Instrumentation and Control (By Waqas Ali Tunio)
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Transcript of Instrumentation and Control (By Waqas Ali Tunio)
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8/9/2019 Instrumentation and Control (By Waqas Ali Tunio)
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7
Wygkc$i$Gzgd Y`kxi~vks{ oh I`jk`ii~k`j%
Vfki`fi ( Sifa`oeoj{% @gzgnvaga
K`vs~ydi`sgsko` ( Fo`s~oe Fegvv Zo~m
VYNDKSSIC SO C^.GESGH ^GB\I^
N[ ZGWGV GEK SY@KO !
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Zgwgv Gek Sy`ko !
K@VS^YDI@SGSKO@ ( FO@S^OE
K`vs~ydi`s2 G` k`vs~ydi`s dg{ ni cih k`ic gv cixkfi ho~ cisi~dk`k`j sai xg eyi o~
dgj`ksyci oh wyg`s ks{ o~ xg~ kgnei.
K`vs~ydi`sgs ko`2 Sai |~ofivv oh digvy~ k`j sai |a{v kfg e wyg`s ks kiv % n{ dig`v oh
k`vs~ydi`s kv fg e eic k`vs~ydi`sgs ko`.
Onbifs kxiv2 Onbifs kxiv oh k`vs~ydi`sgs ko` kv so jis digvy~idi`s oh civ k~i wyge k s{
g`c wyg`s ks{ n{ vgxk`j sai i`i~j{% dgk` |ozi~ gv zie e gv xivs kjiv gffo~ck`j so
fo`s~oe eic dg``i~.
Digvy~idi`s2 Zi g~i doxk`j k` sags vynbifs % zakfa ~ig e e{ cigev zksa digvy~idi`s
oh |a{v kfg e wyge k s kiv % e kmi sid|i~gsy~i% |~ivvy~i% ho~fi% v|iic% fy~~i`s % |osi`s kg e
~iv kvsg`fi% fg|gf ksg`fi g`c dg{ do~i.
S{|iv oh K`vs~ydi`sv
Sai~i g~i dgk` e{ hoy~ s{|iv oh k`vs~ydi`sv .
7. Difag`kfg e e{ O|i~gsic2 Sai k`vs~ydi`sv zakfa g~i o|i~gsic difag`kfg e e{
e kmi jig~v % nies % fag k`% ~o|i% eixi~v oh c k h hi~i`s dgfak`iv isf g~i difag`kfg e e{
o|i~gsic k`vs~ydi`sv .
>. I eifs~ kfg e e{ O|i~gsic2 Sai k`vs~ydi`sv zakfa g~i o|i~gsic n{ dig`v oh
i eifs~ kf k s{ g~i fg e eic gv i eifs~ kfg e e{ o|i~gsic k`vs~ydi`s.
6. A{c~gye kfg e e{ O|i~gsic2 Saivi k`vs~ydi`sv g~i o|i~gsic k` vyfa g dg``i~
sags zgsi~ o~ a{c~gye kf |~ivvy~i kv j kxi` so k`vs~ydi`s% sai` sai{ zk e e zo~m % e kmi
f{e k`ci~v oh f~g`i% n~igmv oh xiakf eiv .
3. \`iydgskfg e e{ O|i~gsic2 K`vs~ydi`sv g~i o|i~gsic n{ g k~ |~ivvy~iv g~i
fg e eic |`iydgs kfg e e{ o|i~gsic k`vs~ydi`sv .
Fegvvkhkfgsko` oh K`vs~ydi`sv
Fegvv k h kfgs ko` oh k`vs~ydi`sv hg e ev k` ho e eozk`j fgsijo~ kiv .
7. Gfs kxi / \gvv kxi
>. @ y e e / C ih eif s ko`
6. Do`kso~ k`j / Fo`s~oe
3. G`geoj / Ckj ksg e
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Zgwgv Gek Sy`ko !
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Zgwgv Gek Sy`ko !. @ye e/Cihifs ko`2 @ye e s{|i k`vs~ydi`sv g~i saovi k` zakfa wyg`s ks{ nik`j
digvy~ic kv cisi~dk`ic n{ sai zikjasv ~iwyk~ic so doxi sai | kvso`% gv vaoz` k`
h kjy~i.
Zikjas
\kvso`
!Cigc Zikjas \~ivvy~i Jgyji+@ye e s{|i k`vs~ydi`sv g~i do~i gffy~gsi sai cih eifs ko` s{|iv.
Cih eifs ko` s{|iv k`vs~ydi`sv g~i saovi k` zakfa wyg`s ks{ nik`j digvy~ic k` si~dv
oh gdoy`s oh doxidi`s oh g |ok`si~ . K sv iqgd|ei kv vgdi gv k` |gvv kxi s{|i
k`vs~ydi`sv .
Do`kso~k`j/Fo`s~oe 2 Sai do`kso~ k`j k`vs~ydi`sv o`e{ j kxi g` k`ckfgs ko` oh sai
dgj`ksyci oh sai wyg`s ks{ % zakfa g~i digvy~ k`j. Saivi s{|iv oh k`vs~ydi`sv o`e{
j kxi o` gycko o~ x kvyg e k`ckfgs ko` vyfa gv e kwykc k` j egvv sai~dodisi~.
Sai fo`s~oe k`vs~ydi`s k`vsigc oh o`e{ dgj`ksyci oh wyg`s ks{ % sai{ g evo |~oxkci
gysodgs kf fo`s~oe . Sai iqgd|ei oh fo`s~oe e k`j k`vs~ydi`s kv g sai~do foy|ei.
G`geoj/Ckj k sg e 2 G` g`geoj k`vs~ydi`s j kxi g` oys|ys % zakfa xg~ kiv fo`s k`yoyve{ gv
sai wyg`s ks{ nik`j digvy~ic. Sai oys|ys oh vyfa k`vs~ydi`sv agxi k`h k` ksi `ydni~
oh xg eyiv zksa k` v|if kh kic ~g`ji oh sai k`vs~ydi`sv .
Sai cih eifs ko` s{|i oh |~ivvy~i jgyji kv sai iqgd|ei oh g`geoj k`vs~ydi`sv .
G c kj ksg e k`vs~ydi`s agv g` oys |ys zakfa xg~ kiv k` c kvf~isi vsi|v g`c vo fg` o`e{
agxi g h k` ksi `ydni~ oh xg eyiv. Sai ~ix$foy`si~ vmisfaic k` h kjy~i kv g` iqgd|ei oh
c kj ksg e k`vs~ydi`s.
