CH 1045 Chemistry I Slides

8/14/2019 CH 1045 Chemistry I Slides

http://slidepdf.com/reader/full/ch-1045-chemistry-i-slides 1/371



3

Mg~~bs gfn Bfbskx - Z`lgcrdgsxLebmh|~sx \lhbflb ~eg~ nb|lshcb| mg~~bs “ h~| qs`qbs~hb|$ ~eb

legfkb| h~ rfnbsk`b|$ gfn ~eb bfbskx legfkb| ~eg~

gll`mqgfx ~e`|b qs`lb||b|

Mg~~bs Gfx~ehfk ~eg~ eg| mg|| gfn `llrqhb| |qglb&

Bfbskx êb lgqglh~x ~` n` {`si `s ~sgf|jbs ebg~&

\lhbf~hjhl %fg~rsgd( dg{ G kbfbsgd |~g~bmbf~ cg|bn ~eb `c|bszbn cbegzh`s `j

mg~~bs ~` {ehle f` bulbq~h`f| gsb if`{f&



<

Fg~rsgd Dg{|

Dg{ `j L`f|bszg~h`f `j Mg|| “ ~`~gdgm`rf~ `j mg|| sbmghf| l`f|~gf~

nrshfk g lebmhlgd legfkbDg{ `j Nbjhfh~b Qs`q`s~h`f| “ hf g khzbflebmhlgd l`mq`rfn$ ~eb bdbmbf~| gsb

gd{gx| l`mchfbn hf ~eb |gmbqs`q`s~h`f| cx mg||



>

\lhbf~hjhl Mb~e`n

@c|bszg~h`f - |~g~bmbf~ ~eg~ gllrsg~bdx nb|lshcb||`mb~ehfk |bbf$ ebgsn$ ~g|~bn$ jbd~$ `s |mbddbn

Exq`~eb|h| - ~bf~g~hzb buqdgfg~h`f| j`s {eg~ {b c|bszbnBuqbshmbf~g~h`f - ~b|~hfk `j ~eb exq`~eb|h|Ng~g “ bmqhshlgd jgl~| l`ddbl~bn nrshfk buqbshmbf~g~h`f/@c|bszg~h`f `s buqbshmbf~

êb`sx - ~b|~bn buqdgfg~h`f `j ~eb cbegzh`s `j fg~rsbL`fldr|h`f “ |~g~bmbf~ ~eg~ h| cg|bn `f {eg~ h| ~e`rke~gc`r~ g |bshb| `j `c|bszg~h`f|Dg{ - kbfbsgdhg~h`f cg|bn rq`f ~eb sb|rd~| `j mgfxbuqbshmbf~|



2

êsbb \~g~b| `j Mg~~bs



:

Qeg|b Nhgksgm



;

Lebmhlgd gfn Qex|hlgd Qs`qbs~hb|Lebmhlgd Qs`qbs~hb| - lebmhlgd legfkb| sr|~hfk `s ùhng~h`f lebmhlgd sbgl~h`f|

Qex|hlgd Qs`qbs~hb| - qex|hlgd legfkb| legfkb| `j |~g~b nbf|h~x$ l`d`s$ |`drchdh~x

Bu~bf|hzb Qs`qbs~hb| - nbqbfn `f wrgf~h~x9 h&b&$

z`drmbHf~bf|hzb Qs`qbs~hb| - n` f`~ nbqbfn `fwrgf~h~x9 h&b&$ l`d`s$ ~bmqbsg~rsb$ nbf|h~x





8

Mhu~rsb|$ \rc|~gflb|$L`mq`rfn|$ gfn Bdbmbf~|

Qrsb \rc|~gflb mg~~bs hf {ehle gdd |gmqdb| egzb hnbf~hlgd

l`mq`|h~h`f gfn qs`qbs~hb| L`mq`rfn|? |rc|~gflb| l`mq`|bn `j g~`m|

`j ~{` `s m`sb bdbmbf~| lebmhlgddx rfh~bn hfjhubn qs`q`s~h`f|

Bdbmbf~|? |rc|~gflb| ~eg~ lgff`~ cbnbl`mq`|bn hf~` |hmqdbs |rc|~gflb| zhglebmhlgd sbgl~h`f|



71


L`mq`rfn|

|rc|~gflb| l`mq`|bn `j ~{` `s m`sb

bdbmbf~| hf g nbjhfh~b sg~h` cx mg|| lgf cb nbl`mq`|bn hf~` ~eb l`f|~h~rbf~

bdbmbf~|

[g~bs h| g l`mq`rfn ~eg~ lgf cb nbl`mq`|bn

hf~` |hmqdbs |rc|~gflb| “ exns`kbf gfn ùxkbf

3 E3@ 3 E3 ) @3



77


Mhu~rsb|

l`mq`|bn `j ~{` `s m`sb |rc|~gflb|

e`m`kbfb`r| mhu~rsb| - q`||b|| ~eb |gmbqs`qbs~hb| ~es`rke`r~ ~eb mhu~rsb

eb~bs`kbfb`r| mhu~rsb| - l`f|h|~| `j ~{`

`s m`sb sbkh`f| ~eg~ nhjjbs hf qs`qbs~hb|



S`rfnhfk @jj Frmcbs|Srdb| Bugmqdb7& Hj ~eb fbu~ nhkh~ h| db|| ~egf 2$ 7&38> 7&38

~ebf ~eb qsbzh`r| nhkh~ sbmghf| ~eb |gmb

3& Hj ~eb fbu~ nhkh~ h| ksbg~bs ~egf 2 `s 2 j`dd`{bn 7&<32117 7&<<cx f`f-bs`b|$ ~ebf ~eb qsbzh`r| nhkh~ h| 1&888 7&11

hflsbg|bn cx `fb

<& Hj ~eb fbu~ nhkh~ h| 2 `s 2 j`dd`{bn cx GDD bs`b|$ 7&352 7&35

êbf ~eb qsbzh`r| nhkh~ sbmghf| ~eb |gmb hj h~ h| bzbf 7&33211 7&33

>& Hj ~eb fbu~ nhkh~ h| 2 `s 2 j`dd`{bn cx GDD bs`b|$ 7&382 7&<1

êbf ~eb qsbzh`r| nhkh~| h| hflsbg|bn hj h~ h| `nn 7&<;2 7&<5



7<

\lhbf~hjhl F`~g~h`f

L`bjjhlhbf~ %gfx frmcbs ~eg~‘| js`m · 7-8(

Buq`fbf~ %gfx f`f-nblhmgd

frmcbs(

F& u 71u

Kbfbsgd J`smrdg



7>

^` l`fzbs~ frmcbs| hf~` \lhbf~hjhlF`~g~h`f

G| x`r m`zb ~eb nblhmgd q`hf~ ~` ~eb dbj~ %h&b&$

mgib ~eb l`bjjhlhbf~ |mgddbs( ~eb q`{bs `j ~bf

%h&b&$ ~eb buq`fbf~( mr|~ hflsbg|b cx ~eb |gmb

gm`rf~

7;21&1 = 7;21&1 u 711 = 7&;211 u 71<

G| x`r m`zb ~eb nblhmgd q`hf~ ~` ~eb shke~ %h&b&$mgib ~eb l`bjjhlhbf~ dgskbs( ~eb q`{bs `j ~bf %h&b&$

~eb buq`fbf~( mr|~ nblsbg|b cx ~eb |gmb gm`rf~

1&1211 = 1&1211 u 711 = 2&11 u 71-3



72

\hkfhjhlgf~ Nhkh~|

\hkfhjhlgf~ nhkh~| hfnhlg~b e`{ gllrsg~bdxmbg|rsbmbf~| egzb cbbf mgnb

^` jhfn e`{ mgfx |hkfhjhlgf~ nhkh~| g frmcbseg|?

7& D`lg~b ~eb jhs|~ f`fbs` nhkh~ %|~gs~ js`m dbj~ ~`shke~($ ~ebf |~gs~hfk {h~e ~eg~ nhkh~$ l`rf~ ~ebfrmcbs `j nhkh~| ~eg~ j`dd`{

1&13211

3& bs`| g~ ~eb bfn `j g frmcbs ~eg~ eg| f` nblhmgd

q`hf~ gsb f`~ |hkfhjhlgf~



7:

\hkfhjhlgf~ Jhkrsb|

‣ Gfx nhkh~ ~eg~ h| f`~ bs` h| |hkfhjhlgf~

7&3<> ik > |hkfhjhlgf~ jhkrsb|‣_bs`| cb~{bbf f`fbs` nhkh~| gsb |hkfhjhlgf~

:1: m < |hkfhjhlgf~ jhkrsb|

‣_bs`| ~` ~eb dbj~ `j ~eb jhs|~ f`fbs` nhkh~ gsb f`~ |hkfhjhlgf~

1&15 D 7 |hkfhjhlgf~ jhkrsb

‣Hj g frmcbs h| ksbg~bs ~egf 7$ ~ebf gdd bs`| ~` ~eb shke~ `j ~eb nblhmgd q`hf~ gsb |hkfhjhlgf~

3&1 mk 3 |hkfhjhlgf~ jhkrsb|‣Hj g frmcbs h| db|| ~egf 7$ ~ebf `fdx ~eb bs`| ~eg~ gsb g~ ~ebbfn gfn hf ~eb mhnndb `j ~eb frmcbs gsb |hkfhjhlgf~

1&11>31 k < |hkfhjhlgf~ jhkrsb| %>&31 mk(



7;

Mgfhqrdg~hfk Q`{bs| `j ^bf

[ebf mrd~hqdxhfk q`{bs| `j ~bf$ ~eb buq`fbf~|

gsb gnnbn&

712

u 71->

= 71%2) ->(

= 717

[ebf nhzhnhfk q`{bs| `j ~bf$ ~eb buq`fbf~| gsb

|rc~sgl~bn&

71>û 71-> = 71 %>- ->( = 715

[ebf sgh|hfk q`{bs| `j ~bf ~` gf buq`fbf~$ ~eb

buq`fbf~| gsb mrd~hqdhbn&

%71>(< = 71 %>u<( = 7173



75

Gnnhfk gfn \rc~sgl~hfk Frmcbs|

[ebf gnnhfk `s |rc~sgl~hfk frmcbs|$ x`rs jhfgd

gf|{bs |e`rdn egzb ~eb |gmb frmcbs `j nblhmgd

qdglb| g| ~eb frmcbs js`m ~eb qs`cdbm {h~e ~eb

jb{b|~ nblhmgd qdglb|

7&;

1& <<

)7<&781

72&3 31 72&3



78

\hkfhjhlgf~ Jhkrsb|

Gnnh~h`f `s \rc~sgl~h`f

êb gf|{bs lgff`~ egzb m`sb nhkh~| ~` ~eb shke~ `j ~eb nblhmgdq`hf~ ~egf gfx `j ~eb `shkhfgd frmcbs|&

58&<<37&7)

81&><3 s`rfn jj ~` 81&>

`fb |hkfhjhlgf~ jhkrsb gj~bs nblhmgd q`hf~

<&;1

-3&87<<1&;5:;

~{` |hkfhjhlgf~ jhkrsb| gj~bs nblhmgd q`hf~

s`rfn `jj ~` 1&;8



31

Mrd~hqdxhfk gfn Nhzhnhfk Frmcbs|

[ebf mrd~hqdxhfk `s nhzhnhfk frmcbs|$ x`rs jhfgd

gf|{bs |e`rdn egzb ~eb |gmb frmcbs `j

|hkfhjhlgf~ nhkh~| g| frmcbs js`m ~eb lgdlrdg~h`f

{h~e ~eb jb{b|~ |hkfhjhlgf~ nhkh~|

7&;:5 u 7&3< = 3&7;>:> = 3&7;

<&:58 û 7&< = 3&5 <;:8 = 3&5



37

\hkfhjhlgf~ Jhkrsb|

Mrd~hqdhlg~h`f `s Nhzh|h`f

êb frmcbs `j |hkfhjhlgf~ jhkrsb| hf ~eb sb|rd~ h| |b~ cx ~eb`shkhfgd frmcbs ~eg~ eg| ~eb |mgddb|~ frmcbs `j |hkfhjhlgf~jhkrsb|

>&27 u <&:::: = 7:&2<:<::= 7:&2

< |hk jhk| s`rfn ~`< |hk jhk|

:&5û

773&1> = 1&1:1:83:

3 |hk jhk| s`rfn ~`3 |hk jhk|

= 1&1:7



33

\hkfhjhlgf~ Jhkrsb|

Bugl~ Frmcbs|

Frmcbs| js`m nbjhfh~h`f| `s frmcbs| `j `cobl~| gsb l`f|hnbsbn~` egzb gf hfjhfh~b frmcbs `j |hkfhjhlgf~ jhkrsb|

êb gzbsgkb `j ~esbb mbg|rsbn dbfk~e|9 :&:>$ :&:5 gfn :&;10

:&:> ) :&:5 ) :&;1

<= :&:;<<< = :&:;

Cblgr|b < h| gf bugl~ frmcbs

= ;



3<

Mhuhfk gnnh~h`f|rc~sgl~h`f {h~emrd~hqdhlg~h`f gfn nhzh|h`f

L`mqdb~b gdd `j ~eb gnnh~h`f|rc~sgl~h`f jhs|~$ ~ebf

l`mqdb~b ~eb mrd~hqdhlg~h`fnhzh|h`f %s`rfn gj~bs ~eb

gnn|rc gfn gj~bs ~eb mrd~nhz|(

7&<>2:;;5 )3&5;:2

7&5

>&3333 = 3&<>2::: = 3&<

7&5



3>

Q`{bs| `j ~bf {h~e gnnh~h`f|rc~sgl~h`fgfn`s mrd~hqdhlg~h`fnhzh|h`f

;&2> u 71-2 %88& u 71311 ) 7&32 u 71317(

%7&;2u 71-<(<

;&2> u 71-2 %8&8 u 71317 ) 7&32 u 71317(

%7&;2u 71-<(<

;&2> u 71-2 %77&3 u 71317(

%7&;2u 71-<(<



32

Q`{bs| `j ~bf {h~e gnnh~h`f|rc~sgl~h`fgfn`s mrd~hqdhlg~h`fnhzh|h`f

;&2> u 71-2 %77&3 u 71317(

2&<: u 71-8

;&2> u 77&3 u 71-2 u 71317

2&<: 71-8

72&;22 u 71312

7&25 u 7131:



