L-08 Introduction to Bridge Engineering (Coloured)

41
7/23/2019 L-08 Introduction to Bridge Engineering (Coloured) http://slidepdf.com/reader/full/l-08-introduction-to-bridge-engineering-coloured 1/41 ^rig. Mr. Qajsar Aej T`jfgirl`m Liflr`t` M`sjhf “ JJ M`parto`ft ig Ljvje @fhjf``rjfh, Pfjv`rsjty ig @fhjf``rjfh afm ]`lbfieihy ^`sbawar E`ltur` - >2 Jftrimultjif ti Drjmh` @fhjf``rjfh Dy; ^rig Mr. Qajsar Aej Ljvje @fhjf``rjfh M`parto`ft P@] ^`sbawar www.mrqajsaraej.lio 1 ^rig. Mr. Qajsar Aej T`jfgirl`m Liflr`t` M`sjhf “ JJ M`parto`ft ig Ljvje @fhjf``rjfh, Pfjv`rsjty ig @fhjf``rjfh afm ]`lbfieihy ^`sbawar ]ipjls Jftrimultjif Drjmh` Liopif`fts ]yp`s ig Drjmh`s Eiams gir Drjmh` M`sjhf  Afaeysjs & M`sjhf ig \jopey \uppirt`m TL \ead Drjmh`s M`sjhf \t`ps gir \jopey \uppirt`m TL \ead Drjmh` @xaope` Gaoius Drjmh`s jf tb` Xirem 4

Transcript of L-08 Introduction to Bridge Engineering (Coloured)

Page 1: L-08 Introduction to Bridge Engineering (Coloured)

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^rig. Mr. Qajsar Aej T`jfgirl`m Liflr`t` M`sjhf “ JJ

M`parto`ft ig Ljvje @fhjf``rjfh, Pfjv`rsjty ig @fhjf``rjfh afm ]`lbfieihy ^`sbawar 

E`ltur` - >2

Jftrimultjif ti Drjmh`

@fhjf``rjfh

Dy; rig Mr. Qajsar Aej

Ljvje @fhjf``rjfh M`parto`ft

P@] ^`sbawar 

www.mrqajsaraej.lio

1

^rig. Mr. Qajsar Aej T`jfgirl`m Liflr`t` M`sjhf “ JJ

M`parto`ft ig Ljvje @fhjf``rjfh, Pfjv`rsjty ig @fhjf``rjfh afm ]`lbfieihy ^`sbawar 

]ipjls

Jftrimultjif

Drjmh` Liopif`fts

]yp`s ig Drjmh`s

Eiams gir Drjmh` M`sjhf

 Afaeysjs & M`sjhf ig \jopey \uppirt`m TL \ead Drjmh`s

M`sjhf \t ps gir \jopey \uppirt`m TL \ead Drjmh`

@xaope`

Gaoius Drjmh`s jf tb` Xirem

4

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^rig. Mr. Qajsar Aej T`jfgirl`m Liflr`t` M`sjhf “ JJ

M`parto`ft ig Ljvje @fhjf``rjfh, Pfjv`rsjty ig @fhjf``rjfh afm ]`lbfieihy ^`sbawar 

Jftrimultjif

Drjmh` js a strultur` bavjfh af ip`fjfh fit e`ss

tbaf 7>>> oo tbat giros part ig a bjhbway ir iv`r,

ir ufm r wbjlb tb` bjhbway pass`s.

\trultur`s 5 7>>> oo h`f`raeey laee m luev`rts.

<

Luev`rtDrjmh`

^rig. Mr. Qajsar Aej T`jfgirl`m Liflr`t` M`sjhf “ JJ

M`parto`ft ig Ljvje @fhjf``rjfh, Pfjv`rsjty ig @fhjf``rjfh afm ]`lbfieihy ^`sbawar 

Jftrimultjif

Drjmh` js tb` c`y `e`o`ft jf a ]rafspirtatjif

\yst`o;

Jt liftries tb` lapaljty ig tb` syst o.

Jt js tb` bjhb`st list p`r oje` ig tb` syst o.

Jg tb` drjmh` gajes, tb` syst o gajes.

=

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^rig. Mr. Qajsar Aej T`jfgirl`m Liflr`t` M`sjhf “ JJ

M`parto`ft ig Ljvje @fhjf``rjfh, Pfjv`rsjty ig @fhjf``rjfh afm ]`lbfieihy ^`sbawar 

Drjmh` Liopif`fts

 A drjmh` lifsjsts ig sup`r strultur` afm sudstrultur`.

0

\up`r strultur`; \trulturae parts ig tb` drjmh` wbjlb privjm`s tb` birjziftae spaf.

\ud strultur`; \trulturae parts ig tb` drjmh` wbjlb suppirts tb` birjziftae spaf.