Vzksfa Foy`si~
!^ix$Foy`si~+ fgd
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Zgwgv Gek Sy`ko ! ng~ |~ocyfiv g cih eifs ko` oh 7< cij~iiv k` |~ivvy~i
s~g`vcyfi~ % sai` vi`v ks kx k s{ oh sai k`vs~ydi`s kv 9 cij~iiv/ng~ .
o Ri~o C~k h s 2
Ri~o c~ k h s civf~ kniv sai ihhifs zai~i sai ri~o ~igck`j oh g`
k`vs~ydi`s kv dockh kic n{ g fag`ji k` gdnki`s fo`cks ko`v. S{|kfg e y`ksv n{ zakfa
ri~o c~ k h s kv digvy~ic g~i xoesv/Q
H4!DC>
- NC - M+Q $Dj
Sakv kv sai iwygsko` ho~ sai sosge ho~fiv gfsk`j o` sai v{vsid. Ho~ fo`s~oe zo~m% ks kv yvygee{ do~i
fo`xi`ki`s so dgmi digvy~idi`sv zksa ~iv|ifs so vodi ~ihi~i`fi o|i~gsk`j |ok`s.
H 4 Hk -
Q
M N
! n +
! g + kjy~i >.3 Vi~kiv dgvv$v|~k`j$cgd|i~ fodnk`gsko`
Sai ho~fi iwygsko` gs sai ~ihi~i`fi o|i~gsk`j fo`cksko` kv
Hk 4 MQk Dj Vyns~gfsk`j sai iwygsko` h
sai ho~fiv gs sai ~ihi~i`fi |ovksko` h~od sags ho~ sai sosge ho~fiv jkxiv sai iwygsko` oh o|i~gsko` ho~
fag`jiv gnoys sai ~ihi~i`fi |ovksko . Sags kv%
H Hk 4!DC>
- NC+Q - M!Q Qk+
Sai |~ifick`j iwygsko` oh o|i~gsko` ho~d zksa ~iv|ifs so sai ~ihi~i`fi |ovksko` dg{ sayv ni z~kssi` k`
sai ho~d.
h 4 !DC>
- NC - M+q
Sakv ~ivyes foyec agxi nii` onsgk`ic ck~ifse{ n{ vyddk`j sai fag`ji k` ho~fiv h~od sai ~ihi~i`fi
o|i~gsk`j fo`cksko`. Sai neofm ckgj~gd ho~ Iw.!>.7:+ kv vaoz` k` Hkj. >.3n.
^osgsko`ge V{vsidvG so~vko`ge v|~k`j kv fag~gfsi~kric n{ sai iwygsko`
Sv 4 MvYZai~i Sv 4 so~wyi si`ck`j so szkvs v|~k`j
Mv4 so~vko`ge v|~k`j ~gsi
Y 4 g`jyeg~ ckv|egfidi`s oh v|~k`jG ziee$m`oz` iqgd|ei oh g so~vko`ge v|~k`j kv g vaghs gv kv vaoz` k` Hkj. >.9. Sai ~kjas i`c oh sai vaghs kv
ckv|egfic g` g`jeiY zksa ~iv|ifs so sai eihs i`c nifgyvi oh sai szkvsk`j so~wyi Sv. Ho~ g vs~gkjas vaghs% sai
so~vko`ge v|~k`j ~gsi kv
Mv 4 Sc3J
6>E
D7
DC> NC-M
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Zgwgv Gek Sy`ko !.8 So~vko`ge k`i~skg$v|~k`j$cgd|i~ fodnk`gsko`
Ieifs~kfge fod|o`i`svSai ~ivkvso~% k`cyfso~% g`c fg|gfkso~ g~i sai sa~ii ngvkf fod|o`i`sv oh ieifs~kf
Fk~fyksv% Sai iwygsko` ho~ sai xoesgji c~o| I^ gf~ovv g ~ivkvso~ kvI^ 4 ^K
Zai~i ^ kv sai ~ivkvsg`fi k` oadv g`c K kv sai fy~~i`s heozk`j sa~oyja sai ~ivkvso~
K` gd|i~iv
Ho~ g` k`cyfso~% sai xoesgji c~o| IE kv jkxi` n{ sai iwygsko`
IE 4 EcK
4 ECK
cs
Zai~i E kv sai k`cyfsg`fi k` ai`~{v.
Vkdkeg~e{% sai xoesgji c~o| If gf~ovv g fg|gfkso~ kv
If 4 7 K cs 4 7 KF FC
Zai~i F kv sai fg|gfksg`fi k` hg~gcv.
Sai ckgj~gddgskf ~i|~ivi`sgsko v oh Iwv. >.>> so >.>3 g~i vaoz` k` Hkj.>.:
I^ IE IF- - -
7
BC> -Nx C-Mv
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Zgwgv Gek Sy`ko !.: ^i|~ivi`sgsko` oh g ~ivkvso~% k`cyfso~% g`c fg|gfkso~
^EF fk~fyksHo~ sai ^EF fk~fyks vaoz` k` Hkj.>.>1g% sai sosge xoesgji c~o| I kv sai vyd oh sags gf~ovv sai k`cyfso~ I E%
sags gf~ovv sai ~ivkvso~ I^% g`c sags gf~ovv sai fg|gfkso~ If2
I 4 IE - I^ - If 4 ! EC - ^ - 7 +K
FC
Sai fag~ji W kv sai skdi k`sij~ge oh sai fy~~i`s% sags kv% W 4!7/C+K oh K4CW n{ `osak`j sags ECK 4EC>W% ^K
4^CW% g`c!7/FC+K 4!7/F+W% sai` Iw% >.>9 nifodiv
I 4 ! EC>
- ^C - 7 +W
F
Sai oxi~gee neofm$ckgj~gd ~i|~ivi`sgsko` ho~ sakv ^EF fk~fyks kv vaoz` Hkj% >.1n
I
IE I^ IF-
!g+ K E ^ F
7 / ^
7 /EC
FC
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Zgwgv Gek Sy`ko !.1 ^EF vi~kiv fk~fyks
Vi~kiv g`c \g~geeie egzvIeidi`sv g~i yvygee{ fo``ifsic k` iksai~ g vi~kiv o~ g |g~geeie g~~g`jidi`sv . G~~kxk`j gs sai iwygsko` ho~
vyfa v{vsid fg` ni j~igse{ vkd|ekhkic n{ yvi oh sai egzv ho~ vi~kiv g`c sai egzv ho~ |g~geeie fodnk`gsko` .