3:

\H Cg|b Rfh~|

Wrgf~h~x Rfh~\xmc`d

dbfk~e mb~bs mmg|| ihd`ksgm ik

~hmb |bl`fn |

lrssbf~ gmqbsb G

~bmqbsg~rsb Ibdzhf I

gm~& |rc|~gflb m`db m`d

Nbshzbn \H Rfh~|



3;

Nbshzbn \H Rfh~|Wrgf~h~x Nbjhfh~h`f `j Wrgf~h~x \H rfh~

Gsbg Dbfk~e |wrgsbn m3

Z drmb Dbfk~e lrcbn m<

Nbf|h~x Mg|| qbs rfh~ z`drmb ikm<

\qbbn Nh|~gflb ~sgzbdbn qbs rfh~ ~hmb m|

Gllbdbsg~h`f \qbbn legfkbn qbs rfh~ ~hmb m|3

J`slb Mg|| ~hmb| gllbdbsg~h`f j `cobl~ ik / m|3

% =fb{~`f$ F(

Qsb||rsb J`slb qbs rfh~ gsbg ik%m|3(

% = qg|lgd$

Qg(

Bfbskx J`slb ~hmb| nh|~gflb ~sgzbdbn ik / m3 |3



35

\H Qsbjhub| %Mb~shl(Fgmb \xmc`d Mrd~hqdhbsmbkg M 71 :

ihd` i 71 <

nbig ng 71

nblh n 71-7

lbf~h l 71-3

mhddh m 71-<

‣ mhls` 71-:

‣ fgf` f 71-8

‣ qhl` q 71-73

‣ jbm~` j 71-72



38

Sbdg~h`f|ehq| `j \`mb R&\& gfn Mb~shlRfh~|

Dbfk~e

7 m = <8&<; hfleb|

3&2> lm = 7 hfle 7 mhdb = 2351 j~

Z`drmb

7 dh~bs = 7&1: w~

7 w~ = 1&8>: dh~bs > w~ = 7 kgd

\bb ^gcdb 7&2 j`s m`sb l`fzbs|h`f jgl~`s|



<1

R|b `j Frmcbs|

Bugl~ frmcbs|

7 n`bf = 73 ~ehfk| j`s bugmqdb

Gllrsglx e`{ ld`|bdx mbg|rsbn zgdrb| gksbb {h~e

~eb l`ssbl~ zgdrb

Qsblh|h`f e`{ ld`|bdx hfnhzhnrgd mbg|rsbmbf~| gksbb

{h~e bgle `~ebs



<7

Gllrsglx “ e`{ ld`|b g mbg|rsbmbf~ h| ~` ~eb ~srb zgdrb

Qsblh|h`f “ e`{ ld`|b g |b~ `j mbg|rsbmbf~| gsb ~` bgle `~ebs

gllrsg~b*

qsblh|b

qsblh|bcr~

f`~ gllrsg~b

f`~ gllrsg~b*

f`~ qsblh|b



<3

êb |qbbn `j |`rfn hf ghs h| gc`r~ <>< m|& [eg~ h|~eh| |qbbn hf mhdb| qbs e`rs0

7 mh = 7:18 m 7 mhf = :1 | 7 e`rs = :1 mhf

<><m|

u7 mh

7:18 m

:1 |

7 mhf

u:1 mhf

7 e`rs

u = ;:;mh

e`rs

mb~bs| ~` mhdb||bl`fn| ~` e`rs|



<<

êb Jgl~`s Dgcbd Mb~e`n

mm715&23lm7

mm71u

hf7

lm3&2>u

j~7

hf73u

xn7

j~<uxn8&<3

mm0xn8&<3

<



<>

êb Jgl~`s Dgcbd Mb~e`nBuqsb|| :3; mhddhdh~bs| hf kgdd`f|&

kgd1&7::

21&7::72w~>

kgd7u

D7

w~7&1:u

mD7111

D7umD:3;



<2


Buqsb|| <&21 %|e`s~( ~`f| hf ksgm|&

k71u75&<

k<7;5111dc

k>2>

~`f

dc3111~`f|<&21

:



<:

êb Jgl~`s Dgcbd Mb~e`nBuqsb|| 3&:7 u 71> lm3 hf j~3&

33

333>3

j~35&7j~835&18<51:7

(hf73

j~7%(

lm3&2>

hf7%lm713&:7j~0



<;


Buqsb|| 3&:7 j~< hf lm<&

<><

<<<<

lm71;&<8lm;<81:&8:8:

(hf7

lm3&2>%(j~7hf73%j~3&:7lm0



<5

Nbf|h~x gfn \qblhjhl Ksgzh~x

nbf|h~x = mg||z`drmb

\qblhjhl ksgzh~x = nbf|h~x|rc|~gflb

nbf|h~x{g~bs

\qblhjhl ksgzh~x = e`{ nbf|b x`rs |rc|~gflb h|sbdg~hzb ~` {g~bs

n

m

z



<8

Nbf|h~x gfn \qblhjhl Ksgzh~xLgdlrdg~b ~eb nbf|h~x `j g |rc|~gflb hj ;>3 ksgm| `j h~ `llrqhb| 8;&< lm<&

Zm nbf|h~x

mD<&8;lm8;&< mD7lm7 <<



>1

Nbf|h~x gfn \qblhjhl Ksgzh~xLgdlrdg~b ~eb nbf|h~x `j g |rc|~gflb hj ;>3 ksgm| `j h~ `llrqhb| 8;&< lm<&

k/mD;&:<nbf|h~x

mD8;&<k;>3

nbf|h~xZ

m nbf|h~x

mD<&8;lm8;&< mD7lm7 <<



>7

Nbf|h~x gfn \qblhjhl Ksgzh~x

\rqq`|b x`r fbbn 732 k `j g l`ss`|hzbdhwrhn j`s g sbgl~h`f& [eg~ z`drmb n`

x`r fbbn0 dhwrhn‘| nbf|h~x = 7&<3 k/mD

mD8>&;

7&<3

k732Z

nbf|h~x

mZ

Z

mnbf|h~x

mD

k



>3

Nbf|h~x gfn \qblhjhl Ksgzh~x G <7&71 ksgm qhblb `j les`mhrm h| nhqqbn hf~` gksgnrg~bn lxdhfnbs ~eg~ l`f~ghf| 2&11 mD `j

{g~bs& êb {g~bs dbzbd sh|b| ~` 8&<3 mD& [eg~ h|~eb |qblhjhl ksgzh~x `j les`mhrm0

31&; 7&11

;&31Lsj Ksgzh~x\qblhjhl

mDk ;&31

mDk ;&7881;

mD>&<3

k<7&71 Lsj nbf|h~x

mDk

mDk



><

Ebg~ gfn ^bmqbsg~rsb

Ebg~ gfn ^bmqbsg~rsbgsb f`~ ~eb |gmb ~ehfk

^ h| g mbg|rsb `j ~ebhf~bf|h~x `j ebg~ hf gc`nx

< l`mm`f ~bmqbsg~rsb|lgdb| - gdd r|b {g~bs g|g sbjbsbflb



>>

Sbdg~h`f|ehq| `j ~eb êsbb

^bmqbsg~rsb \lgdb|

3;<IL

`s 3;<LI

hq|Sbdg~h`f|eLbf~hksgnbgfnIbdzhf

`

`



>2

Sbdg~h`f|ehq| `j ~eb êsbb

^bmqbsg~rsb \lgdb|

7&5

<3JL

s

<3L7&5J

7&52

8

71

75

711

751

hq|Sbdg~h`f|eLbf~hksgnbgfnJgesbfebh~

``

``



>:

L`fzbs~ 7;3&8 1J ~` nbksbb| Lbd|hr|&

1

J = %7&5 u1

L( ) <3

1J “ <3 = %7&5 u 1L(

%1J “ <3( = 1L7&5

1L = %7;3&8 “ <3( = ;5&<7&5



Legq~bs 3G~`m|$ M`dblrdb|$ gfn H`f|



Qbsh`nhl ^gcdb? Bdbmbf~|

:

L73&177

G~`mhl frmcbs =

~eb frmcbs `j qs`~`f|

G~`mhl mg|| =

[bhke~ sbdg~hzb ~``fb m`db

Lebmhlgd |xmc`d

H|`~`qb|



H|`~`qb| “ g~`m| {e`|b frldbh egzb ~eb |gmb g~`mhl frmcbscr~ nhjjbsbf~ mg|| frmcbs|

21

Ls3>

Mg|| frmcbs =Qs`~`f| )fbr~s`f|

G~`mhl frmcbs

23

Ls3>

2<

Ls3>

2>

Ls3>



Lgdlrdg~hfk Gzbsgkb G~`mhl Mg||Mg|| frmcbs H|`~`qb Mg||

"Gcrfngflb21 >8&8>:7

>&<2"

23 27&8>12

5<&;8"2< 23&8>1;

8&21"

2> 2<&8<58

3&<:"

>8&8>:7 u 1&1><2 = 3&7;

27&8>12 u 1&5<;8 =><&2323&8>1; u 1&1821 = 2&1<2<&8<58 u 1&13<: = 7&3;

27&88



‣ B||bf~hgddx gdd bdbmbf~| l`mchfb ~` j`sm

l`mq`rfn|

‣ L`mq`rfn| gsb `j ~{` ~xqb|? “ M`dblrdgs$ {ehle hfz`dzb |egsbn bdbl~s`f| gfn l`f|h|~

`j bdbl~shlgddx fbr~sgd$ nh|lsb~b qgs~hldb| lgddbnm`dblrdb|

“ H`fhl l`mq`rfn|$ {ehle hfz`dzb bdbl~s`f ~sgf|jbs gfn

legskbn qgs~hldb| lgddbn h`f|





G m`dblrdb h| gf gkksbkg~b `j ~{` `s m`sb g~`m| hf g nbjhfh~bgssgfkbmbf~ ebdn ~`kb~ebs cx lebmhlgd c`fn|

E3 E3@ FE< LE>

G nhg~`mhl m`dblrdb l`f~ghf| `fdx ~{` g~`m|

E3$ F3$ @3$ J3$ Ld3$ Cs3$ H3

G q`dxg~`mhl m`dblrdb l`f~ghf| m`sb ~egf ~{` g~`m|

@<$ E3@$ FE<$ LE>



‣ Lebmhlgd j`smrdg| |qblhjx ~eb l`mq`|h~h`f

`j g |rc|~gflb‣ FgLd h| l`mq`|bn `j ~eb bdbmbf~| |`nhrm gfn

led`shfb hf g `fb-~`-`fb %g~`m( sg~h`

‣ Jb3@< h| l`mq`|bn `j ~eb bdbmbf~| hs`f gfn ùxkbf

hf g ~{`-~`-~esbb sg~h`‣ L@%FE3(3 h| l`mq`|bn `j ~eb bdbmbf~| lgsc`f$

ùxkbf$ fh~s`kbf$ gfn exns`kbf

‣ Exnsg~b| gsb lsx|~gd| ~eg~ l`f~ghf {g~bs m`dblrdb|$

j`s bugmqdb qdg|~bs? Lg\@> ‣ 3E3@ “ [ebf gdd ~eb {g~bs h| sbm`zbn %cx ebg~hfk($ ~eb |`dhn ~eg~

sbmghf| h| |ghn ~` cb gfexns`r| %{h~e`r~ {g~bs(



L`rf~hfk G~`m| hf j`smrdg|E`{ mgfx g~`m| `j bgle bdbmbf~ gsb sbqsb|bf~bn cxêb j`smrdg| %g( Gd3%\@>(< gfn %c( L`Ld3 ‣:E3@

3 g~`m| `j Gd< g~`m| `j \73 g~`m| `j @

7 g~`m L`

3 g~`m| Ld73 g~`m| E: g~`m @



‣ Lebmhlgd bwrg~h`f| nb|lshcb {eg~ egqqbf|

hf g lebmhlgd sbgl~h`f|

‣ Exns`kbf gfn ùxkbf l`mchfb ~` j`sm

{g~bs

‣ Exns`kbf gfn ùxkbf gsb lgddbn sbgl~gf~|

‣ [g~bs h| lgddbn ~eb qs`nrl~

‣ Sbgl~gf~| gsb |bqgsg~bn js`m qs`nrl~| {h~e —”

“ 3 E3 ) @3 3 E3@

‣ F`~b ~eg~ ~eb —

” h| dhib gf bwrgd |hkf cblgr|b c`~e|hnb| `j ~eb bwrg~h`f egzb ~eb |gmb frmcbs `j bgle

~xqb `j g~`m



‣ êh| lgf cb sbqsb|bf~bn g|?

