grignard reagent, reduction & alkane theory_e

27
"kbh`sdfukbrpdys`as.`h"  2 ADJK@Q^\P I\@IHB\N \JB IJH^ , \JNZA^@OH & B MFB HJ 2. I\@IHB\N \JBIJH^ 2.2 Ori bhokjtbmm`a aokpou hns Oribhokjtbmm`a aokp ouhns brj tdj oribh`a aokpou hns `h wd`ad b kjt bm btok `s n` rjatm y bttbadjn to abrloh oe or ibh` a kojt`y tdrouid aovbmjht lohn or `oh`a lohn. Eor jxbkp mj A K or  (Ydjrj A `s b abrloh btok oe bh oribh`a komjaumj bhn K `s b kjtbm btok) @e tdj kjtbm btok `s bttbadjn to oxyijh, h`troijh. sumpdur, jta., tdjh suad bh oribh`a aokpouhn `s hot rjibrnjn bs bh oribhokjtbmm`a aokpouhn. ^dj eommow`hi struaturbm eorkumb no hot ljmohi to tdj ebk`my oe oribhokjtbm m`a aokpouhns. \OHb (Qon`uk bmfox`nj). AD 1 AOOHb (Qon`uk bajtbtj), AD 1 AOOBi(Q`mvjrbajtbtj),\QF (Wotbss`uk kjrabpt`nj) \HDF (H-Bmfym potbssbk`nj), (AD 1 AOO) > Wl (Mjb n tjtrbbajtb tj), jta. Ho tj 3  @tsdou mnljhotjn td bt (AD 1 ) > Q` (^ jtr bkjtdyms`mbh j, ^KQ) `s bmso hot bh oribhokjtbmm `a aokpouhn lja bus j s`m`aoh `s b hohkjtbm. Kost `kportbht jxbkpmjs oe oribhokjtbmm`a aokpouhns brj Ir`ihbrn rjbijhts. @h Ir`ihbrn rjbijht, tdj abr loh bhn kbi hjs`uk bt oks brj lohnjn w` td jbad otdjr tdrouid po mbr ao vb mjhtlohn bh n kbi hj s` uk btok `s bttbadjn to dbmoijh ly `oh`a lohn. (Euhat`ohbm pbrt oe b Ir` ihb rn rjb ijh t komjaumj) @h oribhokjtbmm`a aokpouhns, tdj kjtbm btok abh lj lohnjn to abrloh btok oe b dynroabrloh pbrts (Qbturbtjn, uhsbt urbtjn, bm`pdbt` a, bm`ayam`a or brokbt`a) or abrloh btok oe b djtjroayam`a pbrt. Qokj jxbkpmjs brj i`vjh ljmow. Qbturbtjn Bm`pdbt`a Ir`ihbrn rjbijht 3- AD 1  ‑ Ki@ (Kjtdy mkbihjs` uk `on`nj ) Zhsbtur btjn Bm`pdbt `a Ir`ihbrn rjbijh t 3 - (` ) Bm fj h ym Ir `i hbrn rj bi j ht 3 - AD < ; AD AD <  ‑ KiT (Bmmymkbihjs`uk dbm`nj) (` ` ) Bmf yhy m Ir `ih br n rj bi jht 3 - AD A AD <  ‑ KiT (Wropbriymkbihjs`uk dbm`nj) Bm`ayam`a Ir`ihbrn rjbijht 3 - (Ayamodjxymkbihjs`uk dbm`nj) Brokbt`a Ir`ihbrn rjbijht 3 (Wdjhymkbihjs`uk dbm`nj) Djtjroayam`a Brokbt`a Ir`ihbrn rjbijht 3-  (Wyr`n`hj->-kbihjs`uk dbm`nj) Djtjroayam`a Hohbrokbt`a Ir`ihbrn rjbijht 3-  (W`pjr`njhj->-kbihjs`uk dbm`nj) 2. < Wrjpbr bt` oh oe Ir`ihbrn \jbijht \T + Ki Jtdjr purj bhn Nry                \KiT Jtdjr `s usjn bs b somvjht ljabusj `t `s b Mjw`s lbsj tdbt nohbtjs `ts mohj pb`r oe jmjatrohs to jmjatroh- nje`a`jht kbihjs`uk btok, tdjrjeorj prov`n`hi stbl`m`ty to tdj Ir`ihbrn rjbijht ly aokpmjt`hi tdj oatjt oh kbihjs`uk btok.     

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8/12/2019 Grignard Reagent, Reduction & Alkane Theory_E

http://slidepdf.com/reader/full/grignard-reagent-reduction-alkane-theorye 1/26

"kbh`sdfukbrpdys`as.`h"   2

ADJK@Q^\P

I\@IHB\N \JBIJH , \JNZA^@OH & BMFBHJ

2. I\@IHB\N \JBIJH^

2.2 Oribhokjtbmm`a aokpouhnsOribhokjtbmm`a aokpouhns brj tdj oribh`a aokpouhns `h wd`ad b kjtbm btok `s n rjatmy bttbadjn to abrlohoe oribh`a kojt`y tdrouid aovbmjht lohn or `oh`a lohn. Eor jxbkpmj

A ‑ K or  (Ydjrj A `s b abrloh btok oe bh oribh`a komjaumj bhn K `s b kjtbm btok)

@e tdj kjtbm btok `s bttbadjn to oxyijh, h`troijh. sumpdur, jta., tdjh suad bh oribh`a aokpouhn `s hotrjibrnjn bs bh oribhokjtbmm`a aokpouhn. ^dj eommow`hi struaturbm eorkumb no hot ljmohi to tdj ebk`my oe oribhokjtbmm`a aokpouhns.\OHb (Qon`uk bmfox`nj). AD

1AOOHb (Qon`uk bajtbtj), AD

1AOOBi(Q`mvjrbajtbtj),\QF (Wotbss`uk

kjrabpt nj) \HDF(H-Bmfympotbssbk`nj), (AD

1AOO)

>Wl (Mjbn tjtrbbajtbtj), jta.

Hotj 3   @t sdoumn lj hotjn tdbt (AD1)

>Q` ( jtrbkjtdyms mbhj, ^KQ) `s bmso hot bh oribhokjtbmm a aokpouhn ljabusj

s`m`aoh `s b hohkjtbm.Kost `kportbht jxbkpmjs oe oribhokjtbmm`a aokpouhns brj Ir`ihbrn rjbijhts. @h Ir`ihbrn rjbijht, tdj

abrloh bhn kbihjs`uk btoks brj lohnjn w td jbad otdjr tdrouid pombr aovbmjht lohn bhn kbihjs`uk btok`s bttbadjn to dbmoijh ly `oh`a lohn.

(Euhat ohbm pbrt oe b Ir`ihbrn rjbijht komjaumj)

@h oribhokjtbmm`a aokpouhns, tdj kjtbm btok abh lj lohnjn to abrloh btok oe b dynroabrloh pbrts(Qbturbtjn, uhsbturbtjn, bm`pdbt`a,bm`ayam`a or brokbt`a) or abrloh btok oe b djtjroayam`a pbrt. Qokj jxbkpmjs brj i`vjh ljmow.

Qbturbtjn Bm`pdbt`a Ir`ihbrn rjbijht  3- AD1 ‑ Ki@

(Kjtdymkbihjs`uk `on`nj)

Zhsbturbtjn Bm`pdbt a Ir`ihbrn rjbijht 3 -

(`) Bmfjhym Ir ihbrn rjbijht 3 - AD<

; AD ‑ AD< ‑ KiT (Bmmymkbihjs`uk dbm`nj)

(` ) Bmfyhym Ir ihbrn rjbijht 3 - AD A ‑ A D< ‑ KiT (Wropbriymkbihjs`uk dbm`nj)

Bm`ayam`a Ir`ihbrn rjbijht 3 - (Ayamodjxymkbihjs`uk dbm`nj)

Brokbt`a Ir`ihbrn rjbijht 3 (Wdjhymkbihjs`uk dbm`nj)

Djtjroayam`a Brokbt`a Ir`ihbrn rjbijht 3-   (Wyr`n`hj->-kbihjs`uk dbm`nj)

Djtjroayam`a Hohbrokbt`a Ir`ihbrn rjbijht 3-   (W`pjr`njhj->-kbihjs`uk dbm`nj)

2.< Wrjpbrbt`oh oe Ir`ihbrn \jbijht

\T + KiJtdjr 

purjbhnNry                  \KiT

Jtdjr `s usjn bs b somvjht ljabusj `t `s b Mjw`s lbsj tdbt nohbtjs `ts mohj pb`r oe jmjatrohs to jmjatroh-nje`a`jht kbihjs`uk btok, tdjrjeorj prov`n`hi stbl`m`ty to tdj Ir`ihbrn rjbijht ly aokpmjt`hi tdj oatjt ohkbihjs`uk btok.