Vi~kiv ieifs~kf fk~fyksvG ji`i~ge vi~kiv fk~fyks kv vaoz` k` Hkj.>.;g. K` g vi~kiv fk~fyks sai sosge xoesgji c~o| I kv sai vyd oh sai
k`ckxkcyge xoesgji c~o|v gf~ovv igfa ieidi`s% g`c sai vgdi fy~~i`s K heozv sa~oyja igfa ieidi`s. Sai
iwygsko` ho~ sai vyddgsko` oh sai xoesgji c~o|v kv
I 4!E7C - E>C - ^7 - ^> - 7 - 7 +K
F7 C F> C
Sai iwygsko` ~iegsk`j sai xoesgji I g`c fy~~i`s K ho~ g`{ ieifs~kf fk~fyks fg` ni iq|~ivvic k` sai ho~d
I 4R K
R 4 E7C - E>C - ^7 - ^> -7
-7
+K
F7 C F> C
Sai neofm$ckgj~gd ~i|~ivi`sgsko` kv vaoz` k` Hkj%>.;n
I
7
> - -
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Zgwgv Gek Sy`ko !
-
K E7 E> ^7 ^> F7 F>
!g+
I K
!n+ Hkjy~i >.; Ji`i~ge vi~kiv fk~fyks
\g~geeie Ieifs~kf Fk~fyksv
G ji`i~ge fodnk`gsko` oh ieifs~kf ieidi`sv k` |g~geeie kv vaoz` k` Hkj.>.7C ^7 ^> 7/F7C 7/F> C
o~I 4
7K4RK
7/E7C - 7/ E>C - 7/^7 - 7/^> - F7C - F> C
Sai kd|icg`fi R kv
R 4 7
7/E7C - 7/ E>C - 7/^7 - 7/^> - F7C - F> C
Sai neofm$ckgj~gd ~i|~ivi`sgsko` kv vaoz` k` Hkj. >.7
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Zgwgv Gek Sy`ko ! ^7 ^> F7 F>
!g+
I K
!n+ Hkjy~i >.7< Ji`i~ge |g~geeie fk~fyks.
J~oy`cic$Fagk~ ^i|~ivi`sgsko`
Sai ji`i~ge |~oficy~i ho~ fo`vs~yfsk`j sai j~oy`cic$fagk~ ~i|~ivi`sgsko` kv gv hoeeoz.
7. C~gz foo~ck`gsiv vyfa sags sai foo~ck`gsi gs zakfa sai ho~fi gfsv kv gs sai so| g`c j~oy`c kv gssai nossod.
>. K`vi~s igfa ieidi`s k` ksv fo~~ifs o~ki`sgsko` zksa ~iv|ifs so saivi foo~ck`gsiv.
q M {
M7 M>
N
!g+
q
7 / R
D7 D>
q
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Zgwgv Gek Sy`ko !
Hkjy~i >.78 Ji`i~ge Difag`kfge v{vsid
Ho~ sai v{vsid vaoz` k` Hkj >.78g% sai foo~ck`gsiv g~i q% {% g`c j~oy`c Vsi| 7 kv fg~~kic oys n{ c~gzk`j
sai foo~ck`gsiv gv vaoz` k` Hkj. >.78n. So co Vsi| > zi dyvs `osi sags ho~ sai v|~k`j M 7 g`c dgvv D7 sai
foo~ck`gsiv g~i q g`c j~oy`c% ho~ sai v|~k`j M g`c cgd|i~ N sai foo~ck`gsiv g~i . g`c {% g`c hk`gee{ ho~ sai
dgvv D> g`c v|~k`j M> sai foo~ck`gsiv g~i { g`c j~oy`c. K`vi~sk`j saivi ieidi`sv niszii` sai |~o|i~
foo~ck`gsiv gv vaoz` k` Hkj. >.78f fod|eisiv sai j~oy`cic$fagk~ ~i|~ivi`sgsko`. Sai vi~kiv g`c |g~geeie
fodnk`gsko`v g~i `oz ~ifoj`kric ck~ifse{ h~od sakv j~oy`cic$fagk~ ~i|~ivi`sgsko`. Sai iwygsko` ho~ sai
ho~fi kv
4] D7 C>
- M7 - 7 Tq7/! M - NC + - 7/!M> - D> C
>+
G`geojkiv
Sai iwygsko` oh o|i~gsko` ho~ sai vi~kiv difag`kfge v{vsid oh Hkj. >.3g kv jkxiv n{ Iw. !>.7:+% g`c sai
iwygsko` ho~ sai vi~kiv ieifs~kf fk~fyks oh Hkj. >.1g kv jkxiv n{ Iw. !>.>8+. Sags kv%
4 ! DC>
- NC - M +q
I 4 !EC> - ^C - 7 + W
F
Fod|g~kvo` oh fo~~iv|o`ck`j si~dv k Iwv. !>.7:+ g`c !>.>8+ vaozv sags sai ckhhi~i`skge iwygsko` oh
o|i~gsko` ho~ igfa v{vsid agv sai vgdi ho~d. Sai si~d zkfa offy|{ fo~~iv|o`ck`j |ovksko`v g~i fgeeic
g`geojoyv wyg skskiv. Sakv |g~skfyeg~ g`geoj kv ~ihi~~ic so gv sai ck~ifs g`geoj. Sai g`geojoyv wyg`skskiv ho~
ck~ifs g`geoj g~i vaoz` k` Sgnei >.7.
Sgnei >.7G`geojoyv wyg`skskiv k` g ck~ifs !ho~fi$xoesgji+ g`geoj
S~g`vegsko`gedifag`kfge
v{vsid
Ho~fi
Xieofks{
Q 4 Cq
Ckv|egfidi`s
q
Dgvv
D
Xkvfoyvcgd|k`j
foihhkfki`s
N
V|~k`jfo`vsg`s
M
Ieifs~kfge
v{vsid
Xoesgji Fy~~i`s Fag~ji K`cyfsg`fi ^ivkvsg`fi ^ifk|~ofge
oh
fg|gfksg`fi
D7 D>{
! f+! n+
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Zgwgv Gek Sy`ko !.>.
