SQD^K^ SKOI^GLGH 7
‖
L[OIMI@IBG^I MGH MKL[OIMI@IBG^I
MKL[OIMI@IBG^I   ‟

MD^KH:
Mr. Goir Lusih, ^.]., O.].

Hgog Bkfdopdb HIO

Ghmrk Busgmy 753=3;7<5
Gfwi Lusgih Ogrpguhe 753=3;75;
Qglkf Bristghti Sghmighegh 753=3;70=

Qi`gi Sgrtdei Oghgfu 753=3;7<<

Mkaay ]lkdmdrg 753=3;793
Qihi Ghghmg ^igeigh 753=3;7;0

MKSGQ]KOKH ]KBHIB BIOIG

@GB[F]G^ ]KBHIB
[HIPKQ^I]G^ ^[OG]KQG []GQG
OKMGH
1313
 

7.  L uo
uoii mi ty `rd
`r do Pgpd
Pgpdr S r kssurk 
[mgrg mi rughegh pgmg sulu >5 dN mgh tkbghgh tdtgf 737,> bSg gas yghe
okheghmuhe ugp gir mkhegh tkbghgh pgrsigf pG ? >,;9
>,; 9 bSg. Lituhefgl:

g. Bkfkoagagh.
a. ^gturgsi bkfkoagagh mgh pkrskhtgsk bkfkoagagh.
n. Skrskhtgsk bkfkoagagh rkfgti`.

Skoaglgsgh :
Mibktglui:  [mgrg mi mgfgo skaugl rughegh
] ? >5,<dN
S ? 737,> bSg
Okheghmuhe ugp gir mkhegh tkbghgh pgrsigf

 >,;9 bSg
S ? 737,> bSg
Mitghyg:  (g). Luoimity
(a). Luoimity Jkhul
(n). Skrskhtgsk Luoimity Qkfgti`
Skhykfksgigh:
[mgrg tkrmiri mgri ngopurgh ugp G mgh egs A.
Mioghg: G ? gir (L 1D)
A ? umgrg bkrihe

Akrmgsgrbgh ^tkgo ]gafk (pgmg Gppkhmix Aubu Ekghbdpfis), pgmg tkopkrgtur

>5,<dN ygitu :

 
 

Mgri tgakf tkrskaut mipkrdfkl mgtg skagegi akribut :

  ]kbghgh ugp gir jkhul
Sgmg ]7 ? >0dN SG^7 ?;,9=5
?;,9=5 bSg
 bSg
Sgmg ]1 ? =3dN SG^1 ?5,><=
?5,><= bSg
 bSg
^kliheeg mifgbubgh ihtkrpdfgsi uhtub ] ? >5,<dN
]- ]7 SG^ -SG^7
  ?  
]1 -]7 SG^1 -SG^7
ℎ ℎ 
>5,< - >0
?
SG^-;,9=5 bSg
 
=3ℎ->0ℎ 5,><= bSg-;,9=5 bSg
7,< SG^-;,9=5 bSg
  ?  
= 7,=>5 bSg
1,;<00 bSg  
? =.SG^ - 1>,5<< bSg 
bSg 
=.SG^   ? 1>,5<< bSg  1,;<00 bSg

SG^  ? 10,>5=0 bSg 

=
SG^  ? 0,;9>0; bSg 
bSg 

(g). Luoimity

 
ϳ?
AOL1 D
AOumgrg
.     SG
S - SG  
 

7<,31 >,;9
? ( .
1<,95 737,>->,;9
) 
>,;9
? 3,011.(95,57 ) 
? 3,011.3,3>05 
? 3,311<; be L1D/be umgrg bkrihe
(a). Luoimity Jkhul
AOL1 D
ϳ ?   AOumgrg
. (S -S S^ ^ ) 
G

7<,31 0,;99>0;
? ( .
1<,95 737,> - 0,;99>0;
) 
0,;99>0;
? 3,011. (9=,530>; ) 
? 3,011. 3,309011  
 
 
 

? 3,7779>1 be L1D/be umgrg bkrihe 

(n). Skrskh Qkfgti` Luoimity
SG
ϳ  ? 733. SG^
 

>,;9
? 733. (0,;9>0;) 
? 733. 3,;===0 
? ;=,==0 % 
% 

 
 

