grignard reagent, reduction & alkane theory_e
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8/12/2019 Grignard Reagent, Reduction & Alkane Theory_E
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"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.
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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
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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
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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
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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
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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.