Sgnei >.> G`geojoyv wyg`skskiv k` g` k`xi~vi !ho~fi$fy~~i`s+ g`geojS~g`vegsko`ge
difag`kfge
v{vsid
Ho~fi
Xieofks{
q
V|~k`j
fo`vsg`s
M
Cgd|k`j
foihhkfki`s
N
Dgvv
D
Ieifs~kfge
v{vsid
Fy~~i`s
K
Xoesgji
I
^ifk|~ofge
Oh
k`cyfsg`fi
K
E
^ifk|~ofge
Oh
~ivkvs`gfi
K
^
Fg|gfksg`fi
F
Sai iwygsko` oh o|i~gsko` ho~ sai |g~geeie difag`kfge v{vsid.
C 7 7
Q 4 - -
M N DC
Sai o|i~gsko` oh sai vi~kiv ieifs~kf fk~fyks.
I 4 EC - ^ -7
K
FC
Fod|g~kvo` oh fo~~iv|o`ck`j si~dv k` Iwv. !>.>9+ g`c !>.31+ {kiecv sai g`geojoyv wyg`skskiv ho~ g` k`xi~vi
g`geoj sai g~i vaoz k` Sgnei. >.>.
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Zgwgv Gek Sy`ko !.7: G`geojv !g+ difag`kfge fk~fyks !n+ ck~ifs g`geoj !f+ k`xi~vi g`geoj.
Sai iwygsko` o~ o|i~gsko` ho~ sai difag`kfge v{vsid
47
q 4M !DC> - NC+
q
7/M - 7/!DC>
-NC + DC> - NC - M7
Sai iwygsko` oh o|i~gsko` ho~ sai ieifs~kf fk~fyks.
I 4 EC -7
K
FC - 7/^
O~ K47
I 47
I
EC - 7/!FC>
- 7/^+ E- 7/]F>
- !7/^+CT C
!7/E+ ]FC>
- !7/^+CT I
FC> - !7/^+C - 7/E C
I
D
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Zgwgv Gek Sy`ko !
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Zgwgv Gek Sy`ko !.:: zksa Iw. >.:9 g`c oh Iw. >.:1 zksa Iw. >.:8 vaozv sai hoeeozk`j wyg`skskiv so ni
g`geojoyv2
S p I W p K
^S p ^ FS p F
Sakv kv sai ck~ifs% o~ sid|i~gsy~i$xoesgji% g`geoj. Sai iwygsko` oh o|i~gsko` ho~ sakv sai~dge fk~fyks kv
W 4S7
S
4 FS CS
^S
Voexk`j ho~ S jkxiv
S4S7
7 - !^S FS + C
Sai ieifs~kf fk~fyks zakfa kv sai ck~ifs g`geoj oh sai sai~dge fk~fyks kv vaoz` k` Hkj >.71f
Sai iwygsko` oh o|i~gsko` ho~ sai ieifs~kf fk~fyks kv
K 4I7 I
4 FCI
^
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Zgwgv Gek Sy`ko !.:9 g`c >.:8 ~ixigev sai hoeeozk`j g`geojoyv ~iegsko`vak|v2
S p K W p I
^S p7
FS p E
^
Sai iwygsko` oh o|i~gsko` ho~ sai k`xi~vi g`geoj Hkj >.71c kv
I 4 ^ !K7 K+ 4 ECK
Voexk`j ho~ K jkxiv
K 4K7
7 - !E / ^+C
Ho~ g`{ fk~fyks% sai~i g~i nys szo |ovvknei g`geojv2 sai k`xi~vi g`geoj k` zakfa sai vi~kiv$|g~geeie
g~~g`jidi`s kv k`xi~sic% g`c sai ck~ifs g`geoj k` zakfa sai vi~kiv$|g~geeie g~~g`jidi`s kv ~isgk`ic.
Heykc v{vsidvK` zo~mk`j zksa heykc v{vsidv% ks kv `ifivvg~{ so ckvsk`jykva kh sai heykc kv k`fod|~ivvknei o~ fod|~ivvknei.
Ho~ k`fod|~ivvknei heykcv% ks vyhhkfiv so zo~m zksa sai xoeydi ~gsi oh heoz. Ho~ fod|~ivvknei heykc% ks kv
`ifivvg~{ so zo~m zksa sai dgvv ~gsi oh heoz.
K`fod|~ivvknei Heykcv
Zai` sai |~ivvy~i ckhhi~i`fi gf~ovv g heoz ~ivs~kfsko` kv vdgee% sai xoeydi ~gsi oh heoz W kv |~o|o~sko`ge so
sai |~ivvy~i c~o| \7 \ gf~ovv sai ~ivs~kfsko`2
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Zgwgv Gek Sy`ko !Q 6Q s!n+
Hkjy~i 6.77 ^iv|o`vi oh hk~vs o~ci~ v{vsid so g y`ks vsi| hy`fsko`.
Gv vaoz` k` Hkj. 6.77n% sai veo|i oh sai sg`ji`s ek`i gs s 4 < kv M/Q. Sai si~d Q kv fgeeic sai skdi fo`vsg`sg`c kv g digvy~i oh sai v|iic oh ~iv|o`vi zai` Q kv vdgee% sai v{vsid g||~ogfaiv ksv `iz o|i~gsk`jfo`cksko` xi~{ hgvs g`c zai` Q kv eg~ji. Do~i skdi kv ~iwyk~ic ho~ sai fag`ji so offy~.
Neofm$ckgj~gd gejin~gKs kv ohsi` civk~gnei so ~ig~~g`ji sai ho~d oh g neofm ckgj~gd. K` Hkj 6.>7 kv vaoz` g `ydni~ oh
~ig~~g`jidi`s zakfa g~i foddo`e{ id|eo{ic. ks kv so ni `oskfic sags k` gee fgviv sai ~ig~~g`jidi`s coiv
`os ghhifs sai oxi~gee ~iegsko`vak| niszii` sai k`|ys ieidi`sv !k.i.% ieidi`sv zksa g~~ozaigcv |ok`sk`j
k`so sai ckgj~gd+ g`c sai oys|ys ieidi`sv !k.i.% ieidi`sv zksa g~~ozaigcv |ok`sk`j gzg{ h~od sai
ckgj~gd+. Sai~i g~i dg`{ |ovvknei ~ig~~g`jidi`sv ho~ v{vsidv. Aozixi~% ks kv yvygee{ civk~gnei so dgmi
sai yeskdgsi ho~d oh sai neofm ckgj~gd sai vgdi gv sags vaoz` k` Hkj. 6.>>. sai ~igvo` ho~ sakv kv sags sai
disaocv so ni |~ivi`sic egsi~ ho~ ixgeygsk`j sai |i~ho~dg`fi oh v{vsidv g~i ngvic o` v{vsid zakfa g~i
~i|~ivi`sic sk` sakv ji`i~ge ho~d.