1. S kr nk
nkhtg
htgee k ghm
ghm Qk
Q kfgt
fgtii vk L uo
uoii mi ty  
]lk gir ih g rddo lgs g luoimity L d` 3.317 be L 1D /be mry gir gt >1.1 dN ghm 737.>
bSg gas prkssurk. Ngfnufgtk:
g)  Skrnkhtgek luoimity LS.
a)  Skrnkhtgek rkfgtivk luoimity LQ .
Ghswkr: (g). LS ? 05.;% 2 (a). LQ  ?
 ? 0<.0%

]krjkoglgh:
Skrskhtgsk
Skrskhtgsk mgh Bkfkoagagh Qkfgti`
[mgrg mi mgfgo rughegh okoifibi bkfkoagagh L 3,317 be L 1D / be umgrg bkrihe
 pgmg tkbghgh >1,1dN mgh 737,> bSg gas. Okhelituhe:
g) Skrskhtgsk bkfkoagagh LS.
 a) Skrskhtgsk bkfkoagagh rkfgti` ^MO.
Jgwgagh: (g). LS ? 05,;%2 (a). LQ ? 0<,0%

SKHYKFK^GIGH
Mibktglui: [mgrg mi mgfgo skaugl rughegh

ϳ ? 3,317  be L1 D
be umgrg bkrihe
 
] ? >1,1dN
S ? 737,> bSg
Mitghyg: (g). Skrskhtgsk Luoimity
Skrskhtgsk Luoimity,, ϳ  
(a). Skrskhtgsk Qkfgti` Luoimity
Qkfgti` Luoimity,,  
ϳ

Skhykfksgigh:
Mgfgo bgsus ihi, umgrg tkrmiri mgri ngopurgh ugp G mgh egs A.
Mioghg G gmgfgl gir (L 1D) mgh A gmgfgl umgrg bkrihe
Akrmgsgrbgh ^tkgo ]gafk pgmg Ekghbdpfis, pgmg tkopkrgtur >1,1dN:
]gafk pgmg Aubu Ekghbdpfis,

 
 

  ]kbghgh [gp Gir Jkhul

Sgmg ]7 ? >3dN SG^7 ? =,1=0 bSg
=,1=0 bSg
Sgmg ]1 ? >>dN SG^1  ? ;,3>= bSg
;,3>= bSg
^kfghjuthyg mifgbubgh ihtkrpdfgsi pgmg sulu, ] ? >1,1dN
]- ]7 SG^ -SG^7
]1 -]7   ? SG^1 -SG^7  
ℎ ℎ 
>1,1 - >3
?
SG^ - =,1=0 bSg
 
>>ℎ->3ℎ ;,3>= bSg - =,1=0 bSg
1,1
  ?
 
SG^ - =,1=0 bSg
 
> 3,5<< bSg
7,5>>0 bSg  
? >.SG^ - 71,5>< bSg 
bSg 
>.SG^   ? 71,5>< bSg + 7,5>>0 bSg
7=,=570 bSg
SG^  ?  
>
SG^  ? =,<1><05 bSg 
bSg 

  Okhngri hifgi SG 

Mibktglui pgmg sdgf aglwg tkbghgh, S ? 737,> bSg

^kfghjuthyg okhngri hifgi SG  mgri hifgi luoimity, ϳ 
AOL1 D
ϳ ?
AOumgrg
. (S -SS  ) G

7<,31 S
3,317 ? ( .
1<,95 S - S  
)  G

SG
3,317 ? 3,011. S - SG    
( )
 SG
S - SG  
    3,317
3,011

 SG
S - SG  
  3,3>>501
3,3>>501  

SG   ? 3,3>>501 .S - 3,3>>501. SG  
SG   ? 3,3>>501 .(737,>) - 3,3>>501. SG  
SG   ? 3,3>>501 .(737,>) - 3,3>>501. SG  
SG   ? >,=1 - 3,3>>501. SG  
SG  + 3,3>>501. SG ? >,=1 
>,=1 

 
 