   

8/12/2019 Grignard Reagent, Reduction & Alkane Theory_E

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"kbh`sdfukbrpdys`as.`h"   <

ADJK@Q^\P

2.1 \jbat`ohs oe Ir`ihbrn rjbijhts@t dbs ljjh eouhn out ly jst kbt`oh tdbt tdjrj `s 1:% `oh`a adbrbatjr `h abrloh-kbihjs`uk lohn oe Ir`ihbrnrjbijht. ^djrjeorj, tdjrj `s b tjhnjhay oe eork`hi abrlbh`oh ly djtjromys`s oe td`s pombr aoorn`hbtj lohn bseommows.

      +

^dj abrlbh`oh (b huamjopd`mj) eorkjn bs sdowh blovj, bttbafs tdj pos t vjmy, adbrijn jmjatropd`m a ajhtrj oe otdjr aokpouhn. ^djrjeorj. @t abh lj sb`n tdbt `e b Ir`ihbrn rjbijht `s rjibrnjn bs tdj sulstrbtj, tdjh

jmjatropd`mj n`spmbajs KiT, `.j. jmjatropd`m`a sulst`tut`oh (QJ) rjbat`oh tbfjs pmbaj.

\ ‑ KiT        \ ‑ J (QJ Wronuat)

Ir`ihbrn rjbijhts eork bnnuats ly bnn`t`oh oh tdj eommow`hi typjs oe p` lohns.

, , bhn A   H , ‑ H ; O,

ji.   \ ‑ KiT +     

 Bnnuat|

OKiTA\|

Oh dbv`hi sbkj dynroabrloh rbn`abm, tdj ornjr oe rjbat v ty oe Ir`ihbrn rjbijhts w mm lj bs eommows 3\Ki@ 8 \KiLr 8 \KiAm

2.> Qyhtdjt`a `kportbhaj oe Ir`ihbrn rjbijhts

2.>.2 Qyhtdjs`s oe Bmfbhjs

( ) Y`td aokpouhns dbv`hi rjbat`vj dynroijh btok

Ijhjrbm rjbat`oh 3

\ ‑ KiT + D ‑ S        \ ‑ D + SKiT

AD1 ‑ KiT + D ‑ OD        AD

1 ‑ D + Ki(OD)T

A<D

: ‑ KiT + D ‑ O\        A

<D

: ‑ D + Ki(O\)T

A1D

9 ‑ KiT + D ‑ OA

5D

:    A

1D

9 ‑ D + Ki(OA

5D

:)T

A<D

: ‑ KiT + D ‑ HD

<    A

<D

: ‑ D + Ki(HD

<)T

AD1 ‑ KiT + D ‑ HD\        AD

1 ‑ D + Ki(HD\)T

A<D

: ‑ KiT + D ‑ H\

<    A

<D

: ‑ D + Ki(H\

<)T

AD1 ‑ KiT + D ‑ HDA

5D

:       AD

1 ‑ D + Ki(HDA

5D

:)T

A<D

: ‑ KiT + D ‑ Q\     A

<D

: ‑ D + Ki(Q\)T

AD1 ‑ KiT + D ‑ A  H        AD1 ‑ D + Ki(AH)T

A<D

: ‑ KiT + D ‑ A  AD        A

<D

: ‑ D + DA  A ‑ KiT (Jtdyhymkbihjs`uk dbm`nj)

AD1 ‑ KiT + D ‑ A  A\     AD

1 ‑ D + \ ‑ A  A ‑ KiT (Bmfyhymkbihjs`uk dbm`nj)

Kjtdbhj ibs `s rjmjbsjn oh rjbat`hi kjtdymkbihjs`uk `on`nj w`td b aokpouhn aohtb`h`hi rjbat`vjdynroijh btok. ^dj rjbat`oh `s usjn eor jst kbt oh oe rjbat`vj dynroijh btoks prjsjht `h b komjaumj. ^d`skjtdon `s abmmjn Sjrjw`t`hoee kjtdon oe jst kbt oh oe rjbat`vj dynroijh btoks.

(` ) Y`td bmfym dbm`nj (aoupm hi) 3

\ ‑ KiT + T ‑ \     \ ‑ \   + KiTT

2.>.< Qyhtdjs`s oe bmfjhjs

\ ‑ KiT + Tdbm`nj Bmmym

<<   ADADAD      \ ‑ AD< ‑ AD ; AD

<+ KiTT

8/12/2019 Grignard Reagent, Reduction & Alkane Theory_E

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"kbh`sdfukbrpdys`as.`h"   1

ADJK@Q^\P

2.>.1 Qyhtdjs`s oe d`idjr bmfyhjs

Hoh-tjrk`hbm bmfyhjs

\ A  A ‑ D \D

\Kix

            \ ‑ A  AKiT

<KiT

T\

        

\ ‑ A  A ‑ \

2.>.> Qyhtdjs`s oe otdjr oribhokjtbmm`as

>\ ‑ KiAm + <WlAm<

       \>Wl + Wl + >KiAm

<

^wo `kportbht bht fhoaf`hi aokpouhns, tjtrbjtdymmjbn ( .J.M.) bhn tjtrbkjtdymmjbn ( .K.M.) brj kbhuebaturjnly tdj blovj rjbat`oh.

<\ ‑ KiAm + DiAm<

    rauryN`bmmfymkj

KiAm<\Di\   <

<\ ‑ KiAm + AnAm<

  nk`ukN`bmmfymab

KiAm<\An\   <

>\ ‑ KiAm + QhAm>

    t`h^jtrbbmfymKiAm>Qh\   <>  

2.>.: Qyhtdjs`s oe Bmaodoms

^djrj brj eommow`hi kjtdons to oltb`h bmaodoms erok Ir`ihbrn rjbijht.(`) Erok abrlohym aokpouhns

\ ‑ KiT +   |

OKiTA\|

        DOD

bmaodom

|ODA\

|

^d`s `s huamjopd`m`a bnn`t`oh rjbat`oh

(b) Wr`kbry or 2· Bmaodoms

Wr`kbry bmaodoms brj eorkjn oh tbf`hi eorkbmnjdynj

\ ‑ KiT +  

D|

OKiTA\

|D

         DOD

 Bmaodom2D|

ODA\

|D

(l) Qjaohnbry or <· bmaodoms

(2)   Erok \ADO Qjaohnbry bmaodoms brj eorkjn ly tdj rjbat`oh oe bhy bmnjdynj otdjr tdbh eorkbmnjdynj.

\ ‑ KiT +  

 Bmaodom<

D|

ODA\|\

(<) Erok Eork`a Jstjr   3Qjaohnbry bmaodoms brj oltb`hjn oh dynromys`s oe tdj pronuat oltb`hjn ly tbf`hijxajss oe Ir ihbrn rjbijht bhn bnn`hi eork`a jstjr to `t.

OKiT

|||OJtA\

|D

    

O

||A\|D

OD

\KiT

<

        

OD

|\A\

|D

8/12/2019 Grignard Reagent, Reduction & Alkane Theory_E

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"kbh`sdfukbrpdys`as.`h"   >

ADJK@Q^\P

(a) ^jrt`bry or 1· bmaodoms

(2)   jrt`bry bmaodoms brj eorkjn ly tbf`hi bhy fjtohj

\ ‑ KiT +  

\|

OKiTA\|\

 Bmaodom1

\|

ODA\|\

(<)   jrt bry bmaodoms brj bmso oltb`hjn oh dynromys`s oe tdj pronuat oltb`hjn ly tbf`hi

jxajss oe Ir`ihbrn rjbijht bhn bh jstjr oe b d`idjr dokomoiuj oe eork`a ba`n.