F`~b? Mg|| h| l`f|bszbn cblgr|b ~ebfrmcbs `j g~`m| `j bgle ~xqb sbmghf|

~eb |gmb `f bgle |hnb `j ~eb gss`{&

%C`~e |hnb| `j ~eb gss`{ |e`{ > E gfn

3 @ g~`m|&( êh| bwrg~h`f h| |ghn ~` cb

cgdgflbn&

êb —3” hf js`f~ `j j`smrdg| E3 gfn E3@ gsb lgddbn

l`bjjhlhbf~|& êbx hfnhlg~b ~eb frmcbs `j m`dblrdb| `j bgle

~xqb gfn lgf legfkb {ebf cgdgflhfk g lebmhlgd bwrg~h`f&

êb —3” hf ~eb j`smrdg| E3 gfn E3@ hfnhlg~b g~`m sg~h`| j`s

~eb l`mq`rfn gfn mr|~ f`~ legfkb&

^` cgdgflb ~eb bwrg~h`f$ x`r |bdbl~ l`bjjhlhbf~|



` cg g lb ~ b bwrg~ ` $ x`r |b bl~ l`b l b ~|~eg~ {hdd mgib ~eb frmcbs| `j g~`m| `j bglebdbmbf~ bwrgd `f c`~e |hnb| `j ~eb bwrg~h`f

L<E5 ) @3 L@3 ) E3@

Sbgl~gf~ \hnb Qs`nrl~\hnb

L=< L=7

E=5 E=3

@=3 @=<



‣ H~ h| |`mb~hmb| r|bjrd ~` hfldrnb ~eb

qex|hlgd |~g~b `j sbgl~gf~| gfn qs`nrl~|‣ J`s |`dhn| r|b |$ dhwrhn| r|b d$ kg|b| r|b k$ gfn j`s

gwrb`r| |`dr~h`f| r|b gw&

‣ J`s bugmqdb$ ~eb sbgl~h`f cb~{bbf |~`mgle

glhn %gf gwrb`r| |`dr~h`f `j ELd( gfn|`nhrm lgsc`fg~b %gf gf~glhn( lgf cb

{sh~~bf

3 ELd%gw( ) LgL@<%|( LgLd3%gw( ) E3@%d( )L@3%k(

F`~b? X`r lgf zbshjx ~eh| bwrg~h`f h| cgdgflbn cx leblihfk j`s

mg|| cgdgflb? bgle |hnb |e`{| 7 Lg$ 7 L$ 3 Ld$ 3 E$ gfn < @&



‣ G| g kbfbsgd srdb$ m`dblrdgs l`mq`rfn| gsb

j`smbn {ebf f`fmb~gddhl bdbmbf~| l`mchfb

‣ Mgfx m`dblrdgs l`mq`rfn| l`f~ghf

exns`kbf?

‣

‣

‣

‣‣

Ks`rq F`cdb

Qbsh`n HZG ZG ZHG ZHHG Kg|3 LE> FE< E3@ EJ Fb

< \hE> QE< E3\ ELd Gs

> KbE> G|E< E3\b ECs Is

2 \cE< E3 b EH Ub

F`~b? êb frmcbs `j exns`kbf| ~eg~ l`mchfbn {h~e ~eb f`fmb~gd

bwrgd| ~eb frmcbs `j |qglb| ~` ~eb shke~ {b egzb ~` m`zb ~` kb~ ~`

~eb f`cdb kg|



‣ @skgfhl lebmh|~sx h| g mgo`s |qblhgd~x ~eg~

nbgd| {h~e l`mq`rfn| l`f~ghfhfk m`|~dxlgsc`f gfn exns`kbf

‣ Exns`lgsc`f| l`f~ghf `fdx exns`kbf gfn

lgsc`f gfn gsb `skgfhl l`mq`rfn|

‣ Gdigfb| gsb ~eb |hmqdb|~ exns`lgsc`f| “ Kbfbsgd j`smrdg h| LfE3f)3

\qglb-jhddhfk m`nbd|?Cdgli g~`m| = lgsc`f

[eh~b g~`m| = exns`kbf



‣ @~ebs ldg||b| `j exns`lgsc`f| buh|~

‣ Nhjjbsbf~ ldg||b| `j `skgfhl l`mq`rfn| gsbnbshzbn js`m exns`lgsc`f| cx sbqdglhfk

exns`kbf

‣ J`s bugmqdb gdlè`d| sb|rd~ {ebf g E h|sbqdglbn cx @E hf g exns`lgsc`f

Mb~egf`d %{``n gdlè`d($

LE<@E$ h| sbdg~bn ~` mb~egfb$

LE>$ cx sbqdglhfk `fb E {h~e@E&

Gf h`f h| gf g~`m `s ks`rq `j g~`m| ~eg~ eg| g fb~ q`|h~hzb



Gf h`f h| gf g~`m$ `s ks`rq `j g~`m|$ ~eg~ eg| g fb~ q`|h~hzb`s fbkg~hzb legskb&

lg~h`f “ h`f {h~e g q`|h~hzb legskbHj g fbr~sgd g~`m d`|b| `fb `s m`sb bdbl~s`f|h~ cbl`mb| g lg~h`f&

gfh`f “ h`f {h~e g fbkg~hzb legskbHj g fbr~sgd g~`m kghf| `fb `s m`sb bdbl~s`f|h~ cbl`mb| gf gfh`f&

Fg77 qs`~`f|77 bdbl~s`f| Fg) 77 qs`~`f|71 bdbl~s`f|

Ld 7; qs`~`f|7; bdbl~s`f| Ld-

7; qs`~`f|75 bdbl~s`f|



H`f|

Mgkfb|hrm %Mk( eg| 73 qs`~`f|

)q )q )q )q )q)q )q)q )q )q )q )q

-b-b-b -b-b -b -b-b-b -b-b -b

Mgkfb|hrm eg| g ~bfnbflx ~` j`sm gf h`f {h~e gq`|h~hzb legskb hfnhlg~hfk ~eg~ bdbl~s`f| egzb cbbf d`||

Mk 3)



G m`fg~`mhl h`f l`f~ghf| `fdx `fb g~`m

G q`dxg~`mhl h`f l`f~ghf| m`sb ~egf `fb g~`m

Fg)$ Ld-$ Lg3)$ @3-$ Gd<)$ F<-

@E-$ LF-$ FE>)$ F@<

-



Srdb| j`s F`mbfldg~rsb

H`fhl L`mq`rfn|

%7( Fgmb ~eb mb~gd jhs|~ {h~e h~‘| `shkhfgd

fgmb%3( Fgmb ~eb f`fmb~gd {h~e ~eb |rjjhu —“hnb”





Srdb| j`s F`mbfldg~rsb

L`zgdbf~M`dblrdgs L`mq`rfn|

%7( Fgmb ~eb jhs|~ bdbmbf~ hf ~eb j`smrdg

{h~e h~‘| `shkhfgd fgmb%3( Fgmb ~eb |bl`fn bdbmbf~ hf ~ebj`smrdg {h~e ~eb |rjjhu —-hnb”

%<( R|b ksbbi qsbjhub| ~` nbf`~b e`{mgfx `j bgle bdbmbf~ gsb qsb|bf~



‣ êb frmcbs `j bgle ~xqb `j g~`m h|

|qblhjhbn {h~e Ksbbi qsbjhub|

Ksbbi Qsbjhub|

m`f`- = 7 %`j~bf mh~~bn( ebug- = :

nh- = 3 ebq~g- = ;

~sh- = < `l~g- = 5~b~sg- = > f`fg- = 8

qbf~g- = 2 nblg- = 71

Bugmqdb|?QJ2 = qe`|qe`sr| qbf~gjdr`shnb

L@3 = lgsc`f nhùhnb

F3@2 = nhfh~s`kbf qbf~ùhnb

F`~b? mgfxl`mq`rfn| egzb

l`mm`f fgmb|$ dhib

{g~bs j`s E3@&



\ d h h %h h e



‣ \`mb q`dxg~`mhl h`f| %h`f| {h~e ~{` `s

m`sb g~`m|(?

‣

‣

H`f Fgmb H`f FgmbFE>

)gmm`fhrm h`f L@<

3-lgsc`fg~b h`f

@E-

exnsùhnb h`f E<@)

exns`fhrm h`f

F@3-

fh~sh~b h`f \@<3-

|rdjh~b h`f

F@<

-

fh~sg~b h`f \@>

3-

|rdjg~b h`fLd@3

-led`sh~b h`f Ls@>

3-les`mg~b h`f

Ld@<-

led`sg~b h`f Ls3@;3-

nhles`mg~b h`f

Q@><-

qe`|qeg~b h`f



‣ ^` fgmb g l`mq`rfn$ x`r lgf r|b ~eh|

jd`{legs~?

)7 1



)3 )< ·> -< -3 -7

H`fhl Legskb|



J`smrdg `j H`fhl L`mq`rfn|



J`smrdg `j H`fhl L`mq`rfn|

Gd3@<

Gd<) @3-

LgCs3

Lg3) Cs-

Fg3L@<

Fg)

L@<3-



\`mb Q`dxg~`mhl H`f|

FE>)

gmm`fhrm \@>3-

|rdjg~b

L@<3-

lgsc`fg~b \@<3-

|rdjh~b

EL@<

-

chlgsc`fg~b F@<

-

fh~sg~bLd@<

-led`sg~b F@3

-fh~sh~b

Ls3@;3-

nhles`mg~b \LF-

~eh`lxgfg~b

Ls@>3- les`mg~b @E- exnsùhnb



Qs`cdbm|



Qs`cdbm|

Fgmb ~eb j`dd`{hfk l`mq`rfn|?

DhJ

MkLd3

Fg@E

Gd3%\@>(<

FE>F@<

Jb@



Qs`cdbm|

Khzb ~eb l`ssbl~ lebmhlgd j`smrdg j`s~eb j`dd`{hfk l`mq`rfn|

Lgdlhrm cs`mhnb

\~s`f~hrm qe`|qehnb

Q`~g||hrm |rdjg~b

Lgsc`f ~b~sgled`shnb

Dh~ehrm |bdbfhnb



Gf glhn lgf cb nbjhfbn g| g |rc|~gflb ~eg~ xhbdn|



xexns`kbf h`f| %E)( {ebf nh||`dzbn hf {g~bs&

ELd‣Qrsb |rc|~gflb$ exns`kbf led`shnb‣Nh||`dzbn hf {g~bs %E) Ld-($ exns`led`shl glhn

Gf ù`glhn h| gf glhn ~eg~ l`f~ghf| exns`kbf$ ùxkbf$ gfngf`~ebs bdbmbf~&

EF@< fh~shl glhn

E3L@< lgsc`fhl glhn

E3\@> |rdjrshl glhn









Fgmhfk Glhn|

Glhn| ~eg~ l`f~ghf g m`fg~`mhl gfh`fsblbhzb ~eb qsbjhu —exns`-” gfn ~eb

|rjjhu —-hl” ELd %gw( exns`led`shl

ECs %gw( exns`cs`mhl

EH %gw( exns`h`nhl



Fgmhfk Glhn| L`f~‘n

Glhn| ~eg~ l`f~ghf g q`dxg~`mhl gfh`fbfnhfk hf —-h~b” sblbhzb| ~eb |rjjhu —-

`r|” E3\@< %gw( |rdjrs`r|

E<Q@< %gw( qe`|qe`s`r|

EF@3 %gw( fh~s`r|



Fgmhfk Glhn| L`f~‘n

Glhn| ~eg~ l`f~ghf q`dxg~`mhl gfh`f|~eg~ bfn hf —-g~b” sblbhzb ~eb |rjjhu —-hl”

E3\@> %gw( |rdjrshlE<Q@> %gw( qe`|qe`shl

EF@< %gw( fh~shl



G cg|b lgf cb nbjhfbn g| g |rc|~gflb ~eg~ xhbdn|exnsùhnb h`f| %@E-( {ebf nh||`dzbn hf {g~bs&

Fg@E |`nhrm exnsùhnb

I@E q`~g||hrm exnsùhnb

Cg%@E(3 cgshrm exnsùhnb



58

LEGQ^BS <

Lgdlrdg~h`f| {h~e LebmhlgdJ`smrdg| gfn Bwrg~h`f|



81

G~`mhl [bhke~|

[bhke~bn gzbsgkb `j ~ebmg||b| `j ~eb l`f|~h~rbf~h|`~`qb| hj gf bdbmbf~&

^bdd| r| ~eb g~`mhl mg||b| `j bzbsx if`{f bdbmbf~&

D`{bs frmcbs `f qbsh`nhllegs~&



87

êb M`db

G frmcbs `j g~`m|$ h`f|$ `s m`dblrdb|~eg~ h| dgskb bf`rke ~` |bb gfn egfndb&

G m`db = frmcbs `j ~ehfk| Or|~ dhib g n`bf = 73 ~ehfk|

@fb m`db = :&133 u 713< ~ehfk|

Gz`kgns`‘| frmcbs = :&133 u 713<

\xmc`d j`s Gz`kgns`‘| frmcbs h| F G &



83

êb M`db

M`dgs mg|| - mg|| hf ksgm| frmbshlgddxbwrgd ~` ~eb g~`mhl {bhke~ `j ~eb bdbmbf~ hfksgm|&

E eg| gf g~`mhl {bhke~ `j 7&11;8> k

7&11;8> k `j E g~`m| = :&133 u 713< E g~`m|

Mk eg| gf g~`mhl {bhke~ `j 3>&<121 k

3>&<121 k `j Mk g~`m| = :&133 u 713< Mk g~`m|



8<

M`db gfn Gz`kgns`‘| Frmcbs

7 m`d Fg = :&13 u 71 3< Fg g~`m|

7 m`d E3 = :&13 u 71 3< E3 m`dblrdb|

7 m`db FgLd = :&13 u 71

3<

FgLd J`smrdg Rfh~|7 m`db Fg)7 = :&13 u 71 3< Fg)7 h`f|





82

êb M`db

Bugmqdb? E`{ mgfx g~`m| gsbl`f~ghfbn hf 7&:; m`db| `j Mk0

g~`m|Mk717&17

Mkm`d7

g~`m|Mk71:&133 Mkm`d7&:;g~`m|Mk0

3>

3<



8:

êb M`db

Bugmqdb? E`{ mgfx m`db| `j Mk g~`m| gsbqsb|bf~ hf ;<&> k `j Mk0

X`r n` h~'



8;