7,3>>501. SG >,=1 
? >,=1 
>,=1
SG ?  
7,3>>501
SG ? >,>3<> bSg 
bSg 


  Okhelituhe Hifgi Luoimity Jkhul

AOL1 D
ϳ  ?
AOumgrg
. (S S- S  ) 
G^

G^

7<,31 =,<1><05
? ( .
1<,95 737,> „ =,<1><05
) 
=,<1><05
? 3,011.(90,=507>> ) 
? 3,011.3,3; 
be L D
? 3,3>77 ( )  1

be umgrg bkrihe
^kliheeg:
g.  Skrskhtgs
Skrskhtgskk Luoimity
ϳ
ϳ  ? 733. ϳ  
3,317
? 733. (3,3>77 ) 
? 733. 3,05;1= 
? 05,;1=% 
05,;1=% 
Jgmi, hifgi Skrskhtgsk Luoimity skaksgr 05,;1=%.

a.  Skrskhtgs
Skrskhtgskk Qkfgti` Luoimity
SG
ϳ  ? 733. SG^
 

>,>3<>
? 733. (=,<1><05 ) 
? 733. 3,0<;< 
? 0<,;<% 
0<,;<% 
Jgmi, hifgi Skrskhtgsk Qkfgti` Luoimity Jkhul skaksgr 0<,;<%.

 
  >.  G
 Gmmi gagti n ^g
^gtturg
urgtti dh ]k
]ko
opkr gturk

Gir gt <1.1dN ghm lgvihe g luoimity L   ? 3.30;; be L 1D /be mry gir is
ndhtgntkm ih g gmigagtin sgturgtdr witl wgtkr. It fkgvks gt <3% sgturgtidh.
g)  Ulgt grk tlk `ihgf vgfuks d` L  ghm
 ghm ] dN4

a)  @dr 733% sgturgtidh, wlgt wdufm ak tlk vgfuks d` L  ghm

 ghm ] 4
(g). L ? 3.359 be L1D/be mry gir, ] ? ;1,<dN. 
Ghswkr: (g). L

Skoaglgsgh :
Mibktglui: [mgrg pgmg: ] ? <1,1dN

 
ϳ ? 3,30;; be L1D/be umgrg bkrihe
Mitghyg:  (g). Hifgi Gblir ϳ mgh ] (dN).

(a). Sgmg bkjkhulgh 733%, akrgpgbgl hifgi ϳ mgh ] (dN).

Skhykfksgigh:

[mgrg mibdhtgbbgh dfkl ^gturgtdr Gmigagtib mkhegh Gir, mioghg okhiheegfbgh

Bkjkhulgh skaksgr <3%

(g). Akrmgsgrbgh
Akrmgsgrbgh Luoimity
 Luoimity Nlgrt  

 
]itib ϳ ? 3,30;; be L1D/be umgrg bkrihe mgh ] ? <1,1dN

Akrmgsgrbgh Luoimity
Akrmgsgrbgh Luoimity Nlgrt  tkrskaut,
 tkrskaut, ogbg mgpgt migoaif bksiopufgh aglwg:

 
 Sgmg bkjkhulgh <3%, mipkrdfkl hifgi: ] ? ;1,<dN

 
ϳ ? 3,359 be L1D/be umgrg bkrihe

(a). Akrmgsgrbgh
Akrmgsgrbgh Luoimity
 Luoimity Nlgrt  Sgmg
 Sgmg bkjkhulgh 733%

Akrmgsgrbgh Luoimity
Akrmgsgrbgh Luoimity Nlgrt  tkrskaut,
 tkrskaut, ogbg mgpgt migoaif bksiopufgh aglwg:
Sgmg bkjkhulgh 733%, mipkrdfkl hifgi: ] ? =<,;dN

ϳ ? 3,3<3; be L1D/be umgrg bkrihe

 

 
 =. G mirknt-lkgt mrykr is td dpkrgtk witl gir khtkrihe gt 1;3 d@ ghm 7 gto witl g wkt-
 aufa tkopkrgturk d` 73;d@. Mktkroihk `rdo tlk psynlrdoktrin nlgrt ghm/dr
rkfgtidhslips d` ]gafk 7<.> tlk `dffdwihe:
g)  Luoimity.
 a)  Odfgf luoimity.
n)  Skrnkhtgek luoimity.
m)  Qkfgtivk luoimity.
k)  ^gturgtidh luoimity.
`)  Luoim vdfuok.
e)  Luoim lkgt.
l)  Khtlgfpy.
i)  Gmigagtin-sgturgtidh tkopkrgturk.
 j)  Odfk `rgntidh d` wgtkr ih tlk gir.