^rig. Mr. Qajsar Aej T`jfgirl`m Liflr`t` M`sjhf “ JJ

M`parto`ft ig Ljvje @fhjf``rjfh, Pfjv`rsjty ig @fhjf``rjfh afm ]`lbfieihy ^`sbawar 

7

^j`r 

^j`r Lap Mjapbrahos

^je` Lap

Hjrm`r 

M`lc

^je`s

Drjmh` Liopif`fts

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^rig. Mr. Qajsar Aej T`jfgirl`m Liflr`t` M`sjhf “ JJ

M`parto`ft ig Ljvje @fhjf``rjfh, Pfjv`rsjty ig @fhjf``rjfh afm ]`lbfieihy ^`sbawar 

  Drjmh`s laf d` leassjgj m allirmjfh ti;

Oat rjaes (liflr`t , st` e ir wiim `tl),

Psah` (p`m`strjaf, bjhbway, ir rajeriam),

\paf (sbirt, o`mjuo, ir eifh),

\trulturae giro (seads, hjrm`r, truss, arlb, susp`fsjif, ir 

lade`-stay`m).

8

]yp`s ig Drjmh`s

^rig. Mr. Qajsar Aej T`jfgirl`m Liflr`t` M`sjhf “ JJ

M`parto`ft ig Ljvje @fhjf``rjfh, Pfjv`rsjty ig @fhjf``rjfh afm ]`lbfieihy ^`sbawar 

Jt js biw`v`r sujtade` ti leassjgy drjmh`s allirmjfh ti

tb` eilatjif ig tb` oajf strulturae `e o`fts r`eatjv` ti

tb` surgal` if wbjlb tb` us`r trav`es;

Oajf strultur` D`eiw tb` m`lc ejf ,

Oajf strultur  Adiv` tb` m`lc ejf`, ir 

Oajf strultur` Lijfljmjfh wjtb tb` m`lc ejf .

2

]yp`s ig Drjmh`s

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^rig. Mr. Qajsar Aej T`jfgirl`m Liflr`t` M`sjhf “ JJ

M`parto`ft ig Ljvje @fhjf``rjfh, Pfjv`rsjty ig @fhjf``rjfh afm ]`lbfieihy ^`sbawar 

 Oajf \trultur` D`eiw M`lc ejf`

 Arlb`m, ]russ-Arlb`m Drjmh`s, Oasifry Arlb, Liflr`t`

 Arlb, tb` \t``e-]russ Arlb, afm tb` \t``e M`lc ]russ.

:

Oasifry Arlb \t``e M`lc ]russ Drjmh`Oasifry Arlb

]yp`s ig Drjmh`s

^rig. Mr. Qajsar Aej T`jfgirl`m Liflr`t` M`sjhf “ JJ

M`parto`ft ig Ljvje @fhjf``rjfh, Pfjv`rsjty ig @fhjf``rjfh afm ]`lbfieihy ^`sbawar 

 Oajf \trultur` D`eiw M`lc ejf`

1>

Liflr`t` Arlb

\t``e ]russ Arlb

]yp`s ig Drjmh`s

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^rig. Mr. Qajsar Aej T`jfgirl`m Liflr`t` M`sjhf “ JJ

M`parto`ft ig Ljvje @fhjf``rjfh, Pfjv`rsjty ig @fhjf``rjfh afm ]`lbfieihy ^`sbawar 

 Oajf \trultur` D`eiw M`lc ejf`

Xjtb arlb sbap`, hravjty eiams ar` trafsojtt`m ti tb`

suppirts prjoarjey dy axjae liopr ssjv` girl`s.

 At tb` suppirts, ditb v`rtjlae afm birjziftae r`altjifs oust

d` r`sjst m.

11

Arlb

Axjae girl` Axjae girl`

]yp`s ig Drjmh`s

^rig. Mr. Qajsar Aej T`jfgirl`m Liflr`t` M`sjhf “ JJ

M`parto`ft ig Ljvje @fhjf``rjfh, Pfjv`rsjty ig @fhjf``rjfh afm ]`lbfieihy ^`sbawar 

 Oajf \trultur` D`eiw M`lc ejf`

\aej ft g`atur`s ig Arlb ]yp` Drjmh`

]b` arlb giro js jft`fm`m ti r`mul` d`fmjfh oio`fts jf tb`

sup`rstrultur`.

]b` oist sujtade sjt` gir tbjs giro ig strultur js a vaee`y, wjtb

tb` arlb giufmatjif eilat`m if mry rilc seip`s.

]b` lifv`ftjifae lurv`m arlb rjd oay bav` bjhb gadrjlatjif afm

`r`ltjif lists, aetbiuhb tb`s` oay d` liftriee`m dy scjee`m

eadir.

]b` leassjl arlb giro t`fms ti gavir liflr t` as a lifstrultjif

oat`rjae.

14

]yp`s ig Drjmh`s

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^rig. Mr. Qajsar Aej T`jfgirl`m Liflr`t` M`sjhf “ JJ

M`parto`ft ig Ljvje @fhjf``rjfh, Pfjv`rsjty ig @fhjf``rjfh afm ]`lbfieihy ^`sbawar 

 Oajf \trultur` D`eiw M`lc ejf`

\aej ft g`atur`s ig Arlb ]yp` Drjmh`

]b` arlb rjd js usuaeey sbap`m ti tac` m`am eiam wjtbiut

d`fmjfh oio`fts. ]bjs eiam js tb`f laee m tb` giro eiam.