êb M`db

Bugmqdb 3->? E`{ mgfx m`db| `j Mk g~`m|gsb qsb|bf~ hf ;<&> k `j Mk0

Mkm d13&<

Mkk3>&<1g~ m|Mkm d7 Mkk>&;<Mkm d0

H^ H\ HMQBSG^HZB ÊG^ X@R IF@[E@[ ^@ N@ ÊB\B QS@CDBM\

J`smrdg [bhke~|$ M`dblrdgs



85

[bhke~|$ gfn M`db|

E`{ n` {b lgdlrdg~b ~eb m`dgs mg|| `j g l`mq`rfn0

gnn g~`mhl {bhke~| `j bgle g~`mêb m`dgs mg|| `j qs`qgfb$ L<E5$ h|?

gmr>>&77 mg||M`dgs

gmr5&15 gmr7&17 5E5

gmr<:&1<gmr73&17<L<




88

[bhke~|$ gfn M`db|

gmr7:>&71 mg||M`dgs

gmr8:&11 gmr7:&11: @:gmr35&13 gmr7>&173 F3

gmr>1&15 gmr>1&157 Lg7




711

[bhke~|$ gfn M`db|

Bugmqdb? Lgdlrdg~b ~eb frmcbs `j L<E5

m`dblrdb| hf ;>&: k `j qs`qgfb&

m dblrdb|7113&7

ELk>>&77

m dblrdb|EL71:&133

ELk>>&77

ELm db7

ELk;>&:m dblrdb|EL0

3>

5<

5<

3<

5<

5<

5<5<

Qbslbf~ L`mq`|h~h`f gfn



717

J`smrdg| `j L`mq`rfn|

" l`mq`|h~h`f = mg|| `j gf hfnhzhnrgdbdbmbf~ hf g l`mq`rfn nhzhnbn cx ~eb~`~gd mg|| `j ~eb l`mq`rfn u 711"

Nb~bsmhfb ~eb qbslbf~ l`mq`|h~h`f `j Lhf L<E5&

57&:5"

711"k>>&77

k73&17<

711"ELmg||

Lmg|| L"

5<

Qbslbf~ L`mq`|h~h`f gfnj



713


Bugmqdb? Lgdlrdg~b ~eb qbslbf~l`mq`|h~h`f `j Jb3%\@>(< ~` < |hkfhjhlgf~

jhkrsb|& X`r n` h~'

Qbslbf~ L`mq`|h~h`f gfnd j n



71<


Bugmqdb? Lgdlrdg~b ~eb qbslbf~l`mq`|h~h`f `j Jb3%\@>(< ~` < |hk& jhk&

711" ^`~gd

@>5&1"711"k<88&8

k7:&173 711"(%\@Jb

@73 @ "

\ 3>&7" 711"k<88&8

k<3&7< 711"

(%\@Jb

\< \ "

Jb3;&8" 711"k<88&8

k22&53

711"(%\@Jb

Jb3

Jb"

<>3

<>3

<>3

Nbshzg~h`f `j J`smrdg| js`md d L h h



71>

Bdbmbf~gd L`mq`|h~h`f

Bmqhshlgd J`smrdg - |mgddb|~ {e`db-frmcbs sg~h` `j g~`m| qsb|bf~ hf g l`mq`rfn LE3 h| ~eb bmqhshlgd j`smrdg j`s gdibfb|

F` gdibfb buh|~| ~eg~ eg| 7 L gfn 3 E‘|

M`dblrdgs J`smrdg - gl~rgd frmcbs| `j g~`m| `j bgle

bdbmbf~ qsb|bf~ hf g m`dblrdb `j ~eb l`mq`rfn B~ebfb “ L3E>

Qbf~bfb “ L2E71

[b nb~bsmhfb ~eb bmqhshlgd gfn m`dblrdgs j`smrdg| `j g

l`mq`rfn js`m ~eb qbslbf~ l`mq`|h~h`f `j ~ebl`mq`rfn& qbslbf~ l`mq`|h~h`f h| nb~bsmhfbn buqbshmbf~gddx

Nbshzg~h`f `j J`smrdg| js`mBd d L h h



712


Bugmqdb? G l`mq`rfn l`f~ghf| 3>&;>" I$<>&;:" Mf$ gfn >1&21" @ cx mg||& [eg~ h|h~| bmqhshlgd j`smrdg0

Mgib ~eb |hmqdhjxhfk g||rmq~h`f ~eg~ {begzb 711&1 k `j l`mq`rfn&

Hf 711&1 k `j l`mq`rfn ~ebsb gsb? 3>&;> k `j I

<>&;: k `j Mf >1&21 k `j @

Nbshzg~h`f `j J`smrdg| js`mBd ~ d L h~h



71:


sg~h`frmcbs{e db|mgddb|~`c~ghf

@m d3&2<7@k7:&11

@m d7@k>1&21 @m d0

Mfm d1&:<3;

Mfk2>&8>

Mfm d7Mfk<>&;:Mfm d0

Im d1&:<3;Ik<8&71

Im d7I k3>&;> Im d0




71;


Mf71&:<3;1&:<3;Mfj sI7

1&:<3;1&:<3;Ij s


@m d3&2<7@k7:&11

@m d7@k>1&21 @m d0

Mfm d1&:<3;Mfk2>&8>

Mfm d7Mfk<>&;:Mfm d0

Im d1&:<3;Ik<8&71

Im d7I k3>&;> Im d0




715


>IMf@h|j smrdglebmhlgd~eb~er|

@>1&:<3;

3&2<7@j s

Mf7

1&:<3;

1&:<3;Mfj sI7

1&:<3;

1&:<3;Ij s


@m`d3&2<7@k7:&11

@m`d7@k>1&21 @m`d0

Mfm`d1&:<3;Mfk2>&8>

Mfm`d7Mfk<>&;:Mfm`d0

Im`d1&:<3;Ik<8&71Im`d7I k3>&;> Im`d0




718


Bugmqdb? G |gmqdb `j g l`mq`rfnl`f~ghf| :&2>7k `j L` gfn 3&<:5k `j @&[eg~ h| bmqhshlgd j`smrdg j`s ~eh|l`mq`rfn0

X`r n` h~'




771


Bugmqdb? G |gmqdb `j g l`mq`rfnl`f~ghf| :&2>7k `j L` gfn 3&<:5k `j @&[eg~ h| bmqhshlgd j`smrdg j`s ~eh|l`mq`rfn0

sg~h`frmcbs{e db|mgddb|~jhfn

@m`d1&7>51@k7:&11

@m`d7

@k3&<:5@m`d0

L`m`d1&7771L`k25&8<

L`m`d7L`k:&2>7L`m`d0




777


Bugmqdb? G |gmqdb `j g l`mq`rfnl`f~ghf| :&2>7k `j L` gfn 3&<:5k `j @&[eg~ h| bmqhshlgd j`smrdg j`s ~eh|

l`mq`rfn0

><@L`

?h|j smrdg|l`mq`rfn+~ebêr|

@><@7&<<< L`<<L`7

frmcbs{e`db~`jsgl~h`f~rsf~`<cxc`~emrd~hqx

@7&<<<1&7771

1&7>51@j s L`7

1&7771

1&7771L`j s

\`mb @~ebs Hf~bsqsb~g~h`f| `j Le h d J d



773

Lebmhlgd J`smrdg|

Bugmqdb? [eg~ mg|| `j gmm`fhrmqe`|qeg~b$ %FE>(<Q@>$ {`rdn l`f~ghf72&1 k `j F0

Fm`d7&1;Fk7>&1

Fm`d7

F`j k72&1Fm`d0

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Qsblhqh~g~h`f Sbgl~h`f|



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ê e ~e ~ dn e h d d %



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êb l`flbf~sg~h`f `j g |`dr~h`f h| ~eb gm`rf~ `j



êb l`flbf~sg~h`f `j g |`dr~h`f h| ~eb gm`rf~ `j

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M = m`dgsh~x =m`db| `j |`dr~b

dh~bs| `j |`dr~h`f

[eg~ mg|| `j IH h| sbwrhsbn ~` mgib 211& mD `j g 3&51 M IH |`dr~h`f0

z`drmb IH m`db| IH ksgm| IH

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EF@< js`m g |~`li |`dr~h`f `j >&11 M EF@<0

M h Zh = M j Zj

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Zh =M j Zj

M h=

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gnnbn ksgnrgddx gnnbn ~` gf`~ebs |`dr~h`f `j rfif`{fl`flbf~sg~h`f rf~hd ~eb lebmhlgd sbgl~h`f cb~{bbf ~eb ~{`|`dr~h`f| h| l`mqdb~b&

Bwrhzgdbflb q`hf~ “ ~eb q`hf~ g~ {ehle ~eb sbgl~h`f h| l`mqdb~b

Hfnhlg~`s “ |rc|~gflb ~eg~ legfkb| l`d`s g~ %`s fbgs( ~ebbwrhzgdbflb q`hf~

\d`{dx gnn cg|b~` rfif`{f glhn

RF^HD

~eb hfnhlg~`slegfkb| l`d`s

[eg~ z`drmb `j g 7&>31 M Fg@E |`dr~h`f h|Sbwrhsbn ~` ~h~sg~b 32&11 mD `j g >&21 M E3\@>



Sbwrhsbn ~` ~h~sg~b 32&11 mD `j g >&21 M E3\@>

|`dr~h`f0

[SH^B ÊB LEBMHLGD BWRG^H@F'

z`drmb glhn m`db| glhn m`db| cg|b z`drmb cg|b

E3\@> ) 3Fg@E 3E3@ ) Fg3\@>

>&21 m`d E3\@>

7111 mD |`dfu

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u7111 md |`df

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Legq~bs 2? Qs`qbs~hb| `j Kg|b|



q q



Kg|b| egzb g frmcbs `j qs`qbs~hb|~eg~ gsb zbsx nhjjbsbf~ js`m dhwrhn| gfn|`dhn|?

7( Kg|b| gsb l`mqsb||hcdb

3( Kg|b| bubs~ g qsb||rsb

<( Kg| qsb||rsb nbqbfn| `f ~eb gm`rf~ `j l`fjhfbn kg|

>( Kg|b| jhdd ~ebhs l`f~ghfbs

2( Kg|b| mhu jsbbdx {h~e bgle `~ebs

:( Kg| qsb||rsb hflsbg|b| {h~e ~bmqbsg~rsb



êb ebhke~ `j ~eb mbslrsx l`drmf



zgshb| {h~e gd~h~rnb

êb gzbsgkb qsb||rsb g~ |bg dbzbd `s~eb |~gfngsn g~m`|qebsb %g~m( {g|nbjhfbn g| ~eb qsb||rsb fbbnbn ~`

|rqq`s~ g l`drmf `j mbslrsx ;:1 mmehke mbg|rsb| g~ 1`L

êb \H rfh~ `j qsb||rsb h| ~eb qg|lgd

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X`r mgx bfl`rf~bs g frmcbs `j qsb||rsb rfh~|



qsb||rsb rfh~|

êb |~gfngsn g~m`|qebsb h|

Lebmhlgd sbgl~h`f| `j~bf hfz`dzb kg|b|

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qsb||rsb hf|hnb ld`|bn l`f~ghfbs|

@qbf-bfn mgf`mb~bs& %g( êb qsb||rsb `j ~eb ~sgqqbnkg|$ Qkg| bwrgd| ~eb g~m`|qebshl qsb||rsb$ Qg~m& ^sgqqbnkg| qsb||rsb %c( ehkebs gfn %l( d`{bs ~egf g~m`|qebshlqsb||rsb&

G d n n j



G ld`|bn-bfn mgf`mb~bs j`s

mbg|rshfk kg| qsb||rsb| db||~egf 7 g~m& [ebf l`f|~srl~bn%g( ~eb ~rcb h| jrddx bzglrg~bngfn mbslrsx h| gdd`{bn ~` bf~bsgfn jhdd ~eb ld`|bn gsml`mqdb~bdx& %g( Mbslrsx jd`{|`r~ `j ~eb ld`|bn gsm {ebf ~ebcrdc l`f~ghf| kg| g~ d`{qsb||rsb& êb nhjjbsbflb hf

mbslrsx dbzbd|$ QEk$ h| ~ebqsb||rsb `j ~eb l`fjhfbn kg|$Qkg|&

êbsb gsb j`rs zgshgcdb| ~eg~ gjjbl~ ~eb~h j d



qs`qbs~hb| `j g kg|? qsb||rsb$ z`drmb$

~bmqbsg~rsb$ gfn ~eb gm`rf~ `j ~ebkg|

\hmqdb buqbshmbf~| lgf cb l`fnrl~bn

~eg~ sbdg~b e`{ ~eb|b zgshgcdb| legfkbêb kg| dg{| |rmmgshb ~eb|bbuqbshmbf~|



L`mqsb||hfk g kg|

hflsbg|b| h~|qsb||rsb& G m`dblrdgs zhb{ `j {eg~ egqqbf| {ebf

g kg| h| |wrbbbnhf~` g |mgddbsz`drmb& êb frmcbs`j l`ddh|h`f| {h~e gkhzbf gsbg `j ~eb

{gdd| hflsbg|b| {ehlelgr|b| ~eb qsb||rsb~` sh|b&



S`cbs~ C`xdb |~rnhbn e`{ ~eb z`drmb `j g jhubngm`rf~ `j kg| zgshb| {h~e qsb||rsb g~ l`f|~gf~~bmqbsg~rsb& %g( Ghs ~sgqqbn hf g O-~rcb cx mbslrsx&%c( G| m`sb mbslrsx h| gnnbn$ ~eb qsb||rsb `j ~eb~sgqqbn kg| hflsbg|b| gfn ~eb z`drmb nblsbg|b|&



%g( G ~xqhlgd ksgqe `j z`drmb zbs|r| qsb||rsb |e`{hfkz`drmb nblsbg|hfk g| qsb||rsb hflsbg|b|& %c( G |~sghke~dhfb h| `c~ghfbn {ebf z`drmb h| qd`~~bn gkghf|~ %7Q ($

{ehle |e`{| ~eg~

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7

êb sbdg~h`f|ehq cb~{bbf z`drmb gfn



q

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êb z`drmb `j g khzbf gm`rf~ `j kg| ebdn g~ l`f|~gf~ ~bmqbsg~rsb zgshb| hfzbs|bdx