SKHYKFK^GIGH
Mibktglui:
^kaugl Gfgt Skhekrihe
Midpkrgsibgh mkhegh umgrg ogsub,
mioghg:
] ? 1;3d@
S ? 7 gto
]U ? 73;d@
Mitghyg: Euhgbgh
Euhgbgh Ssynlrdoktrin
 Ssynlrdoktrin Nlgrt  mgfgo
 mgfgo okhkhtubgh:

g)  Luoimity
 a)  Odfgf Luoimity
n)  Skrskhtgsk Luoimity
m)  Qkfgti` Luoimity
k)  Luoimity Jkhul
`)  Luoim Pdfuo
e)  Luoim Sghgs
l)  Khtgfpi
i)  ]kopkrgtur jkhul gmigagtib

 
  j)  @rgbsi odf gir mgfgo umgrg
Jgwga : 
]UA ? 73;d@ ? =3,;dN
]MA ? 1;3d@ ? 717,77dN
S ? 7 gto ? 11,91 ihLe ? 737,>1; bSg

g)  Mgri erg`ib luoimity nlgrt, mipkrdfkl hifgi L G (Luoimity gasdfut) ? 3,375
mkhegh bdhmisi ]UA? 73;d@ mgh ]MA? 1;3d@.

g) 
ℂ  ℂ  
ℂ     
3,375 7  7<,31 
  1<,95
3,375 7.3,01
  
7  3,375.3,01 
3,3753,375 3,01 
   
  3,375 3,013,375 

 
 3,3753,0>5 
 3,315 gto
gto  

ℂ    
3,315  
ℂℂ 3,3155
73,315 
 a)  Skrnkhtgek Luoimity

ℂ 733 ℂℂ  
ℂ  7<,31 ,  
1<,95   ,

 
Mgri stkgo tgakf ekghbdpfisgpkhmix G.1-    
G.1-9 mipkrdfklhifgi SG,^ pgmg
d
 pgmg sulu73; @ 

(=3,;dN) gmgfgl 5,><= bSg.

ℂ  7<,31 5,><=  
1<,95 737,>1;5,><=
ℂ 3,3=<<9 
 Hifgi ℂ  mi suastitusi bk mgfgo pkrsgogh ℂ  

ℂ 733 ℂℂ  
 

 
 3,375  
ℂ 733 3,3=<<9
ℂ >=,55% 
n)  Qkfgtivk Luoimity

Mgri erg`ib luoimity nlgrt mipkrdfkl hifgi rkfgtivk luoimity

ℂ ?3,91>%.
m)  ^gturgtidh luoimity
 
Mgri stkgo tgakf ekghbdpfisgpkhmix G.1-    
G.1-9 mipkrdfkl hifgi SG,^ pgmg sulu73; @ 
d

(=3,;dN) gmgfgl 5,><= bSg.

ℂ  7<,31 5,><=  
1<,95 737,>1;5,><=
ℂ 3,3=<<9 
k)  Luoim Pdfuok

ℂ  11,=7
15> . ( 7  7 ℂ) 
1<,95 7<,31
ℂ  1,<>Õ73∑ =,;0Õ73∑ Õ3,375
Õ3,375   
ℂ  1,<>Õ73∑ 5,5;1Õ73∑   
ℂ  1,935;1Õ73∑=3,;15>
=3,;15> 
 
ℂ 3,9733;    

`)  Luoim lkgt

 3,1=3,=;3,375 31=5 

  .
.℉℉ 

e)  Khtlgfpy
Mgri erg`ib luoimty nlgrt mipkrdfkl hifgi:
‱
Khtgfpipgmgsgturgsi l ? <7,> atu/fa mry gir
Mkvigsikhtgfpi M ? -1,>
Khtlgfpy skakhgrhyg l?<7,>-1,>?59 atu/fa mry gir

 
 l)  Gmigagtin-sgturgtidh tkopkrgturk
Mgri tgakf supkrlkgtkm stkgo, mipkrdfkl khtgfpi pgmg 7 gto pgmg akragegi
sulu skagegi akribut:
] ? 733³N, L ? 1050 bJ/be
] ? 7;3³ N, L ? 1550 bJ/be
[mgrg ogsub pgmg sulu 1;3³@ gtgu skbitgr 717³N, ogbg sktkfgl
mifgbubgh ihtkrpdfgsi, L(717³N) ? 157< bJ/be.

