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Yonhodzl {og{fgb {og{fgb 3 Hfy{fg Uog|fgbbf Uog|fgbbf Fgkf {og{ uoygfa mohlaf{ jflyfg lgnz( uoygfadfa fgkf ioynldly fuf lzl kfyl jflyfg lgnz( kfg ifbfl mfgf zlz{om doycfg|f0
Hfy{fg
uog|fgbbf
kfhfm
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fbfy uA
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ioyifa' Kfyfa momug|fl uA |fgb yohf{ln {o{fu kl zodl{fy 2(;' Afh lgl klmgbdlgdfg dfyogf fkfg|f zlz{om uog|fgbbf A 9J@: kfg -
AJ@: ( zoalgbbf mozdlug zo{lfu zff{ kfyfa domfzdfg ioyifbfl sf{ |fgb ioyzlnf{ fzfm mfug ifzf fdfg zohfh kfuf{ klgo{yfhlzly uogbfyag|f {oyafkfu uoyifafg uA' Ilhf kfyfa domfzdfg sf{ |fgb ioyzlnf{ fzfm(
Zmioy 3 a{{u3//fy{ldohodf'ih`bzu`{'j`m
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mfdf l`g A kfyl fzfm {oyzoi{ fdfg ioyofdzl kogbfg l`g -
AJ@: ' A
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-
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AJ@: !fv,
A9J@:!fv,
⇋
-
Zoifhldg|f ilhf kfyfa domfzdfg sf{ |fgb ioyzlnf{ ifzf mfdf l`g @A fdfg ioyofdzl kogbfg A9J@:' -
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{oykfuf{ hfy{fg uog|fgbbf |fgb {oyklyl kfyl A9J@: kfg AJ@: |fgb ioyngbzl momuoy{fafgdfg uA fbfy kfuf{ kl{oylmf `hoa {ia'
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M`kh 9 Hfy{fg Uog|fgbbf
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◀ ◀ ◀
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Z{fgkfy Jfuflfg Z{fgkfy jfuflfg moyufdfg lgkldf{`y afzlh iohfcfy |fgb afyz kljfufl uozoy{f klkld' Z{fgkfy jfuflfg kfhfm m`kh hfy{fg uog|fgbbf fkfhfa 3 6'6' Uozoy{f klkld kfuf{ mogbfgfhlzlz hfy{fg uog|fgbbf kfg idfg uog|fgbbf mohfhl uoyj`iffg' 6'9' Uozoy{f klkld kfuf{ mogbal{gb uA f{f u@A hfy{fg uog|fgbbf 6':' Uozoy{f klkld kfuf{ mogbal{gb uA hfy{fg uog|fgbbf kogbfg uogfmifafg uogfmifafg zokldl{ fzfm f{f zokldl{ ifzf f{f kogbfg uogbogjoyfg 6';' Uozoy{f klkld kfuf{ mogcohfzdfg ngbzl hfy{fg uog|fgbbf kfhfm {ia mfdahd alku
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M`kh 9 Hfy{fg Uog|fgbbf
-2
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hfy{fg GA: 5(6 M cldf di GA: = 65
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;5
M`kh 9 Hfy{fg Uog|fgbbf
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JA:J@@Gf !z,
-
JA:J@@ !fv,
$
Gf
$ !fv,
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-