{h~e ~eb gqqdhbn qsb||rsb

êb qs`q`s~h`fgdh~x lgf cb sbm`zbn cxhf~s`nrlhfk g qs`q`s~h`fgddx l`f|~gf~$ L

sb(~bmqbsg~rgfngm`rf~%l`f|~gf~s7 L QZ L Q

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Q7 Z7 = i Q3 Z3 = i

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i Z

i Q

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Q 3 = 0

Z 3 = 72> mD

Q 3 =

Q 7 u Z 7

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C`xdb‘| dg{ h| sbmgsigcdx |rllb||jrd$b|qblhgddx j`s l`mm`f dgc`sg~`sx



b|qblhgddx j`s l`mm`f dgc`sg~`sx

l`fnh~h`f|E`{bzbs$ f` sbgd kg| `cbx| C`xdb‘| dg{bugl~dx `zbs g {hnb sgfkb `j

~bmqbsg~rsb| gfn qsb||rsb|êb exq`~eb~hlgd kg| ~eg~ n`b|bugl~dx `cbx C`xdb‘| dg{ h| lgddbn gfhnbgd kg|

Sbgd kg|b| gl~ m`sb dhib hnbgd kg|b| g|~ebhs qsb||rsb| nblsbg|b gfn~bmqbsg~rsb| hflsbg|b

Oglwrb| Gdbugfnbs Legsdb| |~rnhbn e`{~e d j d h n h~e



~eb z`drmb `j g kg| |gmqdb zgshbn {h~e~bmqbsg~rsb Legsdb|‘ dg{

qd`~|& Bgle dhfb|e`{| e`{ ~ebkg| z`drmblegfkb| {h~e~bmqbsg~rsb j`snhjjbsbf~ |hbn|gmqdb| `j ~eb

|gmb kg|&

[ebf bu~sgq`dg~bn ~` bs` z`drmb gdd~eb |gmqdb| egzb ~eb |gmb



~eb |gmqdb| egzb ~eb |gmb

~bmqbsg~rsb?

êh| ~bmqbsg~rsb h| lgddbn gc|`dr~b

bs` gfn h| ~eb cg|h| `j ~eb Ibdzhf~bmqbsg~rsb |lgdb?

Legsdb|‘ dg{ `s ~eb ~bmqbsg~rsb-z`drmbdg{ lgf cb buqsb||bn mg~ebmg~hlgddx

L72&3;< `

72&3;<LI ` ^ ^

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Kgx-Dr||gl|‘ dg{ `s ~eb qsb||rsb-~bmqbsg~rsb dg{ |~g~b|?

êb qsb||rsb `j g jhubn gm`rf~ `j kg| ebdn

g~ l`f|~gf~ z`drmb h| nhsbl~dx qs`q`s~h`fgd~` ~eb Ibdzhf ~bmqbsg~rsb

Mg~ebmg~hlgddx ~eh| h|

z drmb(gfngm`rf~%l`f|~gf~#`s ^ L Q^ Q



êb ~esbb kg| dg{| gsb `j~bf r|bn hf g|hfkdb bwrg~h`f lgddbn ~eb l`mchfbnkg| dg{

[ebf r|hfk ~eh| bwrg~h`f ~eb

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q xk

521 m<

g~ :22 ~`ss gfn 32&1`

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GFGDX\H\? R|b ~eb l`mchfbn kg| dg{ {h~e

~bmqbsg~rsb hf ibdzhf|&\@DR^H@F?

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Gmbnb` Gz`kgns` |~rnhbn ~eh| gfn nbzh|bn Gz`kgns`‘|qshflhqdb?

[ebf mbg|rsbn g~ ~eb |gmb ~bmqbsg~rsb gfn



qsb||rsb$ bwrgd| z`drmb| `j kg|b| l`f~ghf bwrgdfrmcbs `j m`db|

êb z`drmb `j g kg| h| nhsbl~dx qs`q`s~h`fgd ~` h~|frmcbs `j m`db|$ f

êr|$ ~eb z`drmb `j `fb m`db `j gfx kg| g~

|~gfngsn ~bmqbsg~rsb gfn qsb||rsb %\^Q( `s1`L gfn 7 g~m h| 33&> D %g l`f|~gf~ j`s gdd hnbgdkg|b|(

êh| h| lgddbn ~eb |~gfngsn m`dgs z`drmb `j g

(gfnl`f|~gf~%g~ Q^ fZ

Gmm`fhg crsf| hf ùxkbf ~` j`sm fh~shl ùhnb %F@(gfn {g~bs zgq`s& E`{ mgfx dh~bs| `j F@ gsb `c~ghfbnjs`m 71 dh~bs| `j gmm`fhg g~ ~eb |gmb ~bmqbsg~rsb



gfn qsb||rsb0 E`{ mgfx dh~bs| `j ùxkbf gsb

sbwrhsbn0>FE< ) 2@3 >F@ ) :E3@

7 m`db FE<

7 m`db F@

G~ l`f|~gf~ ^ gfn Q

7 z`drmb FE< 7 z`drmb F@

êb l`mchfbn kg| dg{ lgf cbkbfbsgdhbn ~` hfldrnb legfkb| hf ~eb



k k

frmcbs `j m`db| `j |gmqdbêb hnbgd kg| dg{ h|

Im d

Dg~m 1&1537

l`f|~gf~kg|rfhzbs|gd

S

fS^ QZ





êb m`dblrdgs mg|| h| `c~ghfbn cx



~gihfk ~eb sg~h` `j mg|| ~` m`db|$ {ehlel`rdn cb nb~bsmhfbn r|hfk ~eb hnbgd kg|dg{

Kg| nbf|h~hb| %n ($ g sg~h` `j kg| mg||~` z`drmb$ lgf cb lgdlrdg~bn cx ~gihfk~eb sg~h` `j ~eb m`dgs mg|| ~` m`dgsz`drmb

Bugmqdb? êb m`dgs mg|| `j ùxkbf h|<3&1 km`d& [eg~ h| ~eb nbf|h~x `j ùxkbfg~ \^Q0

7

@ Dk>3&7D/m d33&>

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n

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[b f`{ fbbn ~` l`f|hnbs mhu~rsb| `j

kg|b|@fb r|bjrd {gx ~` nb|lshcb gl`mq`|h~h`f `j g mhu~rsb h| hf ~bsm| `j

h~| m`db jsgl~h`f| êb m`db jsgl~h`f h| ~eb sg~h` `j ~ebfrmcbs `j m`db| `j g khzbf l`mq`fbf~~` ~eb ~`~gd m`db| `j gdd l`mq`fbf~|

g~ \^Q& Lgsc`f

nhùhnb h| m`sbnbf|b ~eg~ ùxkbfnrb ~` m`dgs mg||nhjjbsbflb|&

J`s g mhu~rsb `j G $ C $ … |rc|~gflb|$~eb m`db jsgl~h`f `j |rc|~gflb h %Uh( h|



~eb m`db jsgl~h`f `j |rc|~gflb h %U h ( h|

êh| qs`zhnb| g l`fzbfhbf~ {gx ~`

aqgs~h~h`f‘ ~eb ~`~gd qsb||rsb `j gmhu~rsb `j kg|b|

Ngd~`f‘| dg{ `j qgs~hgd qsb||rsb|

|~g~b|? ~eb ~`~gd qsb||rsb `j g mhu~rsb`j kg|b| h| ~eb |rm `j ~ebhs hfnhzhnrgdqgs~hgd qsb||rsb|

hffff

f U h

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G G `j m`db| $

&&&

J`s g |x|~bm `j `fdx kg|b|$ m`dbjsgl~h`f| gfn qgs~hgd qsb||rsb qgs~h~h`f



jsgl~h`f| gfn qgs~hgd qsb||rsb qgs~h~h`f

~eb ~`~gd qsb||rsb hf ~eb |gmb jg|eh`f

Kg|b| gsb `j~bf l`ddbl~bn `zbs {g~bs hf~eb dgc`sg~`sx

êb|b %l`ddbl~bn( kg|b| gsb |g~rsg~bn{h~e {g~bs

&&&7

&&&&

&&&&

C G

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êb |qglb gc`zb gfx dhwrhn l`f~ghf||`mb `j ~eb dhwrhn‘| zgq`s



|`mb `j ~eb dhwrhn | zgq`s

êb qsb||rsb ~eh| zgq`s bubs~| h| lgddbn~eb zgq`s qsb||rsb

G| ~eb kg| crccdb| ~es`rke ~eb {g~bs$ {g~bs zgq`s kb~|hf~` ~eb kg| |` ~eb ~`~gd qsb||rsb hf|hnb ~eb c`~~dbhfldrnb| ~eb qgs~hgd qsb||rsb `j ~eb {g~bs zgq`s&

>&2;8 1

%~`ss(Qsb||rsbZgq`sL(%b^bmqbsg~rs `



êb ~`~gd qsb||rsb h| ~eb qsb||rsb `j ~ebkg| qdr| ~eb zgq`s qsb||rsb `j {g~bs

;:1&1 711

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Zgq`sqsb||rsb `j {g~bs g~zgsh`r|~bmqbsg~rsb|

&

gq`s {g~bs ~`~gdkg|

gq`s {g~bs kg|~`~gd

QQQQQQ

z

z s

Bugmqdb? G |gmqdb `j ùxkbf h| l`ddbl~bn`zbs {g~bs g~ 31`L gfn g qsb||rsb `j ;<5~`ss [eg~ h| ~eb qgs~hgd qsb||rsb `j



~`ss& [eg~ h| ~eb qgs~hgd qsb||rsb `j

ùxkbf0 GFGDX\H\? êb qgs~hgd qsb||rsb `j ùxkbf h|

db|| ~egf ~eb ~`~gd qsb||rsb& Kb~ ~eb zgq`sqsb||rsb `j {g~bs js`m ~gcdb 77&3 %qgkb

>;5(&\@DR^H@F?

Qgs~hgd qsb||rsb| lgf cb r|bn ~`lgdlrdg~b m`db jsgl~h`f|

~`ss;31&~`ss(2>&7;;<5%

77&3(^gcdb%js`m~`ss2>&7;

kg|

zgq`s {g~bs

Q

Q

êh| h| q`||hcdb cblgr|b ~eb frmcbs `j



m`db| `j bgle kg| h| nhsbl~dxqs`q`s~h`fgd ~` h~| qgs~hgd qsb||rsb

R|hfk ~eb hnbgd kg| bwrg~h`f j`s bgle kg|

J`s g khzbf mhu~rsb `j kg|b|$ ~ebz`drmb gfn ~bmqbsg~rsb h| ~eb |gmb j`sgdd kg|b|

R h L Z S^ h

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êb qgs~hgd qsb||rsb `j g kg| lgf cblgdlrdg~bn r|hfk ~eb ~`~gd qsb||rsb gfnm`db jsgl~h`f

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Nhjjr|h`f h| ~eb |q`f~gfb`r|hf~bsmhfkdhfk `j ~eb m`dblrdb| `j `fb



hf~bsmhfkdhfk `j ~eb m`dblrdb| `j `fb

kg| {h~e gf`~ebs

Bjjr|h`f h| ~eb m`zbmbf~ `j kg|m`dblrdb| ~es`rke g ~hfx e`db hf~` g

zglrrmêb sg~b| `j c`~e nhjjr|h`f gfn bjjr|h`fnbqbfn `f ~eb |qbbn `j ~eb kg|

m`dblrdb|êb jg|~bs ~eb m`dblrdb|$ ~eb jg|~bsnhjjr|h`f gfn bjjr|h`f `llrs



Q`|~rdg~b| `j ~eb Ihfb~hl êb`sx `j Kg|b|



7( G kg| l`f|h|~| `j g dgskb frmcbs `j ~hfxqgs~hldb| ~eg~ gsb hf l`f|~gf~$ sgfn`mm`~h`f&

3( êb kg| qgs~hldb| ~ebm|bdzb| `llrqx g

fb~ z`drmb |` |mgdd hf sbdg~h`f ~` ~ebz`drmb `j ~ebhs l`f~ghfbs ~eg~ ~ebhsl`f~shcr~h`f ~` ~eb ~`~gd z`drmb lgf cbhkf`sbn&

<( êb l`ddh|h`f| cb~{bbf qgs~hldb gfn {h~e~eb {gdd| `j ~eb l`f~ghfbs gsb qbsjbl~dxbdg|~hl&

Lgdlrdg~h`f| |e`{ ~eg~ QZ h|



qs`q`s~h`fgd ~` ~eb gzbsgkb ihfb~hlbfbskx gfn ~eb Ibdzhf ~bmqbsg~rsb $~er|

êb ihfb~hl ~eb`sx gd|` buqdghf| ~eb kg|dg{|

IBm dblrdgsgzbsgkb

IBm dblrdgsgzbsgkb

^ ^ QZ

QZ

Ksgegm‘| dg{ sbwrhsb| ~eg~ ~eb sg~b `j bjjr|h`f j`s ~eb nhjjbsbf~ kg|b| cb



l`mqgsbn g~ ~eb |gmb ~bmqbsg~rsb gfnqsb||rsb

[ebf nhjjbsbf~ kg|b| egzb ~eb |gmb

~bmqbsg~rsb$ ~ebx egzb ~eb |gmbgzbsgkb ihfb~hl bfbskx

êb gzbsgkb ihfb~hl bfbskx lgf cb

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~eb gzbsgkb m`dblrdgs |qbbn$ ~er|

êb ihfb~hl ~eb`sx qsbnhl~| ~eg~gc|`dr~b bs` h| ~eb ~bmqbsg~rsb g~{ehle ~eb gzbsgkb ihfb~hl bfbskx `j gfhnbgd kg| h| bs`

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[eg~ h| ~eb z`drmb `j L@3 qs`nrlbn g~ <;1 L gfn 7&11g~m {ebf 2&:1 k `j kdrl`|b gsb r|bn rq hf ~eb sbgl~h`f?