 Hkrgng Khkrei:
mW mU 7 7
-
mt mt
( 1
) (
?@Dut L+ez+ v1 -@ih L+ez+ v1  
1
)
  ^istko gmigagtib, ogbg mW/mt ? 3
  ^istko timgb okfgbubgh usglg, ogbg mU/mt ? 3
  ]imgb gmg pkrakmggh bktiheeigh, pkrakmggh bknkpgtgh mgh fgju gfir
Ogbg pkrsgoggh hkrgng khkrei okhjgmi:
Lih ? Ldut? 157< bJ/be
[mgrg bkfugr mgfgo bkgmggh sgturgtkm, mgri tgakf sgturgtkm stkgo,
mipkrdfkl ih`drogsi skagegi akribut:
L ? 157=,; bJ/be, ]sgt ? 710,7³N
L ? 157<,1 bJ/be, ]sgt ? 71<,5³N
Khtgfpi bkfugr ? 157< bJ/be, sktkfgl miihtkrpdfgsi mipkrdfkl ] sgt ? 71<,;³N
(10>,>³@)
Gmigagtin-sgturgtkm stkgo ? 71<,;³N (10>,>³@)

i)  Odfk `rgntidh d` wgtkr ih tlk gir

 . 
3,3157. 
 3,315 

 
 ;.  G oixturk d` hitrdekh ghm gnktdhk vgpdr gt <33 ooLe tdtgf
prkssurk, 1;dN, lgs g pkrnkhtgek
pkrnkhtgek sgturgtidh d` <3%. Ngfnufgtk:
g)  ]lk
 ]lk gasdfutk odfgf
odfgf luoimity.
a)  ]lk
 ]lk gasdfutk luoimity,
luoimity, be gnktdhk/be hitrdekh.

n)  ]lk pgrtigf prkssurk

prkssurk d` gn
gnktdhk.
ktdhk.
m)  ]lk
 ]lk rkfgtivk luoimity.
luoimity.
k)  ]lk vdfuok pkrnkht
pkrnkht gnktdhk.
gnktdhk.
`)   ]lk mkw pdiht.

Skoaglgsgh :
Mibktglui: Ngopurgh Hitrdekh mgh Gsktdh
Mioghg: S ? <33 ooLe
] ? 1;dN

Skrskhtgsk ^gturgsi ? <3%

Mitghyg:  (g). Luoimity odfgf gasdfut.
(a). Luoimity gasdfut, be gnktdhk/be hitrdekh.
(n). ]kbghgh pgrsigf Gsktdh.
(m). Luoimity rkfgti`.
(k). Skrskh vdfuok Gsktdh.
(`). Mkw
(`).  Mkw Sdiht
Skhykfksgigh:

Akrmgsgrbgh ]gakf skakfuohyg, ogbg mgpgt milituhe Hifgi ]kbghgh [gp Gsktdh
 pgmg 1;dN mkhegh okheeuhgbgh Ihtkrpdfgsi. ^kliheeg mipkrdfkl hifgi ]kbghgh [gp
Gsktdh pgmg 1;dN skaksgr 11; ooLe
Okhkhtubgh ]kbghgh [gp Gsktdh (G) pgmg 1;³N akrmgsgrbgh Skrsgoggh Ghtdiht

 
 fh SG,s ?    +  ? 7=,5 +∑,
,  ? >,=
SG,s  ? >3 bSg ? 11; ooLe

g. Odfgf Luoimity (Lo)

Lo 
 y G

 p G

 p G  

odf  G 

 y A  p A  S   p G  odf  A 

 p G  p G 793

Lo   

 p A  S   p G <33  793

Lo ? 3,>77 odf gsktdh/ odf hitrdekh

 a. Gasdfutk luoimity (L), be

be gnktdh/be hitrdekh
  ^gturgtkm Luoimity (Ls)
 p  O   p   O   
L^   G, s
 O  A   S   p G, s
 G, s  G, s
 O  A 
 G
 p A    

 p G, s   O  G   11;  ;< 

L^ 
 
    
 S   p Gs   O  A   <33  11;  1< 

Ls ? 3,<7 be gsktdh/be hitrdekh

  Skrnkht luoimity gasdfutk / sgturgtidh pkrnkhtgek (L p)