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Zgwgv Gek Sy`ko !7
f
!g+ g - !g n+- g$ n$ f g - g$n$f
$ $
n f n
g $n
!n+ g - gJ !C+$n g - J !C+ g J !C+ n
n
n
!f+ g - !g$n+ J !C+ g - !g$n+ J !C+
n
n
!c+ g n 4gJ !C+ g n
n
n
!i+ g n 4 gJ !C+ g n
g
f 4 ]g f A!C+T J !C+ gJ!C+g
o~ f 47-J !C+ A !C+
!h+ g - g f
n4fA !C+
J !C+ J !C+
7/J !C+
J !C+ J !C+
J !C+
J !C+
J !C+
J !C+
J !C+ J !C+
7/J!C+
J !C+
A !C+
J !C+7-J !C+ A !C+
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Zgwgv Gek Sy`ko !>
Hkjy~i 6.>7 Iwykxgei`s neofm ckgj~gdv2 !g+ fodnk`k`j k`si~fo``ifsic vyddk`j |ok`sv !n+ doxk`j g
vyddk`j |ok`s niak`c gv ieidi`s% !f+ doxk`j g vyddk`j |ok`s gaigc oh g` ieidi`s% !c+ doxk`j g sgmi$ohh
|ok`s niak`c g` ieidi`s% !i+ doxk`j g sgmi$ohh |ok`s gaigc oh g` ieidi`s% !h+ iekdk`gsk`j g dk`o~ hiicngfm
eoo|.
y Ckvsy~ng`fi vkj`ge
Ckvs~yng`fi^ihi~i`fi hy`fsko`ieidi`sv
k`|ys fo`s~oe cieidi`sv ieidi`sv fo`s~oeeic v{vsid
[ ~ - i d - - fFoddg`c
vkj`ge $ Hiicngfm ieidi`sv
Hkjy~i 6.>>2 Ji`i~ge neofm$ckgj~gd ~i|~ivi`sgsko` ho~ g fo`s~oe v{vsid.
Eg|egfi s~g`vho~d disaoc
Sakv disaoc oh voexk`j ckhhi~i`skge iwygsko`v kv vodizags g`geojoyv so sai |~ofivv oh dyesk|e{k`j o~ckxkck`j yvk`j eojg~ksadv. K` sai ziee$m`ozv s~g`vho~dgsko` oh eojg~ksadv% `ydni~v g~i s~g`vho~dic k`so
|ozi~v oh sai ngvi 7< o~ vodi osai~ ngvi. Sakv |~ofivv k` ihhifs dgmiv ks |ovvknei so dyesk|e{ g`c ckxkci
n{ yvk`j sai vkd|ei~ o|i~gsko`v oh gccksko` g`c vyns~gfsko`. Ghsi~ onsgk`k`j sai civk~ic g`vzi~ k`
eojg~ksadv% sai s~g`vho~dgsko` ngfm so sai ~ige$`ydni~ v{vsid kv gffod|ekvaic n{ hk`ck`j g`skeojg~ksadv.
K` sai disaoc oh Eg|egfi s~g`vho~dv% s~g`vho~dgsko` oh sai si~dv oh sai ckhhi~i`skge iwygsko` {kiecv g`
gejin~gkf iwygsko` k` g`osai~ xg~kgnei v. Sai~ighsi~ sai voeysko` oh sai ckhhi~i`skge iwygsko` kv ihhifsic n{
vkd|ei gejin~gkf dg`k|yegsko`v k` sai v codgk` !sai `iz xg~kgnei kv v ~gsai~ sag` skdi s+. so onsgk` sai
civk~ic skdi voeysko`. Ks kv `ifivvg~{ so k`xi~s sai s~g`vho~d oh sai voeysko` h~od sai v codgk` ngfm so sai
skdi codgk`. Gfsygee{% ho~ dyfa fo`s~oe zo~m% k`ho~dgsko` onsgk`ic k` sai v codgk` vyhhkfiv vo sags ks dg{
ni y``ifivvg~{ so k`xi~s ngfm so sai skdi codgk`.
Sai Eg|egfi s~g`vho~dgsko` H!v+ oh g hy`fsko` oh skdi !s+ kv7
H!v+ 4 E ]!s+T 4
!s+i
vs
cs
G J7 !C+
N
J> !C+
A !C+
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Zgwgv Gek Sy`ko !6
Vsi| hy`fsko` G j~g|akfge ~i|~ivi`sgsko` oh g vsi| hy`fsko` kv vaoz` k` hkj 9.>. G vsi| hy`fsko` kv
civkj`gsic n{ sai v{dnoe ay!s+% zai~i a kv sai aikjas g`c y!s+ kv sai v{dnoe ho~ g y`ks vsi| hy`fsko` zaovi
aikjas kv 7. G||ekfgsko` oh Iw. !9.>9+
H!v+ 4 E ] ay!s+ T 4
ai
vs
cs 4 ai
vs
V
4a!i v !
+ - iv!2 vsi| hy`fsko`.
Kd|yevi hy`fsko` G v|ifkge fgvi oh g |yevi hy`fsko` kv g` kd|yevi hy`fsko`. Kh sai aikjas kv civkj`gsic gv a 4
m/s% ks hoeeozv sags sai g~ig kv gezg{v iwyge so m. `oz% gv sai zkcsa s
g||~ogfaiv ri~o% sai aikjas nifodiv
k`hk`ksi nys sai g~ig ~idgk`v iwyge so m. Sakv ekdksk`j fgvi oh g |yevi hy`fsko` kv fgeeic g` kd|yevi. sai
v{dnoe my7 !s+ ~i|~ivi`sv g` kd|yevi hy`fsko` zaovi g~ig kv m. vynvsksysko` oh a 4 ms k`so Iw. !9.>:+ g`csgmk`j sai ekdks gv s
g||~ogfaiv ri~o jkxiv sai hoeeozk`j s~g`vho~d ho~ g` kd|yevi2
H!v+ 4 E ] my7 !s+ T 4 ekd ]m
!7 $ i $sv
+ T 4
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Zgwgv Gek Sy`ko !3
h !s+
gsSakv disaoc i`gneiv o`i so cisi~dk`i sai ~oosv
oh sai fag~gfsi~kvskf iwygsko` !k.i.% sai ri~ov oh sai fag~gfsi~kvskf hy`fsko` n{+ n{ m`ozk`j sai hgfso~ic
h~od oh sai hiic ho~zg~c g`c hiicngfm ieidi`sv oh g fo`s~oe v{vsid. Gv kv ckvfyvvic k` Fag|. 8% sai
s~g`vki`s niagxko~ oh g v{vsid kv joxi~`ic |~kdg~ke{ n{ sai ~oosv oh sai fag~gfsi~kvskf iwygsko` ho~ sai
v{vsid. @iksai~ sai k`kskge fo`cksko`v `o~ sai |g~skfyeg~ iqfksgsko` ghhifsv sai ngvkf o|i~gsko` oh g v{vsid.
Vkj`khkfg`fi oh ~oos eofkSai fag~gfsi~kvskf iwygsko` ho~ sai fo`s~oe v{vsid vaoz` k` Hkj. :.7g kv
v!v - 3+ - M 4 v>- 3v - M 4 4g v bn% k` zakfa >g 43 o~ g 4 > g`c n 4 M g>.Sayv
Ho~ M 0 32 ~7%> 4 > v b M 3
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Zgwgv Gek Sy`ko !9
Ho~ M 4 32 ~7 4 ~> 4 >
Ho~ M 5 32 ~7%> 4 > v b M 3 4 > - 3 M
^!v+ - F!v+ 3
6
!g+
>
8< 7
9 3 6M 4 3 7 7
!n+
Hkjy~i :.7 ^oys$eofyv |eos ho~ v!v - 3+ - M 4 = zai` M 4 1% sai ~oosv g~i ~7%> 4 > v b>= isf.
M 4 78
M 4 1
M 4 6M 4 < M 4 6 M 4
7
M
v!v - 3+
b
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Zgwgv Gek Sy`ko !8
IEIFS^KFGE\AI@ODI@O@
Fy~~i`s 2 Sai h eoz oh i eifs~o`v kv fg e eic fy~~i`s . K s kv f egvv k h kic k`so szo
fgsijo~ kiv o`i kv fg e eic G.F !G esi~`gs k`j Fy~~i`s+ g`c osai~ kv fg e eic C.F !Ck~ifs
Fy~~i`s+ . Gv h~od `gdi g esi~`gsi dig`v zakfa fag`jiv k sv c k~ifs ko` h~od xi so
-xi% g`c kv ci`osic n{ k . Zai~i gv c k~ifs fy~~i`s kv ~i|~ivi`sic n{ g vs~g kjas e k`i%
agxk`j o`i c k~ifs ko` o`e{. Sai v|iic oh sai fy~~i`s kv gnoys 7:8 - ^6
\g~ge ei e F k ~fy k sv 2 Zai` sai ~iv kvso~v g~i fo``ifsic k` vyfa g dg``i~ sags fy~~i`s k`
~iv kvso~v kv c kvs~ knysic nys xoesgji ~idgk`v fo`vsg`s % sai` k s kv fg e eic |g~g e ei e
f k~fy ks % gv vaoz` k` h kjy~i.
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Zgwgv Gek Sy`ko !1
X q K
X 4 K^
H~od h kjy~i !g+ zi h k`c sags
X d 4 Kd ^d
G`c Xv 4 Kv ^v
G v s a i f k ~f y k s k v | g ~g e ei e vo s a g s
K 4 K v - KdG`c Xd 4 Xv
Kd ^d 4 K v ^v
Kd 4 K v ^v
^ d
K 4 Kv - Kv ^v
^d
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Zgwgv Gek Sy`ko !;
\~oneidFgefyegsi sai vay`s ~iv kvsg`fi ~iwyk~ic so dgmi g dk e e k gd|ig~ disi~ digvy~i y|so
7
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Zgwgv Gek Sy`ko !. @o. oh sy~`v oh zk`ck`j
6. V|gfi niszii` sy~`v g`c c kg oh zk~i.
Fg|gfksg`fi2
K s k v sai |~o|i~s{ oh sai fg|gf kso~ vso~i ieifs~ kf k s{ . Sai fg|gf kso~ mii|v sai xoesgji
fo`vsg`s % zak ei h eyfsygs ko`v. K sv y`ks kv hg~gc g`c ci`osic n{ F g`c fg` ni cih k`ic
gv% k h o`i foyeodn fag~ji vso~ic k` g fg|gf kso~ % f ~igsiv |osi`s kg e c k h hi~i`fi oh o`i
xoes sai fg|gf ksg`fi oh fg|gf kso~ kv o`i hg ~gc fg|gf kso~ kv ci`osic n{ v{dnoe.
Ckoci2
C koci kv cixkfi agxk`j szo ieifs~ociv% o`i kc fg e eic g`oci g`c osai~ kv fg e eic
fgsaoci gv vaoz` k` h kjy~i v{dnoe.
4
Ks kv yvic so fo`xi~s G .F fy~~i`s so C.F fy~~i`s .
S~g`vcyfi~2
S~g`vcyfi~ kv g` k`vs~ydi`s zakfa fo`xi~sv |a{v kfg e wyg`s ks kiv k`so ieifs~ kfg e
wyg`s ks kiv e kmi ho~fi% |~ivvy~i% so~wyi isf . Sakv co `os j kxiv g`{ eovv k` fg|gf ks{.
Vyfa s{|i oh k`vs~ydi`sv fo`v kvsv oh ho e eozk`j fod|o`i`sv .