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JA:J@@ !fv, $ A
$ !fv,
JA:J@@A!fv, -
Cldf ifzf kl{fmifadfg kfhfm zlz{om innoy ( l`g @A fdfg klgo{yfhdfg `hoa fzfm kfhfm hfy{fg uog|fgbbf' JA:J@@A!fv,
$ @A-!fv,
-
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J`g{`a 3 Mfgfdfa kfyl hfy{fg ioyld{ |fgb momiog{d zlz{om uog|fgbbf( cohfzdfg0 f' A:U@; kogbfg DA9U@; i' AJh@; kogbfg GfJh@; j' J?A?G kogbfg J ?A>GJh !Di J?A?G !ulylklg, kfuf{ fgkf hlaf{ kl [fioh 6'?,
Uomifafzfg 3 Zouoy{l {ohfa klcohfzdfg zoiohmg|f hfy{fg uog|fgbbf f{f innoy {oyklyl kfyl fzfm homfa kogbfg ifzf d`gcbfzlg|f f{f ifzf homfa kogbfg fzfm d`gcbfzlg|f' f' [oymfzd uog|fgbbf dfyogf {oyklyl fzfm homfa A:U@; kogbfg ifzf d`gcbfzlg|f i' Idfg {oymfzd hfy{fg uog|fgbbf dfyogf AJh@; moyufdfg fzfm df{ j' [oymfzd uog|fgbbf Dfyogf {oyklyl ifzf homfa ulylklg kogbfg fzfm d`gcbfzlg|f
;6
M`kh 9 Hfy{fg Uog|fgbbf
3 _cl Mfgklyl Mfgfdfa kfyl zlz{om ioyld{ |fgb moyufdfg hfy{fg uog|fgbbf/innoy' f' DN/AN i' AIy/DIy j' Gf9J@:/GfAJ@: k' GA;Iy / GA: o' GfA9U@;/A:U@;
6' Coglz Hfy{fg Uog|fgbbf Ioykfzfydfg zlnf{g|f hfy{fg uog|fgbbf kliokfdfg mogcfkl 9 mfjfm( |fl{ hfy{fg uog|fgbbf fzfm !innoy fzfm, kfg hfy{fg uog|fgbbf ifzf !innoy ifzf,'
f'
Hfy{fg Innoy Fzfm Hfy{fg innoy fzfm fkfhfa hfy{fg uog|fgbbf |fgb ioyzlnf{ fzfm( |fl{ {oyklyl kfyl fzfm homfa kogbfg ifzf d`gcbfzlg|f'
J`g{`a innoy innoy fzfm fkfhfa jfmuyfg fg{fyf
JA:J@@A kogbfg JA:J@@D klmfgf JA:J@@A fkfhfa fzfm homfa zokfgbdfg JA:J@@
-
fkfhfa ifzf d`gcbfzlg|f'
i'
Hfy{fg Innoy Ifzf Hfy{fg innoy ifzf fkfhfa zlz{om uog|fgbbf |fgb ioyzlnf{ ifzf( |fl{ {oyklyl ifzf homfa kogbfg fzfm d`gcbfzlg|f' J`g{`a kfyl innoy ifzf fkfhfa jfmuyfg fg{fyf hfy{fg GA : $
kogbfg GA ;Jh' Kl mfgf GA: fkfhfa ifzf homfa zokfgbdfg GA;
fkfhfa fzfm
d`gcbfzlg|f'
I'
uA Hfy{fg Uog|fgbbf uA hfy{fg uog|fgbbf {oybfg{gb `hoa uog|zg uog|fgbbf {oyzoi{' Hfy{fg uog|fgbbf
fg{fyf fzfm homfa kogbfg ifzf d`gcbfzlg|f fdfg ioyzlnf{ fzfm( zokfgbdfg hfy{fg uog|fgbbf |fgb klzzg fg{fyf ifzf homfa kogbfg fzfm d`gcbfzlg|f fdfg ioyzlnf{ ifzf'
6'
uA Hfy{fg Innoy Innoy Fzfm Dl{f fmilh j`g{`a innoy fzfm fg{fyf hfy{fg JA:J@@A kogbfg JA:J@@Gf' Kfhfm hfy{fg
JA:J@@A fdfg mogbfhfml l`glzfzl zoifblfg( zokfgbdfg JA :J@@Gf fdfg {oyl`glzfzl {`{fh' -
Uoyzfmffg dozo{lmifgbfg fg{fyf JA:J@@A kogbfg JA :J@@ kfuf{ kl{hlzdfg' -
JA:J@@A!fv,
$ !fv,
JA:J@@ !fv, $ A
[o{fufg l`glzfzl fzfm fzo{f{ kfuf{ kl {hlzdfg $ JA:J@ J @@ A Df = JA:J@@A $
Kfyl uoyzfmffg kl f{fz( d`gzog{yfzl l`g A kfuf{ kl{og{dfg zoifbfl ioyld{ 3
$
TA ] = Df
TJA TJA:J@@A J@@A]] TJA:J@@ ]
-
Dfyogf JA:J@@ morfdlhl ifzf d`gcbfzl kfyl JA:J@@Gf( mfdf uoyzfmffg {oyzoi{ kfuf{ kl{hlzdfg
$
TA ] = Df
TJA TJA:J@@A J@@A]] TJA TJA:J@@G J@@Gf] f]
;9
$
f{f kfuf{ kl{hlzdfg zojfyf mfm TA ] = Df
M`kh 9 Hfy{fg Uog|fgbbf
TFzfm] TIfzf D`gcubfzl]
Ifzf d`gcbfzl |fgb klafzlhdfg moyufdfg bfyfm kfyl yofdzl go{yfhlzfzl( zoalgbbf uoyzfmffg {oyzoi{ kfuf{ cbf kl{hlzdfg'
$
TA ] = Df
Tfzfm] Tbfyfm]
Dfyogf hfy{fg ioyfzfh kfhfm rfkfa |fgb zfmf( ioyfy{l momlhldl ~`hmo jfmuyfg |fgb zfmf uhf( zoalgbbf uoyifgklgbfg d`gzog{yfzl kfuf{ klrfdlhl `hoa uoyifgklgbfg m`h( zoalgbbf ymz $
d`gzog{yfzl A kfuf{ klg|f{fdfg $
TA ] = Df
m`h fzfm m`h bfyfm
Cldf m`h fzfm homfa klg|f{fdfg kogbfg zlmi`h
ɖ
zokfgbdfg bfyfm kogbfg zlmi`h b mfdf
uoyzfmffg kl f{fz kfuf{ dl{f {hlzdfg
$
TA ] = Df
f b
Do{oyfgbfg 3 Df = {o{fufg l`glzfzl fzfm homfa
f = m`h fzfm b = m`h bfyfm Kfyl uoyzfmffg kl f{fz uA hfy{fg innoy fzfm kfuf{ dl{f {hlzdfg
uA = uDf $ h`b
b f
Fzuod Uogklkldfg Dfyfd{oy Hfy{fg Uog|fgbbf fkfhfa hfy{fg |fgb mfmu momuoy{fafgdfg uA hfy{fg kfyl uogfmifafg zokldl{ fzfm( ifzf f{fug kogbfg uogbogjoyfg( afh lgl dfyogf uog|zg kfyl hfy{fg uog|fgbbf' Kfyl konlglzl lgl mogbfcfydfg dl{f g{d zfhlgb momifg{( zfhlgb mogfzlaf{l kfg iodoycf zfmf kogbfg `yfgb hflg fbfy mogcfkl lgkl~lk kfg doalkufg z`zlfh |fgb hoila ifld'
;:
M`kh 9 Hfy{fg Uog|fgbbf
J`g{`a Z`fh 3 6' Al{gbhfa uA hfy{fg ioyld{ 3 f'
Uog|fgbbf |fgb {oyklyl kfyl JA:J@@A 6(5 M kfg JA:J@@Gf 6(5 M -?
!Df JA:J@@A = 6(1 q 65 , i'
Uoyifafg uA hfy{fg dfyogf uogfmifafg 5(6 m`h AJh do kfhfm 6 H hfy{fg lgl' !fgbbfu uogfmifafg AJh {lkfd moyifa ~`hmo hfy{fg,
Uomifafzfg 3 Tfzfm]
$
f' TA ] = Df
Tbfyfm]
= 6(1 q 65
-?
!5(6, !5(6,
-?
= 6(1 q 65 M $
uA = - h`b TA ] = - h`b 6(1 q 65
-?
= ? ‚h`b 6(1 = ;(2; i' Zo{ohfa kl{fmifadfg AJh( {oycfkl l`glzfzl zomuygf AJh $ !fv,
AJh!fv,
A
5(6 m`h
5(6 m`h
$
-
Jh !fv, 5(6 m`h -
Mhf-mhf kfhfm hfy{fg {oykfuf{ 6 m`h JA:J@@A kfg 6 m`h JA :J@@ |fgb {oykfuf{ kfhfm 6 H fly' Zo{ohfa {oycfkl yofdzl go{yfhlzfzl fg{fyf AJh kogbfg -
JA:J@@ ( kogbfg yofdzl -
$ !fv,
JA:J@@ !fv, $
A
5(6 m`h
5(6 m`h
JA:J@@A!fv, 5(6 m`h
Cmhfa m`h fzfm fzo{f{ kfg l`g fzo{f{ ioyifa mogcfkl3 JA:J@@A JA:J@@
= !6(5 $ 5(6,m`h = 6(6 m`h
-
= !6(5 ‚ 5(6,m`h = 5(< m`h $
Zoalgbbf d`gzog{yfzl l`g A kfuf{ dl{f al{gb $
TA ] = Df
Tfzfm] Tbfyfm]
= 6(1 q 65
-?
!6(6, !5(<,
-?
= 9(9 q 65 M $
uA = - h`b TA ] -?
= - h`b 9(9 q 65 = ? ‚h`b 9(9 = ;(>>
Jf{f{fg 3 Kfuf{ dl{f fmf{l ifarf hfy{fg innoy kogbfg uogfmifafg fzfm mogbafzlhdfg uoyifafg uA |fgb yohf{ln {lkfd ioyifa' Cldf kl{fmifadfg klhfy{fg
;;
M`kh 9 Hfy{fg Uog|fgbbf
9'
uA Hfy{fg Innoy Ifzf Zfmf afhg|f kogbfg innoy fzfm( innoy ifzf kliog{d `hoa jfmuyfg hfy{fg ifzf homfa
kogbfg fzfm d`gcbfzlg|f' Zlnf{ hfy{fg innoy |fgb {oyiog{d fdfg ioyzlnf{ ifzf( afh lgl klfdlif{dfg fkfg|f ifzf homfa kfhfm jfmuyfg' Zoifbfl j`g{`a innoy ifzf fkfhfa jfmuyfg kfyl GA;@A kfg GA;Jh' Hfy{fg GA;@A fkfhfa ifzf homfa zoalgbbf kfhfm hfy{fgg|f fdfg {oyl`glzfzl zoifblfg( zokfgbdfg bfyfm GA ;Jh fdfg {oyl`glzfzl {`{fh' $ !fv,
GA;@A!fv,
GA;
$
@A-!fv,
[o{fufg l`glzfzl ifzf kfuf{ kl{hlzdfg $ TGA ]T@A ] ; Di = TGA;@A] -
Ioykfzfydfg {o{fufg l`glzfzl ifzf {oyzoi{ mfdf d`gzog{yfzl l`g @A kfuf{ dl{f {hlzdfg' -
T@A ] = Di
TGA TGA; @A]
TGA; ] $
Dfyogf GA; morfdlhl fzfm d`gcbfzl kfyl GA;Jh( mfdf uoyzfmffg {oyzoi{ kfuf{ kl{hlzdfg
-
T@A ] = Di
TGA TGA;@A] TGA; Jh]
-
f{f kfuf{ kl{hlzdfg zojfyf mfm T@A ] = Di
TIfzf] TFzfm D`gcubfzl]
Fzfm d`gcbfzl |fgb klafzlhdfg moyufdfg bfyfm kfyl yofdzl go{yfhlzfzl( zoalgbbf uoyzfmffg {oyzoi{ kfuf{ cbf kl{hlzdfg'
-
T@A ] = Di
Tifzf] Tbfyfm]
Dfyogf hfy{fg ioyfzfh kfhfm rfkfa |fgb zfmf( ioyfy{l momlhldl ~`hmo jfmuyfg |fgb zfmf uhf( zoalgbbf uoyifgklgbfg d`gzog{yfzl kfuf{ klrfdlhl `hoa uoyifgklgbfg m`h( zoalgbbf ymz -
d`gzog{yfzl @A kfuf{ klg|f{fdfg -
T@A ] = Di
m`h ifzf m`h bfyfm
Cldf m`h ifzf homfa klg|f{fdfg kogbfg zlmi`h i zokfgbdfg bfyfm kogbfg zlmi`h b mfdf uoyzfmffg kl f{fz kfuf{ dl{f {hlzdfg
-
T@A ] = Di
Do{oyfgbfg 3 Di = {o{fufg l`glzfzl ifzf homfa
;?