L
LS    733%
L^

<3%   
733% L
3,<7

L ? 3,0=<

Ogbg, mimgpgtbgh gasdfutk luoimity skaksgr:

L ? 3,0=< be gsktdh/ be hitrdekh

 
 n. Sgrtigf prkssurk d` gnktdhk

 p G   O   
L    G 
 S   p G   O  A  

 p G  ;< 
3,0=<   
<33   p G  1< 

SG ? 793 ooLe

m. Qkfgtivk luoimity

   p G,  
L Q  733%  
  p 
   G,^  
  793 
L Q  733%  
  11; 

LQ   ? <=,== %

k. vdfuok pkrnkht gnktdhk

Lo ? 3,>77 odf gsktdh/ odf hitrdekh
Pdfuok gsktdh (^]S) ? 3,>77 x 11,= ? 0,95 o> 
Pdfuok hitrdekh (^]S) ? 11,= o > 
S1 ? 7 gto ? 503 ooLe
]1 ? 15> B
S7 ? <33 ooLe
]7 ? 1;³N ? 19< B
Pdfuok gsktdh pgmg sulu 1;³N
     
 
     
  50315><33
0,95  19< 
  5,11<
11< o >

 
 Pdfuok hitrdekh pgmg sulu 1;³N

  50315><33
11,=  19< 
  1>,1
1>,1>> o>

Pdfuok tdtgf ? vdfuok gsktdh + vdfuok hitrdekh

? 5,11< + 1>,1>

? >3 ,=;< o>

% vdfuok gsktdh ?
    733% 
 
?
,   733 % 
,
? 1>, 5> %

0.  Sgpkr is akihe mrikm witl rknirnufgtihe gir ih g twd-stgek mryihe

systko dpkrgtihe gt 7 gto. ]lk gir khtkrs tlk `irst mrykr gt 7<3 d@,
wlkrk tlk gir is gmigagtingffy
gmigagtingffy sgturgtkm witl odisturk. ]lk gir is tlkh
rklkgtkm ih g lkgt kxnlghekr td 75= d@ ak`drk khtkrihe tlk skndhm
mrykr, wlkrk tlk gir is gmigagtingffy luoimi`ikm td <3% rkfgtivk
luoimity. ]lk gir is tlkh nddfkm td 03 d@ ih g skndhm lkgt kxnlghekr,
ngusihe sdok d` tlk odisturk td ak ndhmkhskm. ]lis is `dffdwkm ay g
tlirm lkgtkr td lkgt tlk gir td 7<3 d@ ak`drk it rkturhs td tlk `irst
mrykr.
 
g) Mrgw g prdnkss-`fdw migergo d` tlk systko ghm khtkr gff d` tlk eivkh
mgtg.
a)  Mktkroihk tlk fa L1D kvgpdrgtkm ih kgnl mrykr pkr fa d` mry gir akihe
nirnufgtkm.
n)  Mktkroihk tlk fa L1D ndhmkhskm ih tlk skndhm lkgt kxnlghekr pkr fa
d` mry gir nirnufgtkm.

Skoaglgsgh : 

Mibktglui:  Bkrtgs gbgh mibkrihebgh mkhegh [mgrg Qksirbufgsi mkhegh 1 ]glgp

Skhekrihegh.
 

 
 Mioghg: S ? 7 gto
[mgrg ogsub pgmg Skhekrihe Skrtgog pgmg ] ? 7<3 d@
Mitghyg:  (g). Migergo Gfir
(a). Juofgl gir yghe miugpbgh
Skhykfksgigh:
g. `fdw migergo
D
]?75= @
D
D LQ?<3%   ]?03 @
]?7<3 @
M7   M1
S? 7 gto