OKiT|||

OJtA\|\

 

O||A\|\

OD

\KiT

<

        

OD|

\A\|\

Ubr`ous bmaodoms abh lj prjpbrjn ly adbhi`hi \ `h tdj blovj syhtdjs`s.( ` `) Erok Jpox`njs

  

OKiT|ADAD\   << 

Akorjtwodbv`hi

 Bmaodom2

OD|ADAD\   <<

(`v) Erok Oxyijh

(b) Qyhtdjs`s oe bmaodom

\ ‑ KiT + O ; O     \ ‑ O ‑ O ‑ KiT

\ ‑ O ‑ O ‑ KiT + \ ‑ KiT     <\ ‑ O ‑ KiT

\ ‑ O ‑ KiT + DOD        \ ‑ O ‑ D + Ki(OD)T

Wr`kbry, sjaohnbry bhn tjrt`bry bmaodoms abh lj oltb`hjn ly blovj rjbat`oh

(l) Qyhtdjs`s oepdjhoms

Wdjhom `s oltb`hjn oh dynromys`s oe tdj pronuat oltb`hjn ly rjbat`oh oe brymkbihjs`uk

lrok`nj w td oxyijh.

A5D

:KiLr + O ; O     A

5D

:O ‑ OKiLr 

A5D

:O ‑ OKiLr + A

5D

:KiLr      <A

5D

: ‑ OKiLr 

A5D

: ‑ OKiLr + D

<O        A

5D

: ‑ OD + Ki(OD)Lr 

2.>.5 Qyhtdjs`s oe Bmnjdynjs

Aorrjspohn`hi bmnjdynj `s oltb`hjn oh dynromys`s oe tdj pronuat oltb`hjn ly rjbat`hi oe eork`a jstjr bhn

Ir`ihbrn rjbijht `h jqu`kombr rbt`o.

OKiT|||

OJtA\|D

                ‑JtO ‑

O||A\|D

jtrbdjnrbm `htjrkjn`btj

@h td`s rjbat`oh tjtrbdjnrbm `htjrkjn`btj `s erokjn so td`s kjadbh`sk `s abmmjn  QH

< ^d kjadbh`sk

8/12/2019 Grignard Reagent, Reduction & Alkane Theory_E

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"kbh`sdfukbrpdys`as.`h"   :

ADJK@Q^\P

2.>.9 Qyhtdjs`s oe Fjtohjs

(`) Erok Ba`n njr`vbt`vj

                KiOI ‑

O

||A\|\

Ydjrj I ; -OJt, ‑ Am

^dj blovj rjbat`oh sjqujhaj abh lj s`kpm e`jn bs eommows eor aohvjh`jhaj.

\ ‑ KiT +

O||

\AI       

O||

\A\     + I ‑ KiT

ji.   \ ‑ KiT +

O

||\AJtO       

O

||\A\     + JtO ‑ KiT

ji.   \ ‑ KiAm + Am ‑ AO ‑ \        \ ‑ AO ‑ \ + KiAm<

(` ) Erok Bmfym Aybh`njs

 B fjt`k`hj `s eorkjn oh dynromys`s oe tdj bnnuat oltb`hjn ly tdj rjbat`oh oe Ir`ihbrn rjbijht bhn bh

bmfym aybh`nj, wd`ad i`vjs fjtohj oh eurtdjr dynromys`s.

\KiT + \AH        \<A ; HKiT          DOD

jk`hFjt`

HDA\<            DOD

FjtohjOA\<  

2.>.4 Qyhtdjs`s oe Abrloxym`a ba`ns

 B abrloxym`a ba`n `s eorkjn oh dynromys`s oe tdj bnnuat eorkjn ly pbss`hi abrloh n`ox`nj `h tdj jtdjrjbm

somut`oh oe b Ir`ihbrn rjbijht.

O||

OAKiT\    

O||

OKiTA\   T)OD(Ki

DOD

           

O||

ODA\  

2.>.0 Qyhtdjs`s oe Abrloxym`a ba`n jstjrs

Jstjrs brj eorkjn oh rjbat`hi tdj jtdymadmoroeorkbtj w td Ir`ihbrn rjbijht.

\KiAm + AmAOOJt     \AOOJt + KiAm<

2.>.27 Qyhtdjs`s oe Jtdjrs

D`idjr jtdjrs abh lj syhtdjs`sjn ly rjbat`hi b mowjr admor`hbtjn jtdjr w td Ir`ihbrn rjbijht.

\ ‑ KiAm + Am ‑ AD< ‑ O ‑ \        \ ‑ AD

< ‑ O ‑ \ + KiAm

<

AD1KiAm +

jtdjr jtdymymAdmorokjtd:<<   DAOADAm       

jtdjr N`jtdym:<<1   DAOADAD  

2.>.22 Qyhtdjs`s oe Kjrabptbhs

 Bmfbhjtd oms, `.j. kjrabptbh `s eorkjn oh dynromys`s oe tdj pronuat oltb`hjn ly bnn`hi sumpdur to tdj jtdjrjbm

somut`oh oe Ir`ihbrn rjbijht.

\ ‑ KiAm + Q        \ ‑ Q ‑ KiAm          DOD\ ‑ Q ‑ D + Ki(OD)Am

8/12/2019 Grignard Reagent, Reduction & Alkane Theory_E

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"kbh`sdfukbrpdys`as.`h"   5

ADJK@Q^\P

<. \JNZA^@OH

@htronuat`oh\jnuat`oh aovjrs lotd tdj bnn t`oh oe dynroijh (or njutjr`uk) to b noulmj lohn bhn tdj rjpmbajkjht oe bh

btok or iroup ly dynroijh (or njutjr uk). @h otdjr worns, rjnuat`oh kjbhs dynroijhbt`oh or dynroijhomys`s.

Kjtdons oe \jnuat`oh 3

<.2 Abtbmyt`a dynroijhbt`oh 3 ^dj abtbmysts usjn abh lj n`v`njn `hto two lrobn ambssjs, lotd oe wd`ad

kb`hmy aohs`st oe trbhs`t`oh kjtbms bhn tdj`r aokpouhns 3

<.2.2 Djtjroijhjous abtbmysts 3 (abtbmysts `hsomulmj `h tdj rjbat`oh kjn`uk)

@h djtjroijhjous abtbmyt`a dynroijhbt oh abtbmysts brj usjn `h pownjrjn eork (rbhjy h`afjm (H ), Wbmmbn`ukoh adbraom (Wn/A), Wmbt`huk kjtbm or `ts ox`nj). Qulstrbtj komjaumjs brj bssukjn to uhnjrio dokomys`s`hto btoks wd`ad brj adjk`sorljn bt tdj surebaj oe tdj abtbmyst. ^dj sulstrbtj `s bmso adjk`sorljn oh tdj

surebaj oe tdj abtbmyst.

Ijhjrbm \jbat`oh   A ; A + D<

         Abtbmyst

)bnn`t`ohsyh(DD

||AA||

Dynroijhbt`oh oe bh bmfjhj `s bh jxotdjrk`a rjbat`oh (     ³D   ‑2<7 fC kom ‑2)3

\ ‑AD ; AD ‑ \ + D<

      H`\ ‑ AD

< ‑ AD

< ‑ \ + djbt

^dj proajss `s jxotdjrk`a, tdjrj `s usubmmy b d`id erjj jhjriy oe bat`vbt`oh eor uhabtbmyzjn bmfjhjdynroijhbt`oh, tdjrjeorj, tdj uhabtbmyzjn rjbat`oh nojs hot tbfj pmbaj bt rook tjkpjrbturj. Dynroijhbt oh

w mm tbfj pmbaj rjbn`my bt rook tjkpjrbturj `h tdj prjsjhaj oe b abtbmyst ljabusj tdj abtbmyst prov`njs b hjwpbtdwby eor tdj rjbat`oh tdbt `hvomvjs mowjr erjj jhjriy oe bat`vbt oh .

Djtjroijhjous dynroijhbt`oh abtbmysts typ`abmmy `hvomvj e`hjmyn`v njn pmbt`huk, pbmmbn`uk, h`afjm, or rdon`uk

njpos t`oh oh tdj surebaj oe pownjrjn abrloh ( adbraobm). Dynroijhbt oh batubmmy tbfjs pmbaj bt tdj surebaj

oe tdj kjtbm, wdjrj tdj m`qu`n somut`oh oe tdj bmfjhj aokjs `h aohtbat w`td dynroijh bhn tdj abtbmyst.Dynroijh ibs `s bnsorljn `hto tdj surebaj oe tdjsj kjtbm abtbmysts bhn tdj abtbmyst wjbfjhs tdj D ‑ D

lohn. @h ebat, `e D< bhn N

< brj k`xjn `h tdj prjsjhaj oe b Wt abtbmyst, tdj two `sotopjs qu`afmy sarbklmj to

pronuaj b rbhnok k`xturj oe DN, D< bhn N

<. (Ho sarbklm`hi oaaurs `h tdj blsjhaj oe tdj abtbmyst.)

Dynroijhbt`oh `s bh jxbkpmj oe djtjroijhjous abtbmys`s, ljabusj tdj (som`n) abtbmyst `s `h b n`eejrjht pdbsj

erok tdj rjbatbht somut oh. @h aohtrbst, dokoijhjous abtbmys`s `hvomvjs rjbatbhts bhn abtbmyst `h tdj sbkjpdbsj, bs `h tdj ba`n-abtbmyzjn njdynrbt`oh oe bh bmaodom.

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"kbh`sdfukbrpdys`as.`h"   9

ADJK@Q^\P

Lotd dynroijh btoks usubmmy bnn erok tdj sbkj s`nj oe tdj komjaumj. ^d s konj oe bnn`t`oh `s abmmjn b syh

bnn`t`oh.

^dj jbsj oe rjnuat oh oe vbr`ous euhat`ohbm iroups towbrn abtbmyt`a dynroijhbt`oh (H /Wn/Wt)

M`hnmbr‐s abtbmyst 3   `s b po`sohjn pbmmbn`uk abtbmyst, aokposjn oe pownjrjn lbr`uk sumpdbtj aobtjn

w`td pbmmbn`uk, po`sohjn w`td qu`hom`hj. H`afjm lor`nj H`<L (W-< abtbmyst) (kbnj erok son`uk bajtbtj bhn

son`uk lorod`nr`nj) `s bh jxajmmjht bmtjrhbt vj abtbmyst eor tdj aohvjrs`oh oe bmfyhj `hto bmfjhj. (syh bnn t`oh)

^dj pbrt`bm rjnuat oh oe bmfyhj to bmfjhj s djtjroijhjous dynroijhbt`oh w`td M`hnmbr's abtbmyst.

ji.   AD1 ‑ AD

< ‑ A  A ‑ AD

1LH`or 

abtbmysts'M`hnmbr D

<

<                    (syh bnn t`oh)

 Ba`n admor`nj rjnuajn to bmnjdynj ly us`hi Wn /LbQO> abtbmyst

                 ><   LbQOWn/D AD1 ‑ ADO

^d`s rjbat`oh `s abmmjn \osjhkuhn \jnuat oh

j.i.   AD1 ‑AA‑AD

1

j.i.   O<H ‑ AD ; AD ‑ AD

< ‑ AD

1             Wn/D<   D<H ‑ AD

< ‑ AD

< ‑ AD

< ‑ AD

1

j.i.               Wtor Wn/D<

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"kbh`sdfukbrpdys`as.`h"   4

ADJK@Q^\P

<.< \jnuat`oh ly N`ssomv`hi Kjtbms

^dj ijhjrbm kjadbh`sk oe rjnuat`oh ly n`ssomv`hi kjtbms `s lbsjn oh tdj ebat tdbt tdj kjtbm bats bs b

souraj oe jmjatrohs e`rst bh jmjatroh bnns to tdj sulstrbtj abus`hi e`ss`oh oe b s`himj lohn `hto b erjj

rbn`abm bhn bh bh`oh or `t abh bnns to b noulmj lohn eork`hi b rjsohbhaj - stblm`zjn rbn`abm `oh.

 B ‑ L      ‑j    B   +   ‑L   or    ‑ B   +   L

 B ; L      ‑j  

L ‑ B or   

L ‑ B

<.<.2 \jnuat`oh ly Hb or M` /HD1 (L`rad rjnuat`oh)

Kjadbh`sk 3

\jbijhts Hb(or M`,F) + m`q HD1

       Hb+ + j¯ (somvbtjn jmjatroh)

HbHD< + (bht` bnn`t`oh)

^yp`abm jxbkpmj oe rjnuat`oh eor brokbt`a systjk 3-

           1HD/Hb

           1HD/Hb

\ ‑ A  A ‑ \             1HD/Hb(bht` bnn`t`oh)

j.i.             1HD/Hb

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"kbh`sdfukbrpdys`as.`h"   0

ADJK@Q^\P

<.<.< \jnuat oh ly Hb/A<D

:OD VLouvjbmt - Lmbha rjnuat`oh[

\jnuat`oh oe bmnjdynjs fjtohjs or jstjrs ly kjbhs oe jxajss oe Hb/A<D

:OD or h-lutbhom `s abmmjn Louvjbmt-

Lmbha rjnuat oh rjnuat`oh.

Kjadbh`sk 3

     Hb            ODDA   :<      Hb

\AD<OD            ODDA   :<   \AD< ‑ O ‑       Hb \AD< ‑ O¹            ODDA   :<       Hb \ A D ; O + A<D: O ‑

j.i.   AD1ADO AD

1AD

<OD

 Bajtbmnjdynj Jtdbhom

AD1 ‑AOAD1

 Bajtohj propbhj-<-om

AD1AD

<OD

Jtdym bajtbtj Jtdbhom

<.1 \jnuat`oh ly kjtbm dynr`njs bhn bmfox`njs 3

Ajrtb`h aokpmjx kjtbm dynr`njs, lorbhj bhn bmuk`h`uk `sopropox`nj, brj rjbijhts oe ado`aj eor rjnuat`oh

oe abrlohym iroup.

<.1.2 M`BmD>

(MBD) M`td`uk bmuk`h`uk dynr`nj 3 MBD `s kost aokkoh bhn vjrsbt`mj oe td`s ambss oe rjbijht. @t

`s sjhs t`vj to prot`a somvjht bhn tdjrjeorj usjn `h abrjeummy prjpbrjn hohdynroxym`a somvjht ijhjrbmmy jtdjr `s

usjn bs somvjht, @t kby lj rjibrnjn bs njr`vjn erok kjtbm dynr`nj.

M`D + BmD1    >

 ‑

D BmM`

Kjadbh`sk 3

             OA\<

> \<ADOD       OD1  Bm ‑ (OAD\<)>         

  O\   A<

mDB   (OAD\<)1

<.1.< HbLD>

(Qon`uk lorodynr`nj) 3 @t `s korj spja`e`a tdbh MBD bs b rjnua`hi bijht. @t `s rjnuajs ohmyfjtohjs

bhn bmnjdynjs to tdj aorrjspohn`hi bmaodoms w`tdout beejat hi otdjr euhat`ohbm iroups. @t `s jeejat`vj jvjh `hprot`a somvjht m`fj bmaodom. rjnuajs ba`n admor njs lut hot bhn bhy otdjr njr`vbt`vj oe ba`n.

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"kbh`sdfukbrpdys`as.`h"   27

ADJK@Q^\P

Kjadbh`sk 3

             OA\<

> \<ADOD       OD1 L ‑ (OAD\<)>         

  O\   A<LD   (OAD\<)1

ji.             >M`BmD

ji.             >HbLD

ji.

<.1.1   N@LBM-D (N``solutym Bmuk`h`uk Dynr nj) (BMBHJ) 3Kost `kportbht bmbhj `s n` solutym bmuk`h`uk dynr`nj. @t ruhs pbrbmmjm to MBD (M td`ok bmuk`h`uk dynr`nj) bsb rjnua`hi bijht lut `t `s korj sjmjat`vj.

ji.   Wd‑AD;AD„AOOA<D

:OD

^DEM`BmD

<

>                  Wd‑AD

< ‑AD

< ‑AD

<OD +A

<D

:OD

Wd‑AD;AD„AD<OD

LyN@LBMbt orn hbrytjkpjrbturj jstjrs brjrjnuajn to bmaodoms lut `t mowtjkpjrbturjjxtjrs brjrjnuajnto bmnjdynj.

ji.   A5D

: ‑ A||

O

 ‑OAD1   A³<:tomujhj

N@LBM           A5D

:AD

<OD

A5D

:ADO

MBD rjnuaj \AH to bk`hj lut N@LBM `s eouhn to lj rjnuaj `t to bmnjdynj.

ji.   AD1 ‑AH

OD

^DEM`BmD

<

>                  AD

1 ‑AD

< ‑HD

<

AD1 ‑ADO

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"kbh`sdfukbrpdys`as.`h"   22

ADJK@Q^\P

<.1.>   \jnuat`oh ly `sopropym bmaodom bhn bmuk`h`uk `sopropox`nj. ^d`s `s abmmjn tdj Kjjrwj`h-Wohnore-

Ujrmjy rjnuat`oh

Kjadbh`sk 3

              ADOD)AD(   <1

ji. + +

<.> K`sajmmbhjous \jnuat`ohs

<.>.2 Qtjpdjh‐s \jnuat`ohs

Ydjh rjnuat ohoe aokpouhns `s abrr`jn out w td ba n`e jn stbhhous admor nj (QhAm</DAm) bt rook tjkpjrbturj,

`k`hj dynroadmor`nj `s oltb`hjn wd`ad oh sulsjqujht dynromys`s w`td lo`m`hi wbtjr i`vjs bmnjdynj. ^d`sspja`e`a typj oe rjnuat`oh oe h`tr`mj `s abmmjn stjpdjh‐s rjnuat`oh.

ji.   AD1AH

OD)``(

DAm/QhAm)`(

<

<                  AD1ADO

 Bajtbmnjdynj

ji.

OD)``(

DAm/QhAm)`(

<

<               

Ljhzbmnjdynj

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"kbh`sdfukbrpdys`as.`h"   2<

ADJK@Q^\P

<.>.< Amjkkjhsjh‐s \jnuabt`oh 3

Zsjn to ijt bmfbhj erok abrlohym aokpouhns.

\ ‑A D O                       DAm.aoha/DiSh

\AD1

+ D<O

  \A\||O

                      DAm.aoha/DiSh

\AD<\ + D

<O

ji.   AD1 ‑ ADO

                      DAm.aoha/DiShAD

1AD

1+ D

<O

ji. :<1   DAAAD||O

  + >VD[                       DAm.aoha/DiSh

AD1AD

<A

<D

:+ D

<O

Amjkkjhsjh rjnuat oh `s hot usjn eor aokpouhns wd`ad dbvj ba`n sjhs`t vj iroup.

<.>.1   Yomee-f`sdhjr rjnuat`oh w`td HD<HD< / FODZsjn to ijt bmfbhj erok abrlohym aokpouhns

Kjadbh`sk 3

\ADO

                   FOD/HDHD   <<

\AD1

\AO‑\

                   FOD/HDHD   <<

\AD<\

Yomee-f`sdhjr rjnuat oh `s hot usjn eor aokpouhns wd ad dbvj lbsj sjhs t`vj iroups.

<.>.>   Ly \jn W & D@

             

   D@Wn\j\ ‑ AD1 6

                D@Wn\j

\ ‑ AD1

             

   D@Wn\j\ ‑ AD1 6

                D@Wn\j

\ ‑ AD< ‑ \

ji.

                D@Wn\j

AD1 ‑ AD1

ji.              

   D@Wn\j

AD1 ‑ AD< ‑ AD1

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"kbh`sdfukbrpdys`as.`h"   21

ADJK@Q^\P

(*) noulmj lohn abh lj rjnuajn ly M`BmD> / ^DE ohmy `h a`hhbk`a systjk.

Eor ji. Wd‑AD;AD„ADOOD

^DEM`BmD

<

>                  Wd‑AD

< ‑AD

< ‑AD

<OD

1. BMFBHJ

1.2 Ijhjrbm kjtdon oe prjpbrbt`oh1.2.2. Ly abtbmyt`a rjnuat`oh oe bmfjhjs bhn bmfyhjs

\ ‑ A  A ‑ \Wnor Wt,H`

A<:,D<                \ ‑ AD

< ‑ AD

< ‑ \

\ ‑ AD ; AD ‑ \Wnor Wt,H`

A<:,D<              

\ ‑ AD< ‑ AD

< ‑ \

Dynroijhbt`oh  Bnn`t`oh oe D< to uhsbturbtjn lohn.

Dynroijhbt`oh `s oe two f`hns

(b)D jtjroijhjous (l) Dokoijhjous

(b) Djtjroijhjous 3 @t `s two pdbsj dynroijhbt`oh tdj abtbmyst `s e`hjmy njv`njn kjtbm m`fj H`, Wt or Wn bhnb somut`oh oe bmfjhj.(l) Dokoijhjous 3   @t `s ohj pdbsj dynroijhbt`oh lotd abtbmyst bhn bmfjhjs brj `h somut`oh. @h td`s

dynroijhbt`oh abtbmyst brj oribh`a aokpmjx oe trbhs`t`oh kjtbm m`fj \d or  @r.Dynroijhbt`oh `s jxotdjrk`a, qubht tbt vj bhn nur`hi tdj dynroijhbt`oh, totbm djbt jvomvjn to dynroijhbtjohj komj oe uhsbturbtjnaokpouhn `s abmmjndjbt oe dynroijhbt`oh. Djbt oe dynroijhbt`oh `s tdj kjbsurkjhtoe stbl`m ty oe `sokjr`a bmfjhjs.

stbl`m`ty oe bmfjhj    `ohdynroijhbtoe Djbt

2

Hotj 3 Dynroijhbt`oh oe bmfjhj or bmfyhj `h prjsjhaj oe kjtbm abtbmyst `s syh bnn`t`oh

ji.   + D<

AOODAD

Wn

1

     

(Kjso)

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"kbh`sdfukbrpdys`as.`h"   2>

ADJK@Q^\P

ji.   + D< AOODAD

Wn

1

     

(\bajk`a k`xturj)

1.2.<. Erok bmfym dbm nj

(`) Ly wurtz rjbat`oh

<\ ‑ T + <Hb              jtdjr nry

\ ‑ \ + <HbT

\ ‑ T + \   ‑ T)nry(jtdjr 

Hb                \ ‑ \, \ ‑ \, \ ‑ \

Kjadbh`sk        ^wo kjadbh`sks brj suiijstjn(b) @oh`a kjadbh`sk

<Hb        Hb<   +

)<,2(T\

  + <j¯      

        <HQ \ ‑ \

     HbT

(l) Erjj rbn`abm kjadbh sk

Hb  

\ ‑ T +     \   +

\   +   \     \ ‑ \

Hotj 3 ^dj bmfym dbm`nj sdoumn lj 2· or <·, w`td 1· \ ‑ T QH

< bhn erjj rbn`abm aoupm`hi `s hot poss`lmj nuj to

stjr`a d`hnjrjhaj so `h tdbt absj jm`k`hbt`oh or n`sproport`ohbt`oh `s poss`lmj.

@h tdj `oh`a kjadbh`sk bmfym son`uk i`vjs strohi lbsj bs wjmm bs huamjopd`mj wd`ad i`vjs QH

<

w`td \ ‑ T, jtdjr sdoumn lj nry otdjrw`sj `e ko`sturj `sprjsjht tdbh eorks \ ‑ D `hstjbn oe \ ‑ \ w`td D<O.

j.i. AD1 ‑ AD

< ‑ Lr        Hb   AD

1 ‑ AD

< ‑ AD

< ‑ AD

1

j.i. AD1 ‑ Am + AD

1 ‑ AD

< ‑ Am       Hb   AD

1 ‑ AD

1 + AD

1 ‑ AD

< ‑ AD

1 + AD

1 ‑ AD

< ‑ AD

< ‑ AD

1

(``) Ly rjnuat`oh oe bmfym dbm`njs

(B) w`td kjtbm-ba`n

2T\   \ ‑ D + DT

\jnua`hi bijht

Sh / DAm , Sh ‑ Au / D<O or Sh ‑ Au + AD

1AOOD

Sh ‑ Au / A<D

:OD, Hb ‑ Di / DAm, Bm ‑ Di / D

<O jta.

Kjadbh`sk

Kjtbm  

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"kbh`sdfukbrpdys`as.`h"   2:

ADJK@Q^\P

(L) Y`td kjtbm dynr`njs

(b)   ^WD (Wd1QhD) ^r`pdjhymt`h dynr`nj 3 @t rjnuajs 2·, <· & 1· \ ‑ T

³1/³</³2T ‑\            

  QhDWd1 \ ‑ D

(l)   HbLD>

  3

1&<

T\             >HbLD\ ‑ D

(a)   M`BmD> 3

<&2

T\             >M`BmD\ ‑ D

1

T\             >M`BmD Bmfjhj

1.2.1 Erok oribhokjtbmm`a aokpouhn

(`) Ly Ir`ihbrn \jbijht.

1<,2

T\jtdjr 

iK         \KiT

\KiT +aokpouhn

aohtb`hiD

bat`vjbmm

     \ ‑ D

D O<

\OD

HD1

\ ‑ A AD

\QD

\ ‑ AOOD

\ ‑ D + Ki (OD) T

+ Ki (O\) T

+ Ki (HD ) T<

+ Ki (A A\ )

+ Ki (Q\) T

+ Ki (OAO\) T

\KiT

\ ‑ D

\ ‑ D

\ ‑ D

\ ‑ D

\ ‑ D

T

(``) Ly aorjy dousj bmfbhj syhtdjs`s

)1,<,2(

T\

         M`<      AuT

)rjbijhts'I`mkbh(auprbtj

n`bmfymM`td`ukAuM`\<            

 

)<2(T\

\ ‑ \

Kjadbh`sk

\<AuM` `s tdj souraj oe    \

\ ‑ \

\<AuM` nojs hot rjbats w`td ‑ HO

<, ‑ AH, jta.

(```) Ly Erbhfmbhns rjbijht

\ ‑ T + Sh + \ ‑ T          Jtdjr \ ‑ \ + Sh T

<

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"kbh`sdfukbrpdys`as.`h"   25

ADJK@Q^\P

Kjadbh`sk

1.2.> Erok abrloxym`a ba`ns3 -

(`) Ly sonb m`kj 3 Ebtty ba`ns brj ioon souraj oe dynroabrloh, aoht`huous djbt`hi oe son`uk sbmt oe abrloxym aba`n (\ ‑ AOOHb) w td sonb m`kj (HbOD ‑ AbO) i`vjs dynroabrloh, td`s proajss `s fhowh bs njabrloxymb-t`oh (j.i. rjpmbajkjht oe ‑ AOOD iroup ly ‑ D) njabrloxymbt`oh bmso tbfjs pmbaj oh djbt`hi ohmy, wdjhaokpouhn `s ijk n`abrloxym`a ba`n or tdjrj `s fjto iroup or noulmj lohn oh  abrloh.

O||

ODA\            HbOD

        AbO

\ ‑ D + Hb<AO

1

(` ) LyFomlj‐s jmjatromys`s

<\AOOF + <DOD                 `sJmjatromys \ ‑ \ + <AO< + D

< + <FOD

Kjadbh`sk

\ AO<F \ AO

< ‑ + F+

Bt Bhonj3 -   \ AO< ‑       \  

<AO   + j ‑ (ox`nbt`oh)

(@)

\   <AO        \   + AO

<

(@@)

\   +  \        \ ‑ \

@e h `s tdj hukljr oe abrloh btoks `h tdj sbmt oe abrloxym`a ba`n, tdj bmfbhj eorkjn dbs <(h‑2) abrloh btoks.

j.i.   <AD1 ‑ AOOF + <D

<O                 `sJmjatromys

AD1AD

1 + <AO

< + D

< + <FOD.

1.2.: Ly\jnuat`oh

( ) Ly Amjkkjhsjh‐s rjnuat`oh 3 w`td Sh ‑ Di / aoha. DAm

\ ‑A D O                       DAm.aoha/DiSh

\AD1

+ D<O

  \A\

||O

                      DAm.aoha/DiSh

\AD<

\ + D<

O

j.i.   AD1 ‑ ADO

                      DAm.aoha/DiShAD

1AD

1+ D

<O

:<1   DAAAD||O

  + >VD[

                      DAm.aoha/DiSh AD1AD

<A

<D

:+ D

<O

Amjkkjhsjh rjnuat oh `s hot usjn eor aokpouhns wd`ad dbvj ba`n sjhs`t vj iroup.

(` ) Ly Yomee-f`sdhjr rjnuat`oh w`td HD<HD

< / FOD

\ADO

                 FOD/HDHD   << \AD

1

\AO‑\

                 FOD/HDHD   << \AD

<\

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"kbh`sdfukbrpdys`as.`h"   24

ADJK@Q^\P

1.<.>. Qomul`m ty

@h fjjp`hi w`td tdj popumbr rumj ”m`fj n`ssomvjs m`fj‛ dynroabrlohs brj `hsomulmj `h pombr somvjht m`fj wbtjr ljabusj tdjy brj prjnok`hbhtmy hoh-pombr `h hbturj.

1.<.:. Njhs`ty

^dj njhs`t`js oe bmfbhjs `harjbsj w`td `harjbs`hi komjaumbr wj`idt lut ljaokj aohstbht bt blout7.4 i ak ‑1. ^d`s kjbhs tdbt bmm bmfbhjs brj m`idtjr tdbh wbtjr.

1.1 Adjk`abm \jbat`ohs oe Bmfbhjs 3

Adbrbatjr`st a rjbat`oh oe bmfbhjs brj erjj rbn`abm sulst`tut`oh  rjbat`oh, tdjsj rjbat`ohs brj ijhjrbmmyadb`h rjbat`ohs wd`ad brj aokpmjtjn `h tdrjj stjps.( ) adb`h `h`t bt`oh (` ) adb`h propbibt oh. (` ) adb`h tjrk`hbt oh

1.1.2. Dbmoijhbt`oh 3

\ ‑ D + T<   A>77<:7

tjkpor M`idtZU

                          \ ‑ T + DT

Kjadbh`sk oe dbmoijhbt`oh oe bmfbhj     

(`) Adb`h `h`t`bt`oh  `t `s bh jhnotdjrk`a stjp.

T< A>77<:7

.tjkpor ZU

                   •

T<

(``) Adb`h propbibt oh

T  + \ ‑ D       •

\   + DT

\   + T ‑ T        \ ‑ T +•

T

(```) Adb`h tjrk`hbt`oh    `t `s bmwbys jxotdjrk`a

T   +•

T        T<

\   +•

\        \ ‑ \

•\   +

•T        \ ‑ T

Qtjps oe dbmoijhbt`oh, Ubmuj oe   D eor jbad stjp. (Fabm/komj)

E Am Lr     @

(`) T<

       <•

T   + 14 + :4 +>5 +15

(``)•

T   + AD>

    1

DA   + DT ‑ 1< + 2 + 25 + 11

(```) 1

DA   + T<

       AD1T +

T   ‑ 97 ‑ <5 ‑ <> ‑ <7

\jbat`v`ty oe T< 3 E

< 8 Am

< 8 Lr 

< 8  @

<

\jbat`v`ty oe D 3 1·D 8 <·D 8 2· D

Y`td E<

bmfbhjs rjbat so v`iorousmytdbt jvjh `h tdj nbrf bhn bt rook tjkpjrbturj, rjbatbht `s n mutjn w td bh

@hjrt ibs. @on`hbt`oh `s rjvjrs`lmj rjbat`oh, s`haj D@ eorkjn bs b ly pronuat bhn @t `s b strohi rjnua`hi bijhtbhn rjnuajs bmfym `on`nj lbaf to bmfbhj. Djhaj `on`hbt`oh abh lj nohj ohmy `h prjsjhaj oe strohi ox`n`s`hi

bijht m`fj D@O1, DHO

1or DiO.

\ ‑ D +   @<

  \ ‑  @  + D@

:D@ + D@O1

       1D<O + 1@

<

<D@ +DiO        @<

  + D<O + Di

<D@

+ <DHO1       @

<   + <D<O + HO<Eorkbt`oh oe bmfym erjj rbn`abm `s rbtj njtjrk`h`hi stjp.

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"kbh`sdfukbrpdys`as.`h"   20

ADJK@Q^\P

ornjr oe stbl`m`ty oe Erjj rbn`abm 

1 AWd   8 DAWd•

<  8

<

DAWd   8<

<   DAADAD     8 (AD1)

1

A  8 (AD

1)

<

AD 8 AD

1

<AD   8   1

DA

ji.   AD>

      d

Am<

DAm

AmAD1

        d

Am<

DAm

AmAD   <<

        d

Am<

DAm

ADAm1

 

      d

Am<

DAm

AAm>

Ydjh jqu`kombr bkouht oe kjtdbhj bhn Am< `s tbfjh, b k`xturj oe eour poss`lmj pronuats brj eorkjn, lutwdjh wj tbfj jxajss oe AD> tdjh y`jmn oe AD

1Am w`mm lj d`id.

Jbad pdotoh oe m`idt amjbvjs ohj admor`hj komjaumj to eork two admor`hj rbn`abms, jbad admor hj btok stbrtsb adb`h bhn oh bh bvjrbij jbad adb`h aohtb`hs :777 rjpjbt`t`ohs oe tdj adb`h propbibt`hi ayamj so blout27,777 komjaumjs oe AD

1Am brj eorkjn lyohj pdotoh oe m`idt.

@h b adb`h rjbat`oh eommow`hi rjbijhts brj `hvomvjn -

(`) @h`t`btors  tdjy `h`t`btj tdj adb`h rjbat`oh, @h t`btors brj pjrox`nj (\<O

<), Wjrjstjr's jta.

\ ‑ O ‑ O ‑ \

       

or 

d   •

O\

OO||||

\AOOA\  

        or d

O|| OA\

(``) @hd`l`tors  B sulstbhaj tdbt smows nowh or stops tdj rjbat`oh `s fhowh bs `hd`l`torsEor jxbkpmj O

< `s b ioon `hd`l`tor 

\   + O<

      •

OO\     +•

\        \ ‑ O ‑ O ‑ \

bmm rjbat`vj bmfym erjj rbn`abms brj aohsukjn so rjbat`oh stops eor b pjr`on oe t`kj.

\jmbt`vj rjbat`v`ty oe dbmoijh towbrns kjtdbhj     

Ornjr oe rjbat`v ty `s E< 8 Am

< 8 Lr 

< 8  @

< wd`ad abh lj jxpmb`hjn ly tdj vbmuj oe  D (jhtdbmpy adbhij)

Dbmoijhbt`oh oe d`idjr bmfbhj 3

(`) AD1 ‑ AD

< ‑ AD

1 A<:,m`idt

Am<

          

%::Am|

ADADAD   11     +

%>:

AmADADAD   <<1  

(``) AD1 ‑ AD

< ‑ AD

< ‑ AD

1 A<:,m`idt

Am<

       

%9<Am|

ADADADAD   1<1     +

%<4

AmADADADAD   <<<1  

(```)

1

11

AD|

ADADAD   A<:,m`idt

Am<

       

%5>AD|

AmADADAD

1

<1     +

%15Am|

ADAAD|AD

11

1

(`v) AD1 ‑ AD

< ‑ AD

1 A2<9,djbt

Lr <

          

%1

Lr ADADAD   <<1     +

%09Lr |

ADADAD   11  

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"kbh`sdfukbrpdys`as.`h"   <2

ADJK@Q^\P

1.1.>. Bmfymbt oh 3 @sobmfbhjs bnn to `sobmfjhjs `h prjsjhaj oe aoha. D<QO

>or DE to i`vj d`idjr lrbhadjn bmfbhj

jtbh@solu1

1

1

AD|

DAAD|AD

  +

@solutjhj1

1<

AD|

ADAAD                     ><QOD.aoha

jtbh@sooaADAD||

ADADADAAD|AD

11

1<1

1

1.1.:. Brokbt`sbt`oh 3

 Bmfbhjs aohtb`h`hi 5 or korj hukljr oe A btoks brj ox`n`sjn (njdynroijhbtj & ayam`sjn) `h prjsjhaj oe ox`n`s`hi bijht bt d`idjr tjkpbrbturj bhn eork ljhzjhj or `ts njr vbt`vjs.

AD1 ‑ (AD

<)

> ‑ AD

1

WD`idA577

1<1<  O BmOAr 

             

  + >D

<

AD1 ‑ (AD

<)

: ‑ AD

1

WD`idA577

1<1<  O BmOAr 

             

 

AD1(AD

<)

5AD

1

WD`idA577

1<1<  O BmOAr 

             

  +

1><1

1

ADAD)AD(AD|

AD

WD`idA577

1<1<  O BmOAr 

              

1<1<1

1

ADADAD)AD(AD|

AD

WD`idA577

1<1<  O BmOAr 

             

 

1.1.5 Wyromys`s / Arbaf`hi

AD1 ‑ AD

< ‑ AD

1  AD

1AD

1+ AD

1AD ; AD

<  + AD

< ; AD

<+ AD

> + D

<

D`idjr bmfbhjs brj djbtjn `h blsjhaj oe b`r so tdjsj aokpouhns lrjbf nowh `hto skbmmjr bmfbhjs wd`ad brjljttjr eujm. K`xturj oe pronuats aohtb`hs bmm mowjr bmfbhjs, bmfjhjs & dynroijhs.

1.1.9. Aoklust`oh 3

AhD

<h+< +  

 

  

    <

2h1O

<              aoklust`oh

hAO< + (h + 2) D

<O (D

aoklust`oh ; -vj)

jxotdjrk`a rjbat oh

AxD

y +  

 

  

 

>

yx   O

<              aoklust`oh

xAO< +

<

yD

<O

A:D

2< + 4O

<              aoklust`oh :AO

<+ 5D

<O

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"kbh`sdfukbrpdys`as.`h"   <<

ADJK@Q^\P

Djbt oe aoklust`oh 3 Bkouht oe djbt m`ljrbtjn wdjh 2 komj oe dynroabrloh `s aokpmjtjmy lurht `hto AO<

&D

<O.

  D oe aoklust`oh `s b kjbsurjkjht oe stbl`m`ty oe bmfbhj 3

Aoklust`oh `s usjn bs b kjbsurkjht oe stbl`m`ty.Korj lrbhadjn bmfbhjs brj korj stblmj bhn dbvj mowjr djbt oe aoklust`oh.

j.i.   AD1 ‑

@

<AD   ‑ AD< ‑ AD1

@@

D|

ADAAD

|AD

11

1

Daokl.

  3   @ 8   @@

Qtbl`m`ty 3   @@ 8   @

Wo`hts to rjkjkljr eor   D oe aoklust`oh

Dokomoijs 3 D`idjr dokomoijs dbvj d`idjr djbt oe aoklust oh.AD

>= A

<D

5= A

1D

4

@sokjrs 3 Lrbhadjn `sokjr dbs mowjr djbt oe aoklust`oh.Korj lrbhadjn bmfbhj dbs korj ho. oe pr`kbry

A ‑ D lohns. (tdjrjeorj `t dbs korj lohn jhjriy).

8 8

Ayamo-bmfbhjs 3 Korj strb`hjn r`hi dbs d`idjr djbt oe aoklust`oh pjr ‑ AD< ‑ uh`t.

8 8 8 (Daokl.

 pjr —AD<‐ uh t)

1.1.4 Oatbhj Hukljr 3 @t `s b sabmj oe eujm jee`a`jhay wdjh tdj eujm lurhs nur`hi aoklust`oh, korj lrbhadjnbmfbhjs dbvj mowjr fhoaf`hi (arbaf`hi souhn). so brj ljttjr eujms. Oh aokkjra`bm sabmj `so-oatbhj dbsljjh bmottjn b rbt`hi `.j. oatbhj ho. oe @sooatbhj `s 277 & h-djptbhj `s - —7‐

@e tdj oatbhj ho. oe b eujm `s 47, `t kjbhs tdbt tdj jee`a`jhay oe tdj eujm `s jqu`vbmjht to tdj jee`a`jhay oe k`xturjoe 47% `soatbhj bhn <7% h-djptbhj.

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"kbh`sdfukbrpdys`as.`h"   <1

ADJK@Q^\P

K@QAJMMBHJOZQ QOMUJN W\OLMJKQ

2.   Yd`ad oe tdj eommow`hi eorkumb rjprjsjhts Ir`ihbrn rjbijht ?(B)D

<HKiT (L) DA AKiT (A) \

<Ki (N) Ki(OD)Lr  

Bhs.   LQom.   Ir`ihbrn rjbijht `s rjprjsjhtjn ly \KiT.

<.   Yd`ad oe tdj eommow`hi `s hot b Ir`ihbrn rjbijht ?

(B) (AD1)<ADKiAm (L) AD1AOOKi@   (A)A5D22KiLr (N) A<D:KiAmBhs.   L

Ir`ihbrn rjbijht `s rjprjsjhtjn ly \KiT. Ydjrj \ ; Abrloh.

1.   Ydbt `s tdj kot`vj oe bnn`hi `on`hj `h skbmm bkouht nur hi prjpbrbt`oh oe kjtdymkbihjs`uk `on`nj ?(B) @t bats bs b abtbmyst (L) @t aohvjrts jtdjr hto bmfym on`nj(A) @t njarjbsjs tdj v`omjhaj oe tdj rjbat`oh (N) @t bats bs bh jmjatropd`m a

Bhs.   BQom.   @t bats bs b abtbmyst

>.   ^dj rjbat`oh oe bh bmfym dbm`nj bhn kbihjs`uk `s h`t`bmmy vjry smow, lut mbtjr ljaokjs vjry ebst, ljabusj(B) ^dj rjbat`oh s butoabtbmyt a (L) ^dj Ir`ihbrnrjbijht eorkjn `sjtdjr-somulmj

(A) ^dj rjbat`oh `s jhnotdjrk`a (N) ^dj rjbat`oh `s jxotdjrk`aBhs.   N

\‑T+Ki  \‑KiT   D ; ‑vj

:.   B Ir`ihbrn rjbijht `s eorkjn oh rjbat`hi kbihjs`uk w td(B) Bmfym dbm`nj h tdj prjsjhaj oe nry jtdjr (L) Bmfym dbm`nj `h tdj prjsjhaj oe pdjhom(A) Bmfym dbm`nj `h tdj prjsjhaj oe bmaodom(N) Bmfym dbm nj `h tdj prjsjhaj oe bmaodom`a jtdjr 

Bhs.   BQom.   \‑T+Ki  \‑KiT (Ir`ihbrn \jbijht)

5.   Sjrjw`t hoee's kjtdon `s usjn eor (B) tdj jst`kbt oh oe rjbat`vj dynroijh btok (L) tdj jst`kbt oh oe bmfoxy iroup(A) tdj prjpbrbt`oh oe b d`idjr jtdjr (N) tdj prjpbrbt`oh oe b Ir`ihbrn rjbijht

Bhs. B

Qom.   S‑D + \‑KiT\ ‑D + KiTS^d`s s jst`kbt`oh oe rjbat`vj dynroijh btok.

9.   Wr`kbry bmaodom abhhot lj oltb`hjn ly tdj rjbat`oh oe b Ir`ihbrn rjbijht w`td(B) ^dj s`kpmjst bmfbhbm (L) N`kjtdymjhj ox`nj(A) Jtdymjhj imyaom (N) Oxyijh

Bhs.   A

Qom.   \KiT + DADO  \‑AD<OD\KiT + (AD

<)

<O \‑AD

< ‑AD

< ‑OD

\‑KiT + (AD<OD)

<  \‑D + KiTOAD

<AD

<OD

\KiT+O<  \OD

4.   Wr`kbry, sjaohnbrybhn tjrt`brybmaodoms abh lj oltb`hjn ly dynromys`s oe tdj pronuats eorkjn oh rjbat`oh oe b Ir`ihbrn rjbijht w td(B) @solutyrbmnjdynj (L) Lutbhohj (A) O xyijh (N) Ox`rbhj

Bhs.   A

Qom.   \‑KiT+ O<  \OKiT         

  OD1   \OD

(2³, <³, 1³) (2³, <³, 1³)

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"kbh`sdfukbrpdys`as.`h"   <>

ADJK@Q^\P

0.   Yd`ad oe tdjeommow`hi `s eorkjn ohtdj rjbat oh oe ohj komj oe bajtym admor njw tdohj komj oe kjtdymkbihjs`ukadmor`nj ?(B) <-Lutbhom (L) Bajtohj (A) @solutym bmaodom (N) t-Lutym bmaodom

Bhs.   L

Qom.  

27.   @njht ey tdj pronuat - TD

:A

5 ‑ A  A ‑ A

5D

:                   Abtbmysts'M`hnmbr  T

Qom.

22.   @njht`eyT

           Wn/D< T

Qom.   T ;

2<.   @njht`ey tdj pronuat x bhn y

+ N<                 \dAm)WWd(   11   T

+ N<                 \dAm)WWd(   11   P

Qom.   T ; 6 P ;

(Kjso) (nm) \jajk`a k`xturj

21.   @njht ey pronuat ?

           >M`BmD W

Qom.   W ;

2>.

Ydjrj x bhn y ?

Qom.   x ; A s < lutjhj , y ; trbhs < lutjhj

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"kbh`sdfukbrpdys`as.`h"   <:

ADJK@Q^\P

2:.

Yr`tj tdj pronuats.

Qom.   (b) (l)

25.

Qom.   @h bmm absjs pronuat `s

29.   Brrbhij tdj eommow`hi bmfjhjs `h njarjbs`hi ornjr oe tdj`r stbl`m ty\

<A ; A\

<, AD

< ; AD

<, \

<A ; AD

<, \ ‑ AD ; AD ‑ \ (a`s, trbhs), \

<A ; AD\, \AD ; AD

<

Qom.   \<A;A\

< 8 \

<A ; AD\ 8\

<A ; AD

< 8

trbhs

\ADAD\     8

a`s

AD\\AD     8 \ ‑ AD ; AD< 8 AD

< ; AD

<

24.   Ydbt `s tdj ornjr oe stbl`m`ty oe eommow`hi bmfjhj

@1

<1

AD|

ADADADAD   ,

@@

1<<

1

ADADAAD|AD

,

@@@

1

11

AD|

ADADAAD  

Bhs.   @@@ 8 @@ 8 @

Qom.   Qtbl m`ty oe bmfjhj Dypjraohcuibt`vj Qtruaturj.

20.   A<D

:Am Jtdjr 

Hb         pronuats

Yr`tj bmm poss`lmj pronuat

Qom.   AD1 ‑ AD

< ‑ Am     

kbcor ADADADAD   1<<1  

AD1 ‑ AD

< ‑ Am

<1   DAAD

          aoupm`hi

AD1 ‑ AD

< ‑ AD

< ‑ AD

1

                 `ohn`sproport   AD1 ‑ AD

1  + AD

< ; AD

<

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ADJK@Q^\P

<7.   Yurtz rjbat`oh w mm hot lj olsjrvjn `h

(B) (L) (A)

1

1

AD|

Lr ADAD     (N) hohj oe tdjsj

Bhs.   L

Qom.       Hb   + D<

  ibs

<2.   AD1 ‑ Lr      M`

 B           @AuL     P A

`e A `s AD1 ‑ AD

< ‑ (AD

<)

: ‑ AD

1, tdbh wdbt `s P.

Bhs.   AD1 ‑ (AD

<)

5 ‑ Lr 

Qom.   AD1 ‑ Lr      M`

AD1M`           @Au

(AD1)

<AuM`                      T ‑AD ‑)AD( ‑AD   <:<1   AD

1 ‑ AD

< ‑ (AD

<)

: ‑ AD

1

<<.       B

        /AbO

HbOD L

Ydbt brj B bhn L

Qom.   B `s , L `s

<1.   Jxpmb`h wdy tdj adb`h `h`t`bt`hi stjp `h tdjrkbm admor`hbt`oh oe AD> `s

Am<

     mA•

bhn hot AD>

     1

DA   +  •

D

Qom.   Ljabusj Jbat

 oe Am< `s mjss tdbh J

bat oe AD

>

<>.   Admor`hbt`oh oe AD>

`hvomvjs eommow`hi stjps 3

(`) Am<        mA<

(``) AD> +   mA

•  1

DA   + DAm

(```) 1

DA   +   mA•

    AD1Am

Yd`ad oe tdj eommow`hi `s rbtj njtjrk`h`hi ?(B) Qtjp (`) (L) Qtjp (``) (A) Qtjp (```) (N) Qtjp (``) bhn (```) lotd

Bhs.   L

Qom.   Eorkbt`oh oe bmfym erjj rbn`abm s \ns stjp.