Jg tb` giro eiam js earh`, tb` ejv` eiam d`lio`s `ss`ftjaeey a

soaee mjsturdafl` appej`m ti a liopr`ss`m o`od`r.

1<

]yp`s ig Drjmh`s

^rig. Mr. Qajsar Aej T`jfgirl`m Liflr`t` M`sjhf “ JJ

M`parto`ft ig Ljvje @fhjf``rjfh, Pfjv`rsjty ig @fhjf``rjfh afm ]`lbfieihy ^`sbawar 

1=

\usp`fsjif; M`lc js suppirt`m dy twi oajf lade`s tbriuhb

s`lifmary lade`s (bafh`rs).

]yp`s ig Drjmh`s

  Oajf \trultur` Adiv` M`lc ejf`

\usp`fsjif, Lade \tay`m, afm ]briuhb-]russ drjmh`s ar

jfleum`m jf tbjs lat hiry.

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^rig. Mr. Qajsar Aej T`jfgirl`m Liflr`t` M`sjhf “ JJ

M`parto`ft ig Ljvje @fhjf``rjfh, Pfjv`rsjty ig @fhjf``rjfh afm ]`lbfieihy ^`sbawar 

  Oajf \trultur` Adiv` M`lc ejf`

10

Lade`-stay`m; M`lc js suppirt`m dy tiw`r mjr`ltey tbriuhb lade`s.

]yp`s ig Drjmh`s

^rig. Mr. Qajsar Aej T`jfgirl`m Liflr`t` M`sjhf “ JJ

M`parto`ft ig Ljvje @fhjf``rjfh, Pfjv`rsjty ig @fhjf``rjfh afm ]`lbfieihy ^`sbawar 

  Oajf \trultur` Adiv` M`lc ejf`

17

]briuhb Drjmh`s

]yp`s ig Drjmh`s

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^rig. Mr. Qajsar Aej T`jfgirl`m Liflr`t` M`sjhf “ JJ

M`parto`ft ig Ljvje @fhjf``rjfh, Pfjv`rsjty ig @fhjf``rjfh afm ]`lbfieihy ^`sbawar 

  Oajf \trultur` Adiv` M`lc ejf`

\aej ft g`atur`s ig \usp`fsjif Drjmh`s

]b` ge`xjde` lade`s ig a susp`fsjif drjmh` js sbap`m afm

suppirt`m ti trafsg`r tb` oakir eiams ti tb` tiw`rs afm

aflbirah`s dy mjr lt t`fsjif.

]b` m`lc js bufh grio tb` lade dy bafh`rs lifstrult`m ig bjhb

str`fhtb wjr` rip`s jf t`fsjif.

]bjs us` ig bjhb str`fhtb st``e jf t`fsjif e`ams ti af

`lifiojlae strultur`.

18

]yp`s ig Drjmh`s

^rig. Mr. Qajsar Aej T`jfgirl`m Liflr`t` M`sjhf “ JJ

M`parto`ft ig Ljvje @fhjf``rjfh, Pfjv`rsjty ig @fhjf``rjfh afm ]`lbfieihy ^`sbawar 

  Oajf \trultur` Adiv` M`lc ejf`

\aej ft g`atur`s ig \usp`fsjif Drjmh`s

]b` oajf lade js stjgg`f`m `jtb r dy a pajr ig stjg g fjfh truss`s

ir dy a syst o ig hjrm rs at m`lc e`v`e.

]bjs stjgg`fjfh syst`o s`rv`s ti;

a) Liftrie a`rimyfaojl oiv`o fts,

d) Ejojt eilae afhe lbafh`s jf tb` m`lc.

12

\tjgg`fjfh

truss`s

]yp`s ig Drjmh`s

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^rig. Mr. Qajsar Aej T`jfgirl`m Liflr`t` M`sjhf “ JJ

M`parto`ft ig Ljvje @fhjf``rjfh, Pfjv`rsjty ig @fhjf``rjfh afm ]`lbfieihy ^`sbawar 

  Oajf \trultur` Adiv` M`lc ejf`

\aej ft g`atur`s ig Lade` \tay`m drjmh`s

 As liopar`m wjtb susp`fsjif drjmh`s, tb` lade`s ar` strajhbt

ratb`r tbaf lurv`m. As a r`suet, tb` stjggf`ss js hr`at`r.

 A`rimyfaojls jfstadjejty bas fit giufm ti d` a pride`o jf sulb

strultur`s.

1:

]yp`s ig Drjmh`s

^rig. Mr. Qajsar Aej T`jfgirl`m Liflr`t` M`sjhf “ JJ

M`parto`ft ig Ljvje @fhjf``rjfh, Pfjv`rsjty ig @fhjf``rjfh afm ]`lbfieihy ^`sbawar 

  Oajf \trultur` Adiv` M`lc ