj mlds lcls djhc gks ;k cjkcj gksA pkj pquus ij 44 xq.kk 4 cjkcj gS 176 tks cgqr NksVk gS rFkk 6 pquus ij 46 xq.kk 6cjkcj 276 gksrk gSA rks blh izdkj 46 dks 6 ls xq.kk dj mÙkj ]276 ds uhps fy][kdj ;s ?kVkrs gSa rFkk ikrs gSa fd 'ks"k dqN Hkh ugh cprkA

vr% 676 dk oxZewy gqvk 26 vc blh izdkj 1024 dk oxZewy Hkkx fof/k ls Kkr djrs gSaA

3

3 10 24 9

62 124124

0

Lkcls igys iw.kZ oxZ es vadks ds tksM+s cukrs gSa nkbZa vksj ls ckbZa vksj fQj igys tksM+s 10 dks ,slh la[;k ls Hkkx nsrs gSa ftldk oxZ 10 ;k 10 ls FkksM+k de gks ;kfu ,slh la[;k gS 3 ] 10 es ls 3 dk oxZ ?kVkus ij vkSj vxyk tksM+k 24 uhps ykus ij la[;k cuh 124]3 dks nqxquk djds ;s &&&&& ngkbZ ds LFkku ij fy[krs gSa] vc bdkbZ ds LFkku fd fy, ,slh la[;k pqurs gSa


ftlls xq.kk djus ij 124 vk;s]og vad 2 gSAvc 62 xq.kk 2 cjkcj gS 124 vr%1024 dk oxZewy gqvk 32 ]

127

1 16180 1 61 22 44

1780247

1729

51

vkvks vc blh izdkj dh leL;k,a ] tks dqN gVdj gS] oks gy djrs gSaAog NksVh ls NksVh la[;k crkb;s 16180 es ls ?kVkus ij ,d iw.kZ oxZ la[;k izkIr gksA blla[;k dk oxZewy Hkh Kkr fdft, \ 16180 esa ikap vad gSa vr% blds oxZ ewy es rhu vad gksaxsA (i) vr% 16 gtkj ,d lkS 80 ds ge rhu tksM+s cukrs gSaA fQj ls gesa ;g /;ku j[kuk gS fd tksM+s cukrs le; ges'kk nkbZa vksj ls ckbZa vksj pyuk gSA (ii) bl izdkj igys tksM+s essa ,d gh vad jg x;kA vc ,slh cM+h la[;k crkvks ftldk oxZ 1 ls de ;k 1 ds cjkcj gksA &&&&&&&&&rks ,slh la[;k gS&&&&&&&&St ,slh la[;k gS ,d (iii) Madam osjh xqM vuq] vc 1 dks 1 ls xq.kk dj]


1 ds uhps 1 fy[krh gw¡A(iv) vc ?kVkus ij vk;k 'kwU; o vxyk tksM+k mrkjus ij la[;k cuh bdlBA (v) igyh pquh la[;k dks nksxquk dj ngkbZ ds LFkku ij fy[krs gSa (vi) vc ,d ,slh la[;k bdkbZ ds LFkku ds fy, pqurs gSa ftlls xq.kk djus ij mÙkj bdlB ds cjkcj ;k mlds djhc vk;s ] ysfdu 61 ls vf/kd u gks Avc 2 ls xq.kk djus ij vkrk gS 44] tks 61 ls NksVk gS rFkk 3 ls xq.kk djus ij vkrk gS 66]tks 61 ls cM+k gS ;kfu bdkbZ ds LFkku ij fy[krs gSa 2] vkSj 44 dks fy[krs gSa 61 ds uhps (vii) rks ?kVkus ij] o vxyk tksM+k mrkjus ij la[;k cuh ,d gtkj lkr lkS vLlh A (viii) rks vc 12 dk nqxquk djds ;s ;gk¡ fy[krs gSaA vc bdkbZ ds LFkku ds fy, ,d la[;k pqurs gSa ftlls xq.kk djus ij l=g lkS vLlh ds djhc ;k cjkcj gks A rFkk ;s 6 pquus ij vk;k 246 xq.kk 6 cjkcj 1476 tks cgqr NksVk gS rks 7 pquus ij