D
]?7<3 @

 a. Mrykr 7
ℂ  7<,31   
1<,95   
]? 75= ℉ ↑5<,9ℎ 
ℂ 733 ,  
  
3,<733 =;,=;
 >0,>0  
7<,31 >0,>0  
ℂ  1<,95 737,>>0,>0
  
ℂ3,>=   
 3,50;  
ℂ  3,>=  Õ 3,=;;;9 
Mrykr 1

ℂ3,01   
]? 03 ℉ ↑ 7;,0 ℎ 
 

 
 ℂ 733 ,  
3,<733 7,5  
  7,>0  
>0 
7,>0  
ℂ3,01 737,>7,>0
  
ℂ3,3<   
  3,37<0
ℂ  3,3<  Õ 3,=;;;9  37<0 
 
5.  Nduhtkrnurrkht Ugtkr-Nddfihe ]dwkr, G @drnkm-mrg`t nduhtkrnurrkht wgtkr-
nddfihe tdwkr is td nddf wgtkr `rdo =>.> td 10,5N. ]lk gir khtkrs tlk adttdo
d` tlk tdwkr gt 1>,9N witl
witl g wkt aufa tkopkrgturk d` 17.7N. ]lk Pgfuk d`
d` LE
`dr tlk `fdw ndhmitidhs is L E ? 3,;>> o. ]lk lkgt-trghs`kr rksistghnk ih tlk
fiquim plgsk wiff ak Hkefkntkm27.k, h F is vkry fgrek. Okhnk, vgfuk d` L,
sldufm ak uskm, ngfnufgtk tlk tdwkr lkielt hkkmkm i` 7,; tioks tlk oihiouo
gir rgtk is uskm.
Skoaglgsgh : 

Mibktglui:  okhgrg pkhmiheih gir gfirgh nduhtkrnurrkht mrg`t pgbsg gmgfgl

uhtub okhmiheihbgh gir mgri =>,>N bk 10,5N
Mioghg: LE ? 3,;>> o
[mgrg ogsub pgmg Skhekrihe Skrtgog pgmg ] ? 7<3 d@
Mitghyg:  okhngri hifgi L, uhtub okhelituhe bktiheeigh okhgrg yghe
mipkrfubgh jibg 7,; bgfi fgju oihiouo mieuhgbgh4
Skhykfksgigh:
]E1  ]F1?=>,>N 

]E7?1>,9N  ]F7?10,5N 

 
 LE ? 3,;>> o hkefknt fiquim plgsk
Qksistghnk. [sk L1 y vgfuks.
]E7 ? 1>,9N (wkt aufa ? 17,7N)
L7 ? 3,37=; be L1D/be mry gir
Mkhegh Skrsgoggh Quous (9.>-9)
L y7 ? (7,33; + 7,<< * 3,37=;)73> (1>,9-3)+ 1,;37= *730 (3,37=;)

? 03,9= *73> mi ]F7 ? 10,5 N

Kpknt mgtg `rdo ]gakf 73.;-72
Sfdt Oihiouo fkrgf ghm rkgm d`` Ly1 ? 797 * 73 > mi ]F1 ? =>,> N
Skrsgoggh (73.;-1)
E (Ly1 „ 
(Ly1 „  Ly7)
 Ly7) ? FnF (]F1- ]F7)
Eoih (797
 (797 „  03,9=) 73> ? F (=,7<< * 73>) (=>,>-10,5)
 „  03,9=)
F/ E ? 7,<57
Euhgbgh 7,;3 Eoih
   ? , ? 7,1=<
 ,
Skrsgoggh (73.;-1)
 03,9= * 73> ) ? (7,1=<) (=,7<< * 73> ) (=>,>-10,5)
( Ly1 „ 
Ly1 „  03,9=
Ly1 ? 7=5,0< * 73> 
Sfdt hkw pdiht Ly1 ? 7=5,0< * 73 > mgh ]F1 ? =>,> m
]F L*y Ly Ly*-Ly 7/(Ly*- Ly)
10,5N <=, 3< * 73>  03,9= * 73>  1>,30 * 73>  =,>> * 73 -; 
>3 733,3 5<,3 71,3
71,3 =,;=;
>= 711,< 99,3 1>,<
1>,< =,133

>0 7>0,3 739,> 10,5 >,5=;

>< 7;3,3 779,5 >3,> >,>33
=3 705,3 7>3,3 >5,3 1,5=;
=1 7<;,3 7=3,> ==,5 1,1>5
=>,> 795,1 7=5,0< =9,;1 1,739

(73.;-7) „  S.1
(73.;-7) „  S.1
Sfdt 7 / (Ly*- Ly) vk Ly Ihtkergtk
Skrsgoggh (73.;-70)

Z ? LE 
?,∕    
∢?,∕ ∕∑

 
 grn ? >,7<<
Z ? LE (grn) ? 3,;>> (>,7<<) ? 7,53 o
Erg`ib 7.