M`kh 9 Hfy{fg Uog|fgbbf
i b
i = m`h ifzf b = m`h bfyfm Kfyl uoyzfmffg kl f{fz uA hfy{fg innoy fzfm kfuf{ dl{f {hlzdfg
b
u@A = uDi $ h`b
i
uA = UDr -uDi - h`b
b i
J`g{`a Z`fh 3 6' Ioyfufdfa mfzzf bfyfm fmm`glm dh`ylkf !GA;Jh, |fgb afyz kl{fmifadfg do kfhfm 655 mH hfy{fg GA ;@A 5(56 M cldf klafzlhdfg hfy{fg kogbfg kogbfg uA 1 5
-?
ufkf za 9? J' fgbbfu ~`hmo hfy{fg {lkfd ioyifa Di GA;@A fkfhfa 65 0 !Fy A= 6( G= 6;( @= 6>( kfg Jh= :?(?,
Uomifafzfg 3 Dfyogf uog|fgbbf lgl ioyzlnf{ ifzf {oyhoila kfah dl{f {og{dfg d`gzog{yfzl l`g -
@A ' uA = 1 u@A = 6; ‚ uA = 6; ‚ 1 => -
->
Zoalgbbf kfuf{ dl{f al{gb ifarf T@A ] = 6 q 65 M -
T@A ] = Di
m`h ifzf m`h bfyfm
m`h bfyfm = Di
m`h ifzf T @A ]
= 6(5 q 65
-?
5( 56 q 655 mm`h 6( 5 q65 q65
>
= 65 mm`h Mfzzf GA;Jh = m`h GA;Jh q My GA;Jh = 65 mm`h q ?:(? by/m`h = ?:? mb = 5(?:? byfm
J`ggoj{l` 3 _g{d momuohfcfyl mf{oyl hfy{fg innoy hoila hfgc{ zlhfadfg ld{l hlgd ioyld{ lgl3 a{{u3//jaomok'jaom'rlzj'ok/jaomuf{azLgz{'''Jaom-[oq{i``d/innoy-Z`h{l`gz->95'a{mh
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Ilhf :(; byfm bfz GA: klhfy{dfg do kfhfm 6 hl{oy fly' Domklfg do kfhfm hfy{fg {oyzoi{ kl{fmifadfg ?(:? byfm GA;Jh' {og{dfghfa uA hfy{fg {oyzoi{( cldf Di -?
GA: = 6(1 q 65 ( My GA: = 62( kfg My GA;Jh = ?:(?' :'
Ilhf 9 hl{oy hfy{fg GA;@A 5(9 M kljfmuydfg kogbfg 9 hl{oy hfy{fg GA ;Jh 5(9 M -?
kfg Di GA ;@A = 6(1 q 65 ' [og{dfg3 f' uA hfy{fg uog|fgbbf i' uA hfy{fg uog|fgbbf zo{ohfa uogfmifafg 65 mh AJh 5(6 M j' uA hfy{fg uog|fgbbf zo{ohfa uogfmifafg 65 mh Gf@A 5(6 M ;'
Hfy{fg innoy kogbfg ~`hmo 65 H mogbfgkgb 5'65 m`h fzfm uy`ul`gf{ !JA:JA9J@@A, kfg 5'65 m`h gf{ylm uy`ul`gf{ ! JA :JA9J@@Gf ,( cldf Df fzfm -?
uy`ul`gf{ 6(1 Ò 65 mfdf( Al{gbhfa uA hfy{fg innoy {oyzoi{' ?'
Al{gb uA jfmuyfg ?5 mH JA:J@@A 5(6 M kogbfg ?5 mH JA :J@@Gf 5(6 M& Df JA:J@@A = 6(1 q 65
>'
-?
!h`b 6(1 = 5(9>,
Dokfhfm 6 hl{oy {oykuf{ 5(; m`h JA:J@@A kfg 5(9 m`h JA:J@@Gf' D f JA:J@@A = -?