L:E73@: %| ( ) :@3 %k ( :L@3 %k ( ) :E3@ %d (

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Z =fS^

Q

1&75; m`d u 1&1537 u <71&72 ID‣g~m

m`d‣I

7&11 g~m= = >&;: D

Hnbgd Kg| Dg{ gfn Sbgl~h`f\~`hleh`mb~sx



\`nhrm ghnb %FgF<( h| r|bn hf |`mb ghs cgk| hfgr~`m`chdb|& Lgdlrdg~b ~eb z`drmb `j fh~s`kbf kg|kbfbsg~bn g~ 37 `L gfn 53< mm Ek cx ~ebnbl`mq`|h~h`f `j :1&1 k `j FgF< &

3 FgF< %|( 3 Fg %|( ) < F3 %k(

G |gmqdb `j fg~rsgd kg| l`f~ghf| 5&3> m`db| `j LE>$1&>37 m`db| `j L3E:$ gfn 1&77: m`db| `j L<E5& Hj ~eb~`~gd qsb||rsb `j ~eb kg|b| h| 7&<; g~m$ {eg~ h| ~ebqgs~hgd qsb||rsb `j qs`qgfb %L<E5(0



qgs~hgd qsb||rsb `j qs`qgfb %L<E5(0

Q h = U h Q

U qs`qgfb = 1&77:5&3> ) 1&>37 ) 1&77:

Q = 7&<; g~m

= 1&17<3

Q qs`qgfb = 1&17<3 u 7&<; g~m = 1&1757 g~m



êbsm`lebmh|~sx

egq~bs :

êbsm`lebmhlgd Nbjhfh~h`f|\x|~bm ? êg~ qgs~ `j ~eb Rfhzbs|b {e`|b legfkb {b gsb

k`hfk ~` mbg|rsb&



\rss`rfnhfk| ? Bzbsx ~ehfk bd|b ~eg~ h| sbdbzgf~ ~` ~eb legfkbh| nbjhfbn g| ~eb —|rss`rfnhfk|”&

Hf~bsfgd Bfbskx ? êb |rm `j ~eb ihfb~hl gfn q`~bf~hgd bfbskx

`j gdd ~eb qgs~hldb| hf g |x|~bm&

Ebg~ %w( ? H| ~eb bfbskx ~sgf|jbssbn cb~{bbf g |x|~bm

gfn h~‘| |rss`rfnhfk| g| sb|rd~ hf ~eb nhjjbsbflb| hf

~ebhs ~bmqbsg~rsb| fdx'

[`si %{( ? êb bfbskx ~sgf|jbssbn {ebf gf `cobl~ h| m`zbn cx

g j`slb&

êbsbj`sb? B = w ) {

êbsm`nxfgmhl|

\~g~b jrfl~h`f| gsb qs`qbs~hb| ~eg~ gsb nb~bsmhfbn cx ~eb |~g~b`j ~eb |x|~bm$ sbkgsndb|| `j e`{ ~eg~ l`fnh~h`f {g| glehbzbn&



bfbskx$ qsb||rsb$ z`drmb$ ~bmqbsg~rsb

NB = w ) {

NB h| ~eb legfkb hf hf~bsfgd bfbskx `j g |x|~bm

w = ~eb ebg~ bulegfkb cb~{bbf~eb |x|~bm gfn ~eb |rss`rfnhfk|

{ h| ~eb {`si n`fb `f %`s cx( ~eb |x|~bm

{ = -Q NZ {ebf g kg| buqgfn| gkghf|~g l`f|~gf~ bu~bsfgd qsb||rsb

êbsm`nxfgmhl|



Nb~bsmhfhfk Bfbskx Legfkb hf g \x|~bm

Qs`cdbm? Hf ~eb hf~bsfgd l`mcr|~h`f bfkhfb$ ~eb ebg~ qs`nrlbn cx ~eb

l`mcr|~h`f `j ~eb jrbd lgr|b| ~eb lgsc`f nhùhnb gfn {g~bs ~eg~ h|



qs`nrlbn nrshfk ~eb l`mcr|~h`f ~` buqgfn$ qr|ehfk ~eb qh|~`f|& Bulb||ebg~ h| sbm`zbn cx ~eb l``dhfk |x|~bm& Nb~bsmhfb ~eb legfkb hf bfbskx

% B( hf O$ iO$ gfn ilgd hj ~eb buqgfnhfk kg|b| n` 272 O `j {`si `f ~eb

qh|~`f|$ gfn gfn ~eb |x|~bm d`|b| >1; O `j ebg~ ~` ~eb l``dhfk |x|~bm&

w = - >1; O { = -272

OB = w ) { = - >1; O ) % - 272 O( = - 833 O

B = - 833 O u 7 iO = -1&833 iO

7111 O

B = - 833 O u 7 lgd = - 331 lgd

>&75> O



B h| g |~g~b jrfl~h`f$ w gfn { gsb f`~&

Jhs|~ Dg{ `j êbsm`nxfgmhl|



% Dg{ `j L`f|bszg~h`f `j Bfbskx (

—êb ^`~gd Bfbskx `j ~eb Rfhzbs|b h| L`f|~gf~”

B `j Rfhzbs|b = B\x|~bm ) B\rss`rfnhfk| = 1

Ebg~ h| ~eb ~sgf|jbs `j ~ebsmgd bfbskx cb~{bbf ~{` c`nhb| ~eg~gsb g~ nhjjbsbf~ ~bmqbsg~rsb|&

Bfbskx Legfkb| hf Lebmhlgd Sbgl~h`f|



^bmqbsg~rsb h| g mbg|rsb `j ~eb ~ebsmgd bfbskx&

bmqbsg~rsb = êbsmgd Bfbskx

811L>11L

ksbg~bs ~ebsmgd bfbskx

êbsm`lebmh|~sx h| ~eb |~rnx `j ebg~ legfkb hf lebmhlgdsbgl~h`f|&

êb |x|~bm h| ~eb |qblhjhl qgs~ `j ~eb rfhzbs|b ~eg~ h| `j hf~bsb|~ hf ~eb |~rnx&



hf~bsb|~ hf ~eb |~rnx&

`qbf

mg|| * bfbskxBulegfkb?

ld`|bn

bfbskx

h|`dg~bn

f`~ehfk

\X\^BM\RSS@RFNHFK\

Bu`~ebsmhl qs`lb|| h| gfx qs`lb|| ~eg~ khzb| `jj ebg~ “~sgf|jbs| ~ebsmgd bfbskx js`m ~eb |x|~bm ~` ~eb |rss`rfnhfk|&

3E3 %k( ) @3 %k( 3E3@ %d( ) bfbskx



Bfn`~ebsmhl qs`lb|| h| gfx qs`lb|| hf {ehle ebg~ eg| ~` cb|rqqdhbn ~` ~eb |x|~bm js`m ~eb |rss`rfnhfk|&

3E3 %k ( ) @3 %k ( 3E3@ %d ( ) bfbskx

E3@ %k ( E3@ %d ( ) bfbskx

bfbskx ) 3Ek@ %| ( 3Ek %d ( ) @3 %k (

bfbskx ) E3@ %| ( E3@ %d (

Legfkb hf Bf~egdqx = E

Bf~egdqx h| nbjhfbn g| ~eb |x|~bm‘| hf~bsfgd bfbskx



Bf~egdqx h| nbjhfbn g| ~eb |x|~bm | hf~bsfgd bfbskx

qdr| ~eb qs`nrl~ `j h~| qsb||rsb gfn z`drmb&

E = B ) QZJ`s g legfkb hf bf~egdqx?

E = B ) QZ

Bu`~ebsmhl gfn Bfn`~ebsmhl Sbgl~h`f|?

E = Ejhfgd

- Ehfh~hgd

= Eqs`nrl~|

- Esbgl~gf~|

Bu`~ebsmhl ? E jhfgd E hfh~hgd E 1

Bfn`~ebsmhl ? E jhfgd E hfh~hgd E 1

`s qs`lb||b| `llrss fk gl`f|~gf~ qsb||rsb ~ebbf~egdqx legfkb bwrgd| ~eb



ebg~ kghfbn `s d`|~&

NE = wq

bf~egdqx `j sbgl~h`f `s ebg~ `j

sbgl~h`f& %Bfbskx legfkb )|mgdd l`ssbl~h`f jgl~`s&(

Bf~egdqx %E( h| r|bn ~` wrgf~hjx ~eb ebg~ jd`{ hf~` `s `r~ `j g|x|~bm hf g qs`lb|| ~eg~ `llrs| g~ l`f|~gf~ qsb||rsb&

NE = E %qs`nrl~|( “ E %sbgl~gf~|(



NE = ebg~ khzbf `jj `s gc|`scbn nrshfk g sbgl~h`f g~ l`f|~gf~ qsb||rsb

E qs`nrl~| 4 E sbgl~gf~|

NE 4 1

E qs`nrl~| 6 E sbgl~gf~|

NE 6 1

êbsm`lebmhlgd Bwrg~h`f|

H| NE fbkg~hzb `s q`|h~hzb0



E3@ %| ( E3@ %d ( NE = :&17 iO

\x|~bm gc|`sc| ebg~

Bfn`~ebsmhl

NE 6 1

:&17 iO gsb gc|`scbn j`s bzbsx 7 m`db `j hlb ~eg~

mbd~| g~ 11L gfn 7 g~m&


H| NE fbkg~hzb `s q`|h~hzb0



LE> %k ( ) 3@3 %k( L@3 %k( ) 3E3@ %d ( NE = -581&> iO

\x|~bm khzb| `jj ebg~

Bu`~ebsmhl

NE 4 1

581&> iO gsb sbdbg|bn j`s bzbsx 7 m`db `j mb~egfb

~eg~ h| l`mcr|~bn g~ 321L gfn 7 g~m&

‣ êb |~`hleh`mb~shl l`bjjhlhbf~| gd{gx| sbjbs ~` ~eb frmcbs`j m`db| `j g |rc|~gflb




E3@ %| ( E3@ %d ( NE = :&17 iO

‣ Hj x`r sbzbs|b g sbgl~h`f$ ~eb |hkf `j NE legfkb|

E3@ %d ( E3@ %| ( NE = -:&17 iO‣ Hj x`r mrd~hqdx c`~e |hnb| `j ~eb bwrg~h`f cx g jgl~`s f $

~ebf NE mr|~ legfkb cx ~eb |gmb jgl~`s f &

3E3@ %| ( 3E3@ %d ( NE = 3 u :&17 = 73&1 iO

‣ êb qex|hlgd |~g~b| `j gdd sbgl~gf~| gfn qs`nrl~| mr|~ cb|qblhjhbn hf ~ebsm`lebmhlgd bwrg~h`f|&




E3@ %| ( E3@ %d ( NE = :&17 iO

E3@ %d ( E3@ %k ( NE = >>&1 iO

E`{ mrle ebg~ h| bz`dzbn {ebf 3:: k `j {eh~bqe`|qe`sr| %Q>( crsf hf ghs0

Q> %| ( ) 2@3 %k ( Q>@71 %| ( NE = -<17< iO

3:: k Q>7 m`d Q>

73<&8 k Q>

u <17< iO7 m`d Q>

u = :>;1 iO

êb |qblhjhl ebg~ %| ( `j g |rc|~gflb h| ~eb gm`rf~ `j ebg~ %w (sbwrhsbn ~` sgh|b ~eb ~bmqbsg~rsb `j `fb ksgm `j ~eb|rc|~gflb cx `fb nbksbb Lbd|hr|&

êb ebg~ lgqglh~x %L( `j g |rc|~gflb h| ~eb gm`rf~ `j ebg~ %w(



êb ebg~ lgqglh~x %L ( `j g |rc|~gflb h| ~eb gm`rf~ `j ebg~ %w (sbwrhsbn ~` sgh|b ~eb ~bmqbsg~rsb `j g khzbf wrgf~h~x %m ( `j ~eb |rc|~gflb cx `fb nbksbb Lbd|hr|&

L = m|

Ebg~ %w ( gc|`scbn `ssbdbg|bn?

w = m| N~

w = L N~ N~ = ~ jhfgd -~ hfh~hgd

E`{ mrle ebg~ h| khzbf `jj {ebf gf 5:8 k hs`f cgs l``d|js`m 8>1L ~` 21L0

1



| `j Jb = 1&>>> Ok ‣

1

L

N~ = ~ jhfgd “ ~ hfh~hgd = 21L “ 8>1L = -581L

w = m| N~ = 5:8 k u 1&>>> Ok ‣ 1L u “581L = -<>$111 O

L`f|~gf~-Z`drmb Lgd`shmb~sx



F` ebg~ bf~bs| `s dbgzb|'

w |x| = w {g~bs ) w c`mc ) w suf

w |x| = 1

w suf = - %w {g~bs ) w c`mc

w {g~bs = m |N~

w c`mc = L c`mc N~

Sbgl~h`f g~ L`f|~gf~ Z

NE v w suf

NE = w suf

L`f|~gf~-Qsb||rsb Lgd`shmb~sx



F` ebg~ bf~bs| `s dbgzb|'

w |x| = w {g~bs ) w lgd ) w suf

w |x| = 1

w suf = - %w {g~bs ) w lgd(w {g~bs = m |N~

w lgd = L lgd N~

Sbgl~h`f g~ L`f|~gf~ Q NE = w suf



\~gfngsn bf~egdqx `j j`smg~h`f %NE1( h| ~eb ebg~ legfkb~eg~ sb|rd~| {ebf `fb m`db `j g l`mq`rfn h| j`smbn js`m

j



h~| bdbmbf~| %hf m`|~ |~gcdb j`sm( g~ g qsb||rsb `j 7 g~m&

êb |~gfngsn bf~egdqx `j j`smg~h`f `j gfx bdbmbf~ hf h~|

m`|~ |~gcdb j`sm h| bs`&

NE` %@3( = 1j

NE` %@<( = 7>3 iOm`dj

NE` %L$ ksgqeh~b( = 1j

NE` %L$ nhgm`fn( = 7&81 iOm`dj



êb |~gfngsn bf~egdqx `j sbgl~h`f %NE1 ( h| ~eb bf~egdqx `j gsbgl~h`f lgsshbn `r~ g~ 7 g~m&

suf

g G ) c C l L ) n N



NE`suf n NE` %N(j l NE` %L(j = Y ) ] - c NE` %C(j g NE` %G(j Y ) ]

NE`suf f NE` %qs`nrl~|(j = \ m NE` %sbgl~gf~|(j \-

Eb||‘| Dg{? [ebf sbgl~gf~| gsb l`fzbs~bn ~` qs`nrl~|$ ~eblegfkb hf bf~egdqx h| ~eb |gmb {eb~ebs ~eb sbgl~h`f ~gib|qdglb hf `fb |~bq `s hf g |bshb| `j |~bq|&

%Bf~egdqx h| g |~g~b jrfl~h`f& H~ n`b|f‘~ mg~~bs e`{ x`rkb~ ~ebsb$ `fdx {ebsb x`r |~gs~ gfn bfn&(

Eb||‘| Dg{ `j Ebg~ \rmmg~h`fêb bf~egdqx legfkb `j gf `zbsgdd qs`lb|| h| ~eb |rm `j

~eb bf~egdqx legfkb| `j h~| hfnhzhnrgd |~bq|&



Bugmqdb?

Qs`cdbm? Lgdlrdg~b ~eb bfbskx hfz`dzbn hf ~eb ùhng~h`f `j bdbmbf~gd

|rdjrs ~` |rdjrs ~shùhnb js`m sbgl~h`f|?

7( \ %|( ) @3 %k( \@3 %k( E7 = -38:&1 iO

3( 3 \@3 %k( ) @3 %k( 3 \@< %k( E3 = -785&3 iO

<( \ %|( ) <3 @3 %k( \@< %k( E< = 0



Hj x`r gnn ~{` `s m`sbbwrg~h`f| ~` kb~ g fb{

bwrg~h`f$ x`r mr|~ gnn ~ebE‘| ~` kb~ ~eb E j`s

~eb fb{ bwrg~h`f&

Lgdlrdg~b ~eb |~gfngsn bf~egdqx `j j`smg~h`f `j L\3 %d (khzbf ~eg~?

L%ksgqeh~b( ) @3 %k ( L@3 %k ( NE1 = -<8<&2 iOsuf

\%se`mchl( ) @3 %k ( \@3 %k ( NE1 = -38:&7 iOsuf



L\3%d ( ) <@3 %k ( L@3 %k ( ) 3\@3 %k ( NE1 = -71;3 iOsuf

7& [sh~b ~eb bf~egdqx `j j`smg~h`f sbgl~h`f j`s L\3

L%ksgqeh~b( ) 3\%se`mchl( L\3 %d (

3& Gnn ~eb khzbf suf| |` ~eg~ ~eb sb|rd~ h| ~eb nb|hsbn suf&

sufL%ksgqeh~b( ) @3 %k ( L@3 %k ( NE1 = -<8<&2 iO

3\%se`mchl( ) 3@3 %k ( 3\@3 %k ( NE1 = -38:&7u3 iOsuf

L@3%k ( ) 3\@3 %k ( L\3 %d ( ) <@3 %k ( NE1 = )71;3 iOsuf)

L%ksgqeh~b( ) 3\%se`mchl( L\3 %d (

NE1 = -<8<&2 ) %3u-38:&7( ) 71;3 = 5:&< iOsuf

Cbfbfb %L:E:( crsf| hf ghs ~` qs`nrlb lgsc`f nhùhnb gfndhwrhn {g~bs& E`{ mrle ebg~ h| sbdbg|bn qbs m`db `j cbfbfb l`mcr|~bn0 êb |~gfngsn bf~egdqx `j j`smg~h`f`j cbfbfb h| >8&1> iOm`d&



3L:E: %d ( ) 72@3 %k ( 73L@3 %k ( ) :E3@ %d (

NE1suf f NE1 %qs`nrl~|(j = \ m NE1 %sbgl~gf~|(j \-

NE1suf :NE

1

%E3@(j 73NE1

%L@3(j = Y ) ] - 3NE1

%L:E:(j Y ]

NE1suf = Y 73% “<8<&2( ) :% “352&5( ] “ Y 3%>8&1>( ] = -:2<>&55

-:2<2iO

3 m`d = - <3:; iOm`d L:E:



Qs`qbs~hb| `j [gzb|



[gzbdbfk~e %d( h| ~eb nh|~gflb cb~{bbf hnbf~hlgd q`hf~|`f |rllb||hzb {gzb|&

[gzb| gsb gf `|lhddg~h`f ~eg~ m`zb| `r~{gsn js`m g nh|~rscgflb&

Qs`qbs~hb| `j [gzb|

Jsbwrbflx %f( h| ~eb frmcbs `j {gzb| ~eg~ qg|| ~es`rke g



qgs~hlrdgs q`hf~ hf 7 |bl`fn %E = 7 lxldb|(&

êb |qbbn %r ( `j ~eb {gzb = d u f

Gmqdh~rnb h| ~eb zbs~hlgd nh|~gflb js`m ~eb mhndhfb `j g{gzb ~` ~eb qbgi `s ~s`rke&





[ebf l`qqbs h| c`mcgsnbn {h~e ehke-bfbskx bdbl~s`f|$U sgx| gsb bmh~~bn& Lgdlrdg~b ~eb bfbskx %hf o`rdb|(g||`lhg~bn {h~e ~eb qe`~`f| hj ~eb {gzbdbfk~e `j ~eb Usgx| h| 1&72> fm&



B = ef

B = :&:< u 71-<> %O‣|( u <&11 u 71 5 %m|(1&72> u 71-8 %m(

B = 7&38 u 71 -72 O

B = eld

7& b- lgf `fdx egzb |qblhjhl

Cès‘| M`nbd `j ~eb G~`m %787<(



%wrgf~hbn( bfbskxzgdrb|

3& dhke~ h| bmh~~bn g| b-

m`zb| js`m `fb bfbskx

dbzbd ~` g d`{bs bfbskxdbzbd

Bf = -S E% (7

f 3

f %qshflhqgd wrgf~rm frmcbs( = 7$3$<$…

S E %Sxncbsk l`f|~gf~( = 3&75 u 71-75O

Lgdlrdg~b ~eb {gzbdbfk~e %hf fm( `j g qe`~`fbmh~~bn cx g exns`kbf g~`m {ebf h~| bdbl~s`fns`q| js`m ~eb f = 2 |~g~b ~` ~eb f = < |~g~b&



Bqe`~`f = 3&75 u 71-75 O u %732 - 78(=7&22 u 71-78 O

= :&:< u 71-<> %O‣|( u <&11 u 715 %m|(7&22 u 71-78O

= 7&35 u 71-: m

Bqe`~`f = e u l d

d = e u l Bqe`~`f

h j

NB = S E% (7f 3

7f 3

Bqe`~`f =

= 7&35 u 71-: m u 7fm = 7351 fm

71-8m

Gll`snhfk ~` nb Cs`kdhb gf bdbl~s`f c`rfn ~` g frldbr| cbegzb| dhib

Qs`cdbm| {h~e ~eb Cès m`nbd&Cès‘| gqqs`gle `fdx {`si| j`s ~eb exns`kbf g~`m& H~ lgf f`~ buqdghf ~eb

|qbl~sg `j g~`m| {h~e m`sb ~egf `fb bdbl~s`f&



g |~gfnhfk {gzb&

Gf gdd`{bn bfbskx |~g~b h| `fb hf {ehle gf hf~bksgd frmcbs `j {gzb| {hdd jh~ gs`rfn ~eb lhslrmjbsbflb `j ~eb `sch~&êr| nb Cs`kdhb |rkkb|~bn ~eg~ ~eb {gzb dbfk~e `j g mg~~bs {gzb

h| khzbf cx

[ebsb?e = qdgfli‘| l`f|~gf~ = :&:< u 71-<>

ι = {gzbdbfk~em = mg|| `j qgs~hldbz = zbd`lh~x `j qgs~hldb

d= e

mz

Cès‘| gfn nb Cs`kdhb‘| gqqs`gle nhn f`~{`si j`s g~`m| `~ebs ~egf exns`kbf&

Hf ~eb 7831‘| Ebh|bfcbsk$ \lesúnhfkbs$



gfn Nhsgl nbzbd`qbn ~eb m`nbsf ~eb`sx `j ~eb g~`m {ehle {b lgdd WRGF^RMMBLEGFHL\&

êb Ebh|bfcbsk Rflbs~ghf~x Qshflhqdb? H~ h|hmq`||hcdb ~` if`{ |hmrd~gfb`r|dx c`~e

~eb m`mbf~rm gfn q`|h~h`f `j g qgs~hldb{h~e lbs~ghf~x&

[ebf ~eb \lesúnhfkbs bwrg~h`f h||`dzbn j`s ~eb E g~`m {b kb~ ~eb

e e d



bugl~ bfbskx |~g~b| ~eg~ ~eb bdbl~s`flgf `llrqx& G||`lhg~bn {h~e bgle

bfbskx |~g~b h| g {gzb jrfl~h`f $q|h&

êb |wrgsb `j khzb| ~eb qs`cgchdh~x

~eg~ ~eb bdbl~s`f {hdd cb j`rfn hf gqgs~hlrdgs sbkh`f& êh| sbkh`f h| lgddbn gf`sch~gd&

@sch~gd? ~eb sbkh`f hf |qglb {ebsb



~eb bdbl~s`f h| m`|~ dhibdx ~` cbj`rfn&

F`~b? WM ~bdd| r| f`~ehfk gc`r~ ~ebqg~e `j ~eb bdbl~s`f& @fdx

qs`cgchdh~x hfj`smg~h`f h| khzbf&

[ebf ~eb \lesúnhfkbs bwrg~h`f h|

|`dzbn$ ~eb bfbskhb| gfn `sch~gd| gsb

j n n n d



j`rfn ~` nbqbfn `f |bzbsgd wrgf~rmfrmcbs|&

ÊB QSHFLHQGD WRGF^RM FRMCBS f = 7$ 3$ <$ >$ 2$ …&H~ ~bdd| ~eb qshflhqdb bfbskx dbzbd `j ~eb

bdbl~s`f gfn h~| gzbsgkb nh|~gflb js`m~eb frldbr|&

ÊB GFKRDGS M@MBF^RM W&F&d = 1$7$ 3$ <$ …%f-7(

n j



|$ q$ n$ j H~ ~bdd| ~eb |rc-dbzbd `j ~eb bdbl~s`fgfn ~eb |egqb `j ~eb `sch~gd&

ÊB MGKFB^HL W&F&m

d= - d …& ) d

H~ ~bdd| ~eb frmcbs `j `sch~gd| gfn ~ebhs`shbf~g~h`f hf |qglb&



d = 1 %| `sch~gd|(



d = 7 %q `sch~gd|(

d = 3 %n `sch~gd|(

Bdbl~s`f \qhf

Buqbshmbf~| hfnhlg~b ~eg~ ~eb bdbl~s`f q`||b||b| gf

hf~shf|hl gfkrdgs m`mbf~rm {ehle h| l`f|~gf~ gfn g

c h j e d G h h e



cg|hl qs`qbs~x `j ~eb bdbl~s`f& G |qhffhfk legskb

kbfbsg~b| g mgkfb~hl jhbdn - ~er| ~eb bdbl~s`f

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3 L ~ ~ ~ d c j d



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Bugmqdb?

[eg~ h| ~eb Db{h| \~srl~rsb j`s {g~bs0

E3@




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E L @ EE

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=7

3

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-

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bdbl~s`f| {bsb |egsbn bwrgddx&

J`smgd Legskb



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~eb |qblhb|&

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qdgr|hcdb ~egf ~e`|b {h~e |mgdd j`smgd legskb|&

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E L @ E

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1 1



E L @ EE

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Sb|`fgflb |~srl~rsb| gsb l`ffbl~bn cx g

n`rcdb-ebgnbn gss`{& êb ~srb |~srl~rsb h| gcdbfn `j ~eb sb|`fgflb |~srl~rsb|&

Sb|`fgflb hfnhlg~b| ~eg~ bdbl~s`f nbd`lgdhg~h`f

`llrs| hf ~eb m`dblrdb&

G sb|`fgflb |~srl~rsb h| `fb `j ~{` `s m`sb Db{h||~srl~rsb| j`s g |hfkdb m`dblrdb ~eg~ lgff`~ cb sbqsb|bf~bngllrsg~bdx cx `fdx `fb Db{h| |~srl~rsb&

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êb Hfl`mqdb~b @l~b~

E ECbCb “ 3b-

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>b-3

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C “ <b-

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< |hfkdb c`fn| %<u3( =: 8 d`fb qghs| %8u3( = 75

^`~gd = 3>

Bulbq~h`f| ~` ~eb @l~b~ Srdb

@nn-Bdbl~s`f M`dblrdb|

F “ 2b-

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77b-

êb Buqgfnbn @l~b~ %lbf~sgd g~`m {h~e qshflhqgd wrgf~rm frmcbs f 6 3(

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J

JJ

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: |hfkdb c`fn| %:u3( = 73

75 d`fb qghs| %75u3( = <:^`~gd = >5

E`{ ~eb M`nbd Buqdghf| ~eb Qs`qbs~hb|`j L`zgdbf~ L`mq`rfn|

êb l`zgdbf~ c`fnhfk m`nbd qs`q`|b| ~eg~ bdbl~s`f |egshfk

dbgn| ~` |~s`fk$ d`lgdhbn c`fn|& Cr~ m`|~ l`mq`rfn| {h~e



l`zgdbf~ c`fn| gsb kg|b|$ dhwrhn|$ `s d`{-mbd~hfk |`dhn|&

H`fhl l`mq`rfn gsb ehke-mbd~hfk |`dhn|&

[ex h| ~eh|0 Gsb l`zgdbf~ c`fn| {bgibs ~egf h`fhl c`fn|0

[h~ehf g m`dblrdb ~ebsb gsb |~s`fk hf~sgm`dblrdgs c`fn|&

Cb~{bbf m`dblrdb| ~ebsb gsb {bgi hf~bsm`dblrdgs j`slb|&

êb dg~~bs gsb {eg~ nb~bsmhfb mbd~hfk gfn c`hdhfk q`hf~|&

L`mqgsh|`f `j H`fhl gfn L`zgdbf~ L`mq`rfn|







er| ~eb sbdg~h`f|ehq cb~{bbf c`fn dbfk~e$ c`fn |~sbfk~e$ gfn c`fn bfbskx h| ?

êb |e`s~bs ~eb c`fn dbfk~e$~eb ksbg~bs ~eb c`fn |~sbfk~e$



~eb ksbg~bs ~eb c`fn bfbskx'

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êb d`fkbs ~eb c`fn dbfk~e$~eb d`{bs ~eb c`fn |~sbfk~e$

~eb d`{bs ~eb c`fn bfbskx'



M`dblrdgs Kb`mb~sx gfnExcshnhg~h`f `j G~`mhl @sch~gd|

Legq~bs 71

Zgdbflb \ebdd Bdbl~s`f-Qghs Sbqrd|h`f

%Z\BQS( êb`sx

M`dblrdgs \egqb|



Bgle ks`rq `j zgdbflb bdbl~s`f| gs`rfn g

lbf~sgd g~`m h| d`lg~bn g| jgs g{gx js`m ~eb

`~ebs| g| q`||hcdb hf `snbs ~` mhfhmhbsbqrd|h`f&

Gf bdbl~s`f ks`rq mgx cb g |hfkdb$ n`rcdb$`s ~shqdb c`fn `s g d`fb qghs&

Cgdd``f Gfgd`kx j`s ~eb Mr~rgdSbqrd|h`f `j Bdbl~s`f Ks`rq|



^{` êsbb J`rs Jhzb \hu

Frmcbs `j Bdbl~s`f Ks`rq|



Zgdbflb |ebdd bdbl~s`f qghs sbqrd|h`f %Z\BQS( m`nbd?

Qsbnhl~ ~eb kb`mb~sx `j ~eb m`dblrdb js`m ~eb bdbl~s`|~g~hlsbqrd|h`f| cb~{bbf ~eb bdbl~s`f %c`fnhfk gfn f`fc`fnhfk( qghs|&

, `j g~`m| , d`fb



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71&7

dhfbgs dhfbgs

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71&7

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71&7

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71&7


Ldg||

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71&7

GC>

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71&7


Ldg||

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71&7

GC>

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71&7


Ldg||

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71&7

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71&7

X`r mr|~ nh|~hfkrh|e cb~{bbf ~eb bdbl~s`f-ks`rq

gssgfkbmbf~ gfn ~eb m`dblrdgs |egqb& êb

m`dblrdgs |egqb h| nbjhfbn cx ~eb sbdg~hzb q`|h~h`f|`j ~eb g~`mhl frldbh& Hj ~ebsb gsb f` d`fb qghs| `j

M`dblrdgs \egqb|



`j ~eb g~`mhl frldbh& Hj ~ebsb gsb f` d`fb qghs| `j

bdbl~s`f| ~eb m`dblrdgs |egqb h| ~eb |gmb g| ~eb

bdbl~s`f-ks`rq gssgfkbmbf~&



d`fb-qghs z|& d`fbqghs sbqrd|h`f

C`fnhfk-qghs z|&c`fnhfk qghs

sbqrd|h`f

d`fb-qghs z|& c`fnhfkqghs sbqrd|h`f

4 4

Ldg||

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71&7

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71&7

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71&7

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71&7

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71&7

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71&7

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71&7

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71&7

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71&7

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71&7

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71&7

GC>B > 7~shk`fgd

chqxsgmhngdnh|~`s~bn

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71&7

3



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71&7

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71&7

GC2B 2 7 `l~gebnsgdw

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Ub

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71&7

Qsbnhl~hfk M`dblrdgs Kb`mb~sx[eg~ gsb ~eb m`dblrdgs kb`mb~shb| `j G|E<$@J3$ GdLd>

-$ E<@)$ \fLd2

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71&7

G|E<shk`fgd qxsgmhn

@J3

cbf~

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Q`dgs M`dblrdb| - Nhq`dbm`mbf~|

G q`dgs m`dblrdb h| `fb ~eb eg| g q`|h~hzb bfn gfn gfbkg~hzb bfn& %êb lbf~bs `j q`|h~hzb legskb gfn



~eb lbf~bs j fbkg~hzb legskb n` f`~ l`hflhnb&( G

q`dgs m`dblrdb h| |ghn ~` egzb g nhq`db m`mbf~&

G m`dblrdb {h~e ~{` `s m`sb q`dgs c`fn| lgf cb

f`fq`dgs hj h~ h| |xmmb~shlgd&

Nhq`db M`mbf~| gfn Q`dgs M`dblrdb|

E J

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71&3

n n

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gfn E3@

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@

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L@ @

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êb c`fn| gsb q`dgs$ gfn

~eb m`dblrdb h|

f`f-|xmmb~shlgd&

êb c`fn| gsb q`dgs$

cr~ ~eb m`dblrdb h|

|xmmb~shlgd$ |` ~eg~ ~ebm`dblrdb `zbsgdd h|

f`f-q`dgs&

Qsbnhl~hfk êb Q`dgsh~x `j M`dblrdb|

Qs`cdbm? Js`m bdbl~s`fbkg~hzh~x$ gfn ~ebhs qbsh`nhl ~sbfn|$ qsbnhl~

{eb~ebs bgle `j ~eb j`dd`{hfk m`dblrdb| h| q`dgs gfn |e`{ ~eb nhsbl~h`f

`j c`fn nhq`db| gfn ~eb `zbsgdd m`dblrdgs nhq`db&

%g( Qe`|qehfb$ QE<

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%g(

Q E

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71&3

[ehle `j ~eb j`dd`{hfk m`dblrdb| egzb g nhq`db m`mbf~0E3@$ L@3$ \@3$ gfn LE>

@

nhq`db m`mbf~q`dgs m`dblrdb

\

nhq`db m`mbf~q`dgs m`dblrdb



71&3

q`dgs m`dblrdb

L@ @

f` nhq`db m`mbf~f`fq`dgs m`dblrdb

q`dgs m`dblrdb

L

E

E

EE

f` nhq`db m`mbf~f`fq`dgs m`dblrdb

Zgdbflb C`fn êb`sx

Cg|hl Qshflhqdb `j Zgdbflb C`fn êb`sx?

g l`zgdbf~ c`fn j`sm| {ebf ~eb `sch~gd| js`m

~{` g~`m| `zbsdgq gfn g qghs `j bdbl~s`f|`llrqhb| ~eb sbkh`f cb~{bbf ~eb frldbh&

R dd ~eh ~e ~ e c nh ch~ d



êb c`fn |~sbfk~e nbqbfn| `f ~eb g~~sgl~h`f `j frldbh j`s

~eb |egsbn bdbl~s`f|$ |` ~eb ksbg~bs ~eb `sch~gd `zbsdgq$~eb |~s`fkbs ~eb c`fn&

R|rgddx ~eh| mbgf| ~eg~ bgle c`fnhfk `sch~gd

|e`rdn l`f~ghf `fb bdbl~s`f& êb bdbl~s`f|

mr|~ egzb `qq`|h~b |qhf|&



êb |q Excshn @sch~gd| hf Kg|b`r| CbLd





Excshnhg~h`f h| ~eb mhuhfk `j g~`mhl`sch~gd| hf gf g~`m ~` kbfbsg~b g |b~ `j

fb{ `sch~gd| lgddbn excshn `sch~gd|&

êb ~`~gd frmcbs `j `sch~gd| n`b|f‘~



legfkb&

L`zgdbf~ c`fn| gsb j`smbn cx?

g& @zbsdgq `j excshn `sch~gd| {h~e g~`mhl `sch~gd|

c& @zbsdgq `j excshn `sch~gd| {h~e `~ebs excshn`sch~gd|







71&>



71&>

, bdbl~s`f ks`rq|

)Bdbl~s`f kb`mb~sx

Excshnhg~h`f Bugmqdb|

E`{ n` H qsbnhl~ ~eb excshnhg~h`f `j ~eb lbf~sgd g~`m0

L`rf~ ~eb ks`rq| `j bdbl~s`f|gfn nb~bsmhfb ~eb bdbl~s`f kb`mb~sx&



Excshnhg~h`f Bugmqdb|

3 %dhfbgs(

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êb |q<n3 Excshn @sch~gd| hf\J:



\rdjrs Ebugjdr`shnb -- \J:

Qsbnhl~ l`ssbl~

c`fn gfkdb



Gdd ~eb c`fn| {b egzb |bbf |` jgs gsb lgddbn

|hkmg c`fn|? ~eb ehkeb|~ bdbl~s`f nbf|h~x h| gd`fk

~eb c`fn guh|& Gdd |hfkdb c`fn| gsb |hkmg c`fn|

gfn ~eb jhs|~ c`fn hf n`rcdb `s ~shqdb c`fn| h| g|hkmg c`fn&



G qh c`fn h| j`smbn cx g |hnb-~`-|hnb `zbsdgq `j

q `sch~gd|& êbsb gsb sbkh`f| `j ehke bdbl~s`fnbf|h~x gc`zb gfn cbd`{ ~eb c`fn guh|& êb |bl`fn

c`fn `j g n`rcdb c`fn h| g qh c`fn$ g| gsb ~{` `j ~eb

c`fn| hf g ~shqdb c`fn&



71&2



\hkmg c`fn %|( “ bdbl~s`f nbf|h~x cb~{bbf ~eb 3 g~`m|Qh c`fn %q( “ bdbl~s`f nbf|h~x gc`zb gfn cbd`{ qdgfb `j frldbh

`j ~eb c`fnhfk g~`m| 71&2



71&2

\hkmg %|( gfn Qh C`fn| %q(

\hfkdb c`fn 7 |hkmg c`fn

N`rcdb c`fn 7 |hkmg c`fn gfn 7 qh c`fn^shqdb c`fn 7 |hkmg c`fn gfn 3 qh c`fn|



E`{ mgfx | gfn q c`fn| gsb hf ~eb glb~hl glhn

%zhfbkgs( m`dblrdb LE<L@@E0

L

E

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LE

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q c`fn| = 7

71&2

\ihq qgkb| <75-<3: m`dblrdgs `sch~gd|

Sb|`fgflb hmqdhb| bdbl~s`f nbd`lgdhg~h`f& êh|

lgf cb buqdghfbn cx zgdbflb c`fn gfn m`dblrdgs

`sch~gd ~eb`sx&

êh| `llrs| {ebf g q `sch~gd `zbsdgq| {h~e m`sb



~egf `fb `~ebs q `sch~gd& êb q bdbl~s`f| gsb jsbb

~` m`zb gs`rfn ~esbb `s m`sb g~`m|&Bugmqdb|? ``fb$ cbfbfb$ |rdjrs ~shùhnb&

\~srl~rsb| {h~e nbd`lgdhbn bdbl~s`f| gd{gx|

egzb ksbg~bs |~gchdh~x ~egf |hmhdgs |~srl~rsb|{h~e`r~ nbd`lgdhbn bdbl~s`f|&

Nbd`lgdhbn bdbl~s`f| gsb f`~ l`fjhfbn cb~{bbf ~{`

gnoglbf~ c`fnhfk g~`m|$ cr~ gl~rgddx bu~bfn `zbs ~esbb `sm`sb g~`m|&



71&5



Bfbskx dbzbd| `j c`fnhfk gfn gf~hc`fnhfk m`dblrdgs`sch~gd| hf exns`kbf %E3(&



G c`fnhfk m`dblrdgs `sch~gd eg| d`{bs bfbskx gfn ksbg~bs|~gchdh~x ~egf ~eb g~`mhl `sch~gd| js`m {ehle h~ {g| j`smbn&

Gf gf~hc`fnhfk m`dblrdgs `sch~gd eg| ehkebs bfbskx gfnd`{bs |~gchdh~x ~egf ~eb g~`mhl `sch~gd| js`m {ehle h~ {g|j`smbn& 71&:



71&:



71&:

M`dblrdgs @sch~gd %M@( L`fjhkrsg~h`f|

7& êb frmcbs `j m`dblrdgs `sch~gd| %M@|( j`smbn h| gd{gx|bwrgd ~` ~eb frmcbs `j g~`mhl `sch~gd| l`mchfbn&

3& êb m`sb |~gcdb ~eb c`fnhfk M@$ ~eb db|| |~gcdb ~ebl`ssb|q`fnhfk gf~hc`fnhfk M@&

< êb jhddhfk `j M@| qs`lbbn| js`m d`{ ~` ehke bfbskhb|



<& êb jhddhfk j M@| qs`lbbn| js`m d`{ ~` ehke bfbskhb|&

>& Bgle M@ lgf gll`mm`ng~b rq ~` ~{` bdbl~s`f|&

2& R|b Erfn‘| srdb {ebf gnnhfk bdbl~s`f| ~` M@| `j ~eb|gmb bfbskx&

:& êb frmcbs `j bdbl~s`f| hf ~eb M@| h| bwrgd ~` ~eb |rm `j

gdd ~eb bdbl~s`f| `f ~eb c`fnhfk g~`m|&

71&;

c`fn `snbs =7

3

Frmcbs `j bdbl~s`f| hfc`fnhfkM@|

Frmcbs `j bdbl~s`f| hfgf~hc`fnhfkM@|

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