¼127½2

;kfu 16384 ?kVk 16180 = 204

vk;k 247 xq.kk cjkcj 1729 tks l=g lkS vLlh ds djhc gSA (ix) rks vc vad 7 ls xq.kk djus ij ]247 xq.kk 7 cjkcj ,d gtkj lkr lkS muÙkhl vk;k] ;sa ;gk¡&&&&&&&(x) vc ?kVkus ij vk;k 51 ;kfu ;s la[;k 161 80] 127 ds oxZ ls bD;kou vf/kd gSA vr% 51 gh og la[;k gS ftls 16180 es ls ?kVkus ij ,d iw.kZ oxZ la[;k izkIr gksrh gS] vkSj oxZewy 16180 ?kVk 51 cjkcj gS 16129] ,d iw.kZ oxZ la[;k gS] ftldk oxZewy gS 127 ]vr% 127 bl la[;k dk oxZewy gS ;gk¡ ij] vki yksx /;ku nks fd ;fn iz'u es fn;k gks fd oks dkSu&lh NksVh ls NksVh la[;k gS ftldks 16180 esa tksM+us ij izkIr la[;k iw.kZ oxZ la[;k gks rks ,slh fLFkfr es ge 127 ls vxyh la[;k ;kfu 128 dk oxZ Kkr djsaxs tks gqvk 16384 vc pwafd 128 dk oxZ gS lksyg gtkj rhu lkS pkSjklh ] tks fd 16180 ls 204 cM+k gS] vr% ;fn eSa 16 gtkj ,d lkS vLlh esa 204 tksM+


n¡w rks iw.kZ oxZ la[;k cu tk,xh tks gksxh ,d lkS vB~BkbZl dk oxZA ;kfu oxZewy 16384 cjkcj ,d lkS vB~BkbZl

vFkkZr~ iz'u esa ;fn ?kVkus ds ckjs esa dgk x;k gks rks 'ks"kQy tks Hkh vk, ] mls iz'u es nh gqbZ la[;k es ls ?kVk nks ] rks vc tks 'ks"k cpsxk ogh okafUNr oxZ la[;k gksxh A vkSj ;fn iz'u esa tksM+us ds ckjs esa dgk gks rks 'ks"kQy cpus ds ckn ] HkkxQy ls vxyh ;kfu Next la[;k dk oxZ djds mles ls iz'u es nh xbZ la[;k dks ?kVk nksA tks Hkh la[;k feys ogh gekjh og fo'ks"k la[;k gksxh ftls iz'u es nh gqbZ la[;k esa tksM+us ij iw.kZ oxZ la[;k feysxhAvkvks vc ,d ckj fQj ls d{kk NVh esa ykSV pysA NVh d{kk esa geus fofHkUu vadks dh NksVh ls NksVh rFkk cM+h ls cM+h la[;k ds ckjs esa i<+k Fkk Hkwys rks ugh Uk;fn gesa 5]6 ;k vU; vadks dh cM+h ls cM+h


la[;k dk oxZewy Kkr djuk gks rks ge 99999] ;k 999999 ;k blh izdkj dh la[;k dk iz;ksx dsjasxsA;fn gesa 4]5 ;k vU; vadks dh NksVh ls NksVh la[;k Kkr djuh gks tks iw.kZ oxZ la[;k gS rks ge 1000 ;k 10000 ;k blh izdkj dh la[;k dk mi;ksx djsaxsA vkvks vH;kl djsaA