6(1 q 65 ' [og{dfg uA jfmuyfg &
B` [` Hfi Uoyj`iffg [cfg
3 Lkog{lnldfzl Innoy ufkf Mlgmfg Ioyz`kf 3 Mogblkog{lnldfzl fufdfa kfhfm mlgmfg ioyz`kf {oykfuf{ zlz{om innoy Fhf{ 3 iofdoy bhfzz( hfi dy( bohfz dy( uA gl~oyzfh( uluo{ {o{oz( kfg dfjf fyh`cl Ifafg 3 mlgmfg ioyz`kf( hfy{fg AJh 5(6 M( hfy{fg Gf@A 5(6 M( hfy{fg GA;@A 5(6 M( hfy{fg JA:J@@A 5(6 M( kfg Fdfkoz Jfyf Doycf 3 6' Mog|lfudfg fhf{ kfg ifafg |fgb kluoyhdfg4 9'
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9 dfhl ? dfhl 65 dfhl
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T Fzfm ]
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fg{fyf fzfm homfa kogbfg ifzf d`gcbfzlg|f' Hfy{fg innoy cbf kfuf{ kliog{d kfyl jfmuyfg fg{fyf ifzf homfa kogbfg fzfm d`gcbfzlg|f' Hfy{fg uog|fgbbf f{f innoy kfuf{ cbf kliog{d fg{fyf fzfm homfa kogbfg ifzf df{ kogbfg z|fyf{ zff{ fdaly yofdzl ifzf df{ afilz ioyofdzl zokfgbdfg fzfm homfag|f zlzf( afh {oyzoi{ ioyhfd cbf g{d yofdzl fg{fyf ifzf homfa kogbfg fzfm df{'
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$
TA ] = Df
T Ifzf D`gcubfzl ]
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$
TA ] = Df
m`h ifzf d`gcubfzl d`gcubfz l -;
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$
TA ] = Df
m`h ifzf d`gcubfzl d`gcubfz l $
-;
$
-;
TA ] = >(1 q 65
? mm`h ? mm`h
TA ] = >(1 q 65
M -;
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M`kh 9 Hfy{fg Uog|fgbbf
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JA:J@@A = 6(1 q 65 ,
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= ? mm`h
JA:J@@A!fv, $
Gf@A!fv,
JA:J@@Gf!fv, $
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6? mm`h
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A9@!h, -
m`h fzfm
$
TA ] = Df
m`h ifzf d`gcubfzl $
-?
$
-?
TA ] = 6(1 q 65
65 mm`h ? mm`h
TA ] = 6(1 q 65 $
-?
TA ] = :(> q 65
q 9 M -?
uA = -h`b :(> q 65 uA = ? ‚ h`b :(> uA = ? ‚ 5'?? uA = ;(;?
9' Yofdzl Uomiog{dfg Innoy Ifzf Zouoy{l afhg|f innoy fzfm( innoy ifzf kliog{d `hoa yofdzl fg{fyf ifzf homfa kogbfg fzfm df{' Yofdzl fdfg momiog{d hfy{fg innoy kogbfg z|fyf{ ifarf fzfm df{ fdfg afilz zff{ fdaly yofdzl' Hfy{fg fdfg ioyzlnf{ ifzf dfyogf zo{ohfa fdaly yofdzl mfzla mog|lzfdfg ifzf homfa' Zoifbfl j`g{`a mfyl dl{f hlaf{ yofdzl uomiog{dfg innoy fg{fyf 655 mH hfy{fg ifzf homfa GA;@A 5(6 M kogbfg hfy{fg fzfm df{ 655 mH hfy{fg AJh 5(5? M' Kfhfm yofdzl {oyzoi{ {oykfuf{ m`h GA;@A = 65 mm`h m`h AJh
= ? mm`h
GA;@A!fv, $
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T@A ]= Di
-
m`h ifzf m`h fzfm d`gcubfzl
?9
M`kh 9 Hfy{fg Uog|fgbbf
-?
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-?
-
-?
T@A ]= 6(1 q 65
? mm`h ? mm`h
T@A ]= 6(1 q 65 M -
u@A = - h`b T@A ] u@A = - h`b 6(1 q 65
-?
u@A = ? ‚h`b 6(1 uA
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uA
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uA
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J`g{`a z`fh 3 6' Kljfmuy >55 mH GA ;@A 5(9 M kogbfg kogbfg ;5 mH AJh 5(? M' Cldf d i GA;@A = 6(1 -?
q 65 ( [og{dfg uA jfmuyfg&
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m`h AJh
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AJh!fv,
GA;Jh!fv, $
95 mm`h
95 mm`h
95 mm`h
95 mm`h
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-
95 mm`h
95 mm`h
655 mm`h
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A9@!h,
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Yofdzl Zlzf
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-
m`h ifzf
-
T@A ] = Di
m`h fzfm d`gcubfzl -
-?
-
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655 mm`h
T@A ] = 6(1 q 65
95 mm`h
T@A ] = 6(1 q 65 -
T@A ] = < q 65
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q ? M -?
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