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Hkk"kkfoKku vkSj fganh Hkk"kk
uksV ;fn ^d* ds uhps ^gy* yxk, rc Hkh bls mi;qDr ugha ekuk tk ldrkA ud~@my ftl izdkj jatd fØ;k,¡ ewy
fØ;k dk vFkZ FkksM+k&lk ifjofrZr djrh gSa] mlh izdkj ek=kk,¡ Hkh O;atu dks oqQN fHkUu :i nrh gSaA ;g iw.kZr%
O;atu osQ nks ;k vfèkd :i gSaµA-a-a, B-b-b, C-c, D-d, E-e, F-f, G-g, H-h vkfnA ogk¡ ;g Hkh vfu;ferrk gS
fd fdlh oxZ osQ nks fpUg gSa vkSj fdlh osQ rhuA fgaUnh esa fliZQ m rFkk Å dh nks izdkj dh ek=kk,¡ gSaµoqQ] owQ&:A
buesa ^j* esa yxus okyh ek=kkvksa dks uhps yxk;k tk ldrk gSµ jq] jA
(8) èofu;ksa osQ vHkko osQ lUnHkZ esa ;gh dgk tk ldrk gS fd ukxjh esa fganh dh lHkh èofu;ksa osQ y, fyfi fpÉksa
dks ysus esa Hkh ladksp ugha djrhA ejkBh fpÉ ^G* bl n`f"V ls ukxjh esa fy;k tk ldrk gSA vU; èofu;ksa osQ fy,
fganh us u, fpÉ Hkh Lohdkj fd, gSa] tSlsµ vkW] o+Q] [k+] x+] t+] i+QA
(9) u~] e~] y~ d egkizk.k :iksa osQ fy, fganh esa izkjEHk ls gh dksbZ fpã ugha gSA Ug~] Eg~] Yg~ vFkkZr~ vYiizk.k
esa g~ feykdj vc rd dke pyk;k tk jgk gSA oqQN fo}ku buosQ blh :i osQ i{kèkj gSa vkSj oqQN buosQ uhps
fcUnq yxkdj dke pykuk pkgrs gSaµUg~] Eg~] Yg~A eq>s yxrk gS fd blls Hkze lekIr ugha gksxkA [k~] ?k~] >~] B~]
èk~ vkfn osQ leku buosQ Hkh LorU=k fpÉ gksus pkfg,A esjh n`f"V esa buosQ fuEufyf[kr fpÉksa dk iz;ksx fd;k tk
ldrk gSµ
Ug~&u~~Q Eg~&e~Q Yg~&y~Q
(10) ^b* dh ek=kk i;kZIr fooknkLin jgh gSaA ;g tgk¡ yxkbZ tkrh gS] ogk¡ cksyh ugha tkrhA dbZ 'kCnksa esa rks ;g
vius mPpkj.k LFkku ls nks&rhu o.kZ igys yxkbZ tkrh gS] tSlsµpfUædkµp~ $ v $ b $ u~ $ n~ $ j~ $ d~ $
vkA mPpkj.k dh n`f"V ls bls ^j~* osQ ckn yxkuk pkfg, ijUrq ;g ^u~* dh ek=kk ^b* dh ^f* osQ Øe esa ifjorZu
dk lq>ko fn;k gSA lkFk gh blosQ :i esa ifjorZu djus osQ fy, Hkh vyx&vyx lq>ko fn, x, gSa tSlsµ
b bZ
(1) h
(2) h~ h~
(3) h `
mi;qZDr lq>koksa esa ^b* dh ek=kk dks NksVh djuk O;kogkfjd n`"V ls mfpr ugha gS D;ksafd ys[ku esa blls =kqfV dh
laHkkouk ges'kk cuh jgsxhA nwljs vkSj rhljs lq>ko esa ys[ku izfØ;k dks vkSj c<+k;k x;k gS] tks mfpr ugha izrhr
gksrkA lkFk gh] vU; ek=kkvksa dh rqyuk esa og oqQN vlaxr Hkh tku iM+rk gSA h dk h osQ lkFk Hkze Hkh gks ldrk
gSA esjk lq>ko gS fd bl ek=kkk dks cM+k&NksVk ;k de&T;knk u dj fliZQ Åij yxus okys fpÉ dk fn'kk&ifjorZu
dj fn;k tk, rks ys[ku esa vlqfoèkk Hkh ugha gksxh vkSj ek=kk dk Øe Hkh Bhd gks tk,xk tSlsµ
h > µfn'kk (n~ $ b $ 'kk) ª nh'kk
h > µfn;k (n~ $ b $ ;k) ª nh;k
h > µnh;k (n~ $ bZ $ ;k) ª nh;k
gk¡] ;g vo'; è;ku j[kuk gksxk fd ^b* rFkk ^bZ* nksuksa dh ek=kk,¡ Åij xksykdkj u vkdj oqQN frjNh vk,axhµ
h] hµrHkh ;g lq>ko lkFkZdrk izkIr djsxkA
(11) vjch&iQkjlh ls x`ghr èofu;ksa osQ fy, fuf'pr fd, x, fpUgksa ^o+Q*] ^[k*] ^X+k*] T+k*] ^I+kQ*] osQ lEcUèk esa
esjk ekuuk gS fd lkekU; fganh Hkk"kh budk iz;ksx vojksgh Øe esa bl izdkj djrs gSaµ
1- d [k x t iQ (lokZfèkd iz;ksx)
2- d [k x T+k iQ + (lcls de iz;ksx)
3- d [+k x T+k i+Q
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