7. K`|ys cixkfiv
>. Vkj`ge fo`cks ko`k`j cixkfiv
6. Oys|ys cixkfiv
K`|ys V kj`ge Fo`cks ko`k`j Oys|ys Ckv| eg{\~ofivv k`j
Gd|ek h kfgs ko` H k e s ~gs ko` Docyegs ko`
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Zgwgv Gek Sy`ko !. Hk e s ~gs ko`
6. Docyegs ko`
Gd|ek h kfgs ko` 2
V kj`ge gd|e k h kfgs ko` kv fg~~ kic oys zai` s{|kfg e v kj`ge oys|ys eixie oh g
digvy~idi`s. S~g`vcyfi~ kv fo`v kci~ic so ni soo eoz gd|e k h kfgs ko` n{ g`geoj dig`v
kv fg~~ kic nys n{ g` o|i~gs ko`ge gd|e k h ki~ vdge e oys|ys oh gd|e k h ki~ sai oys|ys h~od
sai gd|e k h ki~ agv g` k`f~igvic dgj`ksyci zakfa kv sag` do~i yvihye ho~ ~ifo~ck`j o~
ckv| eg{ |y~|oviv.
H k e s ~gs ko` 2
Sa kv |~ofivv kv co`i so |y~ k h{ o~ so ~idoxi y`zg`sic sa k`jv ho~ vdoosa ~y``k`j oh
wyg`s ks kiv .
Docyegs ko` 2
Sa kv |~ofivv kv yvic zai` s~g`vdks ko` |gsa kv eo`j. Docyegs ko` ~icyfiv sai ihhifsv
oh `okvi k` s ~g`vdks ko` |gsa. K s kv yvic s o fo`s~oe v kj`ge do`kso~ k`j.
Sgfaodisi~2
G sgfaodisi~ kv g` k`vs~ydi`s zakfa kv yvic ho~ digvy~ k`j c k~ifs e{ g`jyeg~ xieof ks{
oh g ~osgs k`j v{vsid !vaghs + . Hoe eozk`j g~i sai dgk` s{|iv oh sgfaodisi~ .
7. K`cyfs ko` \ kfmy| Sgfaodisi~
>. Fg|gf ks kxi \ kfmy| Sgfaodisi~
6. \aoso$ieifs~ kf Fie e Sgfaodisi~
3. Ve k||k`j F eysfa Sgfaodisi~
9. Xkn~gs ko` / ^ivo`g`fi Sgfaodisi~
8. Icc{ Fy~~i`s / Dgj`is kf C~gj Sgfaodisi~
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Zgwgv Gek Sy`ko !
K`cyfs ko` \ k fmy| Sgfaodisi~ 2
G s{|kfg e v{vsid yv k`j k`cyfs ko` | kfmy| kv vaoz` k` h kjy~i. Igfa soosa oh zaiie
|~ocyfiv dgj`is kf h eyq gv k s |gvviv . Sayv zi jos iq| k` sai ho~d oh |yeviv . @oz
saivi |yeviv g~i hiic so c kj ksg e foy`si~ % zakfa foy`sv sai `ydni~ oh |yeviv ho~ vgdi
s kdi k`si~xg e . Sai hy`fs ko` oh sai v kj`ge dockh ki~ kv so vag|i c kj ksg e v kj`gev g`c
yvignei gd|e ksyci.
Ckv| eg{
Soosaic
Zaiie
Fg|gfks kxi \ k fmy| Sgfaodisi~ 2
Fg|gf ks kxi sgfaodisi~ agv xg`v% zakfa g~i gssgfaic so sai doxk`j vaghs . Gv sai xg`
~osgsiv niszii` h kq fg|gf kso~ | egsiv fag`ji k` fg|gf ksg`fi so ig~sa ~gs ko kv
|~ocyfic. @oz sa kv fg|gf ksg`fi kv hiic so v kj`ge dockh ki~ % zakfa ~ivag|i sai |yeviv
g`c c kj ksg e e{ foy`s said% gv vaoz` k` h kjy~i.
Ckv| eg{
Xg `
Fg|gf ks kxi \ egsiv
\aoso$I eifs~ kf Fi e e Sgfaodisi~ 2
Sa kv k`vs~ydi`s fo`v kvsv oh g |aoso$ieifs~ kf fie e % zakfa kv gfs kxgsic n{ e kjas |yeviv
~ih eifsic h~od g ~osgs k`j dgfak`i vaghs .
^osgs k`j vaghs
Hofyv k`j Dk~~o~
Ckv|eg{
E kjas ^g{v
Sai vaghs agv g` k`si~dickgsi ~ih eifs k`j vy~hgfi g`c zai` g nigd oh e kjas kv hofyvic
o` sai vaghs % sai` `ydni~ oh |yeviv oh e kjas g~i onsg k`ic. Sai h~iwyi`f{ oh e kjas
|yeviv kv |~o|o~s ko`ge so sai v|iic oh vaghs . Gjg k` |yeviv g~i vag|ic so |~oxkci
vyksgnei k`|ys ho~ c kj ksg e foy`si~ gv vaoz` k` h kjy~i. C kj ksg e digvy~ k`j v{vsid dg{
ni yvic ho~ v|iic y|so 6
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Zgwgv Gek Sy`ko !
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Zgwgv Gek Sy`ko !
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Zgwgv Gek Sy`ko !. V{vsidgs kf I~ ~o ~ 2 Saivi i~~o~v fgyvic n{ yvyge e{ v{vsidv% e kmi cyi so
fg e kn~gs ko`v o~ cyi so gsdov|ai~ kf fo`cks ko`v e kmi |~ivvy~i% sid|i~gsy~i%
aydkcks{ isf .
6. E kdks k`j I~ ~o ~ 2 Sai |i~dg`i`s i~~o~v k`v kci sai k`vs~ydi`sv kv fg e eic e kdks k`j
i~~o~v . Soei~g`fi kv nivs iqgd|ei oh e kdks k`j i~~o~ .
3. ^g`cod I ~~o~2 ^g`cod i~~o~ yvyge e{ g~ kviv % zai` g`geoj ~igck`j disi~ kv
yvic. K s fg` ni vg kc sags k s kv dig` i~~o~ . I eifs~ kfg e `okvi fg` g evo ni g voy~fi
oh ~g`cod i~~o~ .
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Zgwgv Gek Sy`ko !. Ciheifs ko` S{|i
@ye e S{|i 2 Sakv s{|i kv yvic so digvy~i eoz g`c dickyd ~iv kvsg`fiv g`c gv o|i~gsic
o` C.F vy||e{.
Ciheifs ko` S{|i 2 Sakv s{|i kv yvic so digvy~i a kja ~iv kvsg`fiv g`c kv o|i~gsic o`
G.F vy||e{.