9 99

9 99 99 99

-81

189 18 99

-(17) 01

1989 198 99

- 179 01

1998

999999 -1998998001

vr% 1998 og NksVh

N% vadks dh cM+h ls cM+h la[;k Kkr dhft, tks fd iw.kZ oxZ la[;k gS ] la[;k dk oxZewy Hkh Kkr dhft, A vc N% vdksa dh cM+h ls cMh+ la[;k D;k gksxhSt. - Madam, N% ckj 9 ];s bl izdkj fy[k ns] rks gesa N% vadks dh cMh+ ls cMh la[;k 9 yk[k 99 gtkj 9 lkS 99 izkIr gksxhA F 9 yk[k 99 gtkj 9 lkS 99 vc ;g rks iw.kZ oxZ ugh gS rks og NksVh ls NksVh la[;k Kkr djus ds fy, ftls ;fn 9 yk[k 99 gtkj 9 lkS 99 esa lsa ?kVkus ij iw.kZ oxZ vk, ] ogh fof/k fQj ls nksgjkrs gSa tks vHkh &vHkh viukbZ FkhA lcls igys Hkkx fof/k ls Kkr djrs gSa oxZewy ;s & ,sls vc 'ks"k vk;k ,d gtkj 9 lkS 98 vc 9 yk[k 99 gtkj 9 lkS 99 es ls ,d gtkj 9 lkS 98 ?kVkus ij vk;k 9 yk[k 98 gtkj ,d] tks fd iw.kZ oxZ gSA


ls NksVh l0 gS ftls 999999 es ls ?kVkus ij 999999&1998=1998001 vkrk gS tks ,d iw.kZ oXkZ gS vkSj 999

vr% la[;k 9 yk[k 98 gtkj ,d] dk oxZewy gqvk 999 vkvks blh izdkj dh ,d vksj leL;k ysrs gSa

87

8 76 09 64 1209 167 1169

40

og NksVh ls NksVh la[;k crkb;s ftldks 7609 esa tksM+us es la[;k iw.kZ oxZ cu tk, rks blds fy, lcls igys rks Hkkx fof/k ls bldk oxZewy fudky yks ;s ,sls ! rks 'ks"kQy vk;k pkyhlA vc D;ksafd ge og NksVh ls NksVh la[;k crkuh gSS ftldks 7609 es ls tksM+us ij ,d iw.kZ oxZ la[;k izkIr gks] rks tSlk fd eSus rqEgs igys Hkh crk;k Fkk ] vc ge HkkxQy ls vxyh ;kfu Next la[;k dk oxZ Kkr djrs gSa ;kfu 88 dk oxZ tks fd vk;k 7744] vc 7609 dks 7744 es ls ?kVkrss gSa rks gesa feyrk gS


135 vr% 135 og NksVh ls NksVh la[;k gS ftldks 7609 esa tksM+us ij la[;k iw.kZ oxZ cu tk,xh A vkSj la[;k 7744 dk oxZewy gS 88 ]

ßvkvks vc ,slk gh feyrk tqyrk mnkgj.k gy djrs gSaA bl ckj gesa N% vadks dh og NksVh ls NksVh la[;k Kkr djuh gS Tkks fd iw.kZ oxZ gS rFkk ml la[;k dk oxZewy Hkh Kkr djuk gS Þ

vr% N% vadks dh NksVh ls NksVh la[;k tks iw.kZ oxZ gSA 100000 489 = 100489 gS vkSj gS

vc N% vadks dh NksVh la[;k gqbZ 1 yk[k vc ge Step By Step mlh izdkj bl la[;k dk Hkkx fof/k ls ;s&&&&&&&bl izdkj&&&&&&oxZewy Kkr djrs gSa vr% ;gk¡ 'ks"kQy vk;k 144 ;kfu fd ;fn 1 yk[k es ls 144 ?kVk;saxs rks vadks dh la[;k 5 jg tk,xh A gesa 6 vadks dh NksVh ls NksVh iw.kZ oxZ la[;k Kkr djuh gS vr% ;gk¡ ge HkkxQy ls vxyh la[;k ;kfu 317 dk oxZ Kkr djrs gSa tks vk;k ;s 100489 vc bl la[;k es ls 100000 ;kfu 1


yk[k dks ?kVkrsgSa rks gesa feyrk gS 489 ;kfu ;fn 6 vadks dh NksVh ls NksVh la[;k ,d yk[k es 489 tksM+ nsaxs rks og la[;k 1 yk[k 489 ,d iw.kZ oxZ la[;k gksxh A