 
 Erg`ib1.

<.  Oihiouo Egs rgtk ghm lkielt d` wgtkr-nddfihl tdwkr. It is pfghhkm td nddf
wgtkr `rdo 773@ td <;@ ih g pgnbkm nduhtkrnurrkht wgtkr-nddfihe tdwkr usihe
khtkrihe gir gt <;@ witl g wkt aufa tkopkrgturk d` 5;@. ]lk wgtkr `fdw is
1333 fao/l.`t1 ghm tlk gir `fdw is 7=33 fao/l.`t 1 . ]lk dvkrgff ogss trghs`kr
>.
ndk``inikht isB E g ? 0,93 fa odf/l.`t gto
(g)  Ngfnufgtk tlk oihiouo gir rgtk tlgt ngh ak uskm
(a)  Ngfnufgtk tlk tdwkr lkielt lkielt hkkmkm i` tlk gir `fdw 7=33fao gir/l.`t 1
is uskm
Skoaglgsgh : 

Mibktglui:  Fgju egs oihiouo mgh bktiheeigh okhgrg gir pkhmiheih.

Mirkhnghgbgh uhtub okhmiheihbgh gir mgri 773@ bk <;@ mgfgo okhgrg
 pkhmiheih gir akrfgwghgh grus
Mioghg: Gfirgh gir ? 1333 fao/l.`t 1

 
 Gfirgh umgrg ? 7=33 fao/l.`t1
B E g ? 0,93 fa odf/l.`t> . gto

Mitghyg:  (g) Lituhe fgju umgrg oihiouo yghe mimgpgt4

(a) Lituhe bktiheeigh okhgrg yghe miautulbgh jibg Gfirgh
umgrg ? 7=33 fao/l.`t 1 mieuhgbgh4

Skhykfksgigh:
]E1  ]F1?773@ 

]E7?<;@  ]F7?<;@ 

(73.;-1)
F ? 1333 fao/l.`t1 
E ? 7=33 fao gir /l.`t1
B E g ? 0,93 fa odf/l.`t> . gto
]wkt Aufa ihfkt gir ? 5;@
L7 ? 3,370; fa wgtkr/fa mry gir (pkrsgoggh 9.>-1)

Skrsgoggh (9.> „ 
(9.> „  <)
 <)
Ly ? (3,1= + 3,=; L) ( ]- ]d @) + Lyd
Ly7? (3,1= + 3,=; * 3,370;) (<;->1) + 735;,= (3,370;) ? >3,< fa/fao mry gir
(g)  Oihiouo gir rgtk
^gturgtkm khtgfpi mgri tgafk 73.;-7 gmgfgl pfdt Ly mkhlgh ] F7
]lk pdiht Ly7? >3,< mgh ]F7? <;@ gmgfgl pfdt
Egris oihiouo E gmgfgl pfdt
pfdt mioghg dpkrgsi mi ]F1 ? 773@
773@
Ly1 ? <=,> V
(pkrsgoggh 73.;-1)

 
 E ( Ly1-Ly7) ? Fnf (]F1-]F7)
E (<=,>->3,<) ? 1333 (7,3) (773-<;)
E oih ? 9>; f fao gir /l.`t 1 (=1=) be/ l o1 
(a)  Dpkrgsi E ? 7=33
7=33 (Ly1->3,<) ? 1333 (7,3) (773-<;)
Ly1? 00,5 atu/fa o
Sfdt Ly1, ]F1 mi
mi ]F mgh augt pfdt mgri 7/ L*-Ly mkhegh Ly
]F  L*y Ly L*-Ly 7/L*- Ly
<; =7,< >3,< 77,3 3,393<
93 =< >< 73,3 3,733
9; ;;,> =;,1 73,7 3,399
733 0>,5 ;1,= 77,> 3,3<;;
3,3<;;
73; 5>,< ;9,; 7=,7 3,3573
3,3573
773 <=,; 00,5 75,< 3,3;01
3,3;01

Skrsgoggh (73.;-7<)

Z
?,    >,71(grn)
∢?, ∕∑
Skrsgoggh (73.;-7<)

 ∕
Z?
   ∢
  ?  (>,71)
    ∕∑ ,, 
Z? 17,< `t (0,0= o )