N
^ 7 ^>
-
G F
$
^ 6 ^3
C
^ 7 4 Y`m`oz` ~iv kvso~
^ > 4 Gcbyvsgnei ~iv kvso~
^ 6 g`c ^ 3 4 fo`vsg`s ~iv kvso~
H~od h kjy~i zi agxi jis iwygs ko`
3
6
>
7
^
^
^
^'
o ~
^ 7 4 ^ 6 /^ 3 q ^>
^ > 4 ^ 7 /^ 6 q ^3
^ 6 4 ^ 7 /^ > q ^3 ^ 3 4 ^ 6 /^ 7 q ^>
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Zgwgv Gek Sy`ko !
7q^
^
^^ '
6>.7
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Zgwgv Gek Sy`ko !
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Zgwgv Gek Sy`ko !
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Zgwgv Gek Sy`ko !. Dyes k C kv| eg{ Cixkfiv .
6. K e eydk`gs k`j Ckv| eg{ Cixkfiv
Vk`jei Ckv| eg{ Cixkfiv2 Sai c kv| eg{ cixkfiv % zakfa vaozv ~igck`jv oh o`e{ o`i
xg~ kgnei gs g s kdi% g~i fg e eic v k`j ei c kv| eg{ cixkfiv e kmi Oaddisi~% gddisi~ %
xoesdisi~ % GXO disi~ % ny~ci`v syni |~ivvy~i jgyji isf .
Dyes k Ckv| eg{ Cixkfiv2 Sai c kv| eg{ cixkfiv zakfa vaozv ~igck`jv oh do~i sag` o`i
xg~ kgnei gs sai vgdi s kdi% g~i fg e eic dyes k c kv| eg{ cixkfiv e kmi ovf k e eovfo|i% zakfavaozv xoesgji g`c h~iwyi`f{ gs vgdi s kdi% vsgnk e kri~ isf .
K e eydk`gs k`j Cixkfiv2 Saivi g~i c kv| eg{ cixkfiv % zakfa agxi gnk e k s{ % sags sai{ fg`
vaoz sai ~ivyes oh xg~ kgnei g j eozk`j o~ k e eydk`gs k`j h~od e kmi cixkfiv zakfa agxi
vixi` vijdi`sg e c kv| eg{.
H o ~d v o h C k v| e g { 2
Sai~i g~i dgk` e{ szo ho~dv oh c kv | eg{
7. Ckj ksg e
>. G`geoj
Ckjk sg e 2 K` sa kv ho~d ~igck`jv g~i vaoz` k` c kj ks !`ydni~v+ foddo`e{ o` vixi`
vijdi`sg e c kv| eg{ v{vsid kv yvic. I ksai~ EIC !E kjas Idkss k`j Ckoci+ kv yvic o~ EFC
!E kwykc F~{vsg e C kv| eg{+ kv yvic.
G`geoj2 K` sa kv ho~d ~igck`jv g~i vaoz` o` sai fg e kn~gsic vfg ei n{ dig`v oh doxk`j
|ok`si~ .
Fegvvk h kfgs ko` oh Ckv| eg{
Ckv|eg{ dg{ ni f egvv k h kic gv ho e eozv
7. Doxk`j \ok`si~ .
>. Doxk`j Vfg ei.
6.
J~g|a.
Doxk`j \ok`si~2 K` sa kv s{|i oh c kv| eg{ |ok`si~ zk e e doxic o` h kqic fg e kn~gsic vfg ei.
Sai vfg ei dg{ ni k` v kd|ei fy~xi o~ k` f k~fy eg~ vag|i. K` sa kv s{|i oh c kv| eg{ |ok`si~
doxiv cyi so vodi |ai`odi`o`.
Doxk`j Vfg ei Ckv| eg{ Cixkfiv2 K` sa kv s{|i oh c kv| eg{ cixkfiv % vfg ei kv doxk`j% zksa
~iv|ifsv so h kqic |ok`sv h k ei kv |~obifs |~oh k ei dgfak`i.
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Zgwgv Gek Sy`ko !
J~g|a Ckv| eg{ Cixkfiv 2 Saivi g~i saovi cikfiv % zakfa vaozv ~igck`jv oh szo o~
do~i xg~ kgnei gs g s kdi o` g j~g|a |g|i~ k` sai ho~d oh e k`i o~ cosv e kmi cixkfiv
yvic k` y`kxi~vg e sivs k`j dgfak`iv o~ ~if k|~ofgs k`j fod|~ivvo~ .
KEEYDK@GSK@J CKV\EG[ CIXKFIVK e eydk`gs k`j c kv| eg{ cixkfiv g~i saovi cixkfiv zakfa g~i yvic so c kv| eg{ ~igck`jv oh
xg~ kgneiv k` k e eydk`gs k`j ho~d. Fgsaoci ^g{ ovf k e eovfo|i kv o`i oh sai k e eydk`gs k`j
cixkfi% zakfa kv yvic so digvy~i xoesgji g`c h~iwyi`f{ gs sai vgdi s kdi k` sai
vag|i oh zgxiv. K sv v kd|eivs ho~d fo `v kvsv oh ho e eozk`j |g~sv .
F^ syni
Fgsaoci
Aigsi~H k egdi`s I eifs~o` jy`
Ao~kro`sg e | egsi
\egs k`yd gffiei~gs k`j g`oci Xi~s kfg e | egsi
\egsiv hofyv k`j VzksfaivAr J~ kc Fgsaoci
X
O`/Ohh X A r
Zai` sai fy~~i`s |gvv k`j sa~oyja sai aigsi~ sai` h k egdi`s zk e e ni aigsic% zakfajkxiv aigs so sai fgsaoci gv sai ~ivyes oh zakfa ieifs~o`v doxiv so sai ieifs~o`
jy`% zakfa vao~sv i eifs~o` o` gffiei~gs k`j g`oci% g`c sai` h k`g e e{ n{ |gvv k`j
sa~oyja sai | egsiv oys fgdi kv c kv| egfic o` sai vf~ii `
Sakv ovf k e eovfo|i zo~mv o` 8.6 xoesv . Fogs k`j o` fgsaoci kv |~oxkcic cyi so
|~osifs ko`.
Vf~ii`
!7+!:+
!9+!8+
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Zgwgv Gek Sy`ko !
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Zgwgv Gek Sy`ko !B 4 7 f g eo~ k
Sid|i~gsy~i Y`ksv