4.5

4 20.25 +4 (-)16

85 425-425 0

vki iw.kZ la[;kvksa dk oxZewy lh[k pqds gSa vc ge n'keyo la[;kvksa dk oxZewy Kkr djsxsA n'keyo la[;kvks dk oxZewy Kkr djrs le; ge n'keyo la[;kdksa ij /;ku nsrs gSaA ;fn ;g la[;akd le gS rks tksM+s vklkuh ls cu tk,axs vU;Fkk n'keyo la[;kvks ds vUr esa 'kwU; yxkdj tksM+s cuk, tk ldrs gSaA

vkb, dqN lEcfU/kr leL;k ns[ks %mnkgj.k% ,d oxkZdkj fp= dk {ks=Qy 20.25 lseh2 gks rks ml fp= ds fdukjsa dh yEckbZ Kkr dhft, A gy% ;fn fdukjs dh yEckbZ = x lseh rks fp= dk {ks=Qy =x2 lseh2

vc fn;s x;k fp= dk {sk=Qy = 20.25 oxZ lseh0vr% x dk oxZ = 20.25


rks x = oxZewy 20.25 = 4.5oxkZdkj fp= ds fdukjs dh yEckbZ gqbZ x lseh = 4.5 lseh

fHkUukas dk oxZewy

vkvks rks vc ge pyrs &pyrs dqN fHkUuksa dk oxZewy Hkh Kkr dj ysrs gSa ijUrq /;ku j[kuk fd fHkUuks dk oxZewy fudkyrs le; ge va'k vkSj gj dk oxZewy vyx&vyx fudkyrs gSa tSls % ;fn gesa oxZewy 625 cVk 196 dks gy djuk gks rks ;g rks vc rqe vklkuh ls Kkr dj gh ldrs gks fd oxZewy 625 cVk 196 cjkcj gksrk gS 25 cVk 14vr% oxZewy 625 cVk 196 cjkcj gqvk 25 cVk 14vkvks ,d vkSj leL;k ys &&&&&&&& mnkgj.k oxZewy 1 lgh 56 cVk 169 Kkr dhft,A


gy% 1 lgh 56 cVk 169 cjkcj gqvk oxZewy 225 cVk 169] vc rqe oxZewy fudkyus es rks ijQsDV gks gh] rks&&&&&& oxZewy 225 cjkcj gqvk 25 rFkk oxZewy 169 cjkcj gqvk 13 vr% oxZewy 225 cVk 169 cjkcj gqvk 15 cVk 13] vc laVh tjk rqe ;s leL;k gy djds crkvks rks tjk] M D;ksa ugh ese]

4.5825

4 21.000000 16 500 85 425

7500 908

7264

oxZewy 3 cVk 7 dk eku] pkj n'keyo LFkku rd Kkr dhft, A M ese ] ;s rks vkius crk;k gh Fkk fd tgk¡ rd lEHko gks] ge gj dk oxZewy gVkus dh dksf'k'k djrs gSA rks oxZewy 3 cVk 7 dks ;fn igys eSa 7 cVk 7 ls xq.kk dj nw¡ ]rks gesa feyrk gS oxZewy 3 xq.kk 7 cVk 7 ]rks vc gesa feyrk gS oxZewy 21 cVk 7 vr% oxZewy 21 cVk 7 ]vc Hkkx dh fof/k ls gy


9162 23600 18324

91645 527600

djus ij gesa izkIr gksrk gS , 4.5825 cVk 7 tks fd

gy djus ij vk;k 0.6546

F osjh xqM] vc rqe oxZ vkSj oxZewy Kkr

djus esa Expert gks x, gks blfy, vkSj Hkh

lEcfU/kr iz'uks dk vH;kl djuk A

= galeq[k %& D;ww HkkbZ uV[kV] dqN le> vk;k uV[kV %& gkWa HkkbZ ]cgqr vPNs ls le> es vk;k galeq[k %& rks fQj ls rsjh ,d NksVh lh ijh{kk gks tk, A rks vkt rqeus tks Hkh u;k lh[kk & tjk la{ksi es rks crkvksa \uV[kV %& vkt eSus lh[kk && fd oxZ esa & & & galeq[k %& ugh ugha xkdj lqukvks uV[kV %& rks fQj lkj lquks dfo uV[kV dh tqckuhla[;k dks djds xq.kk la[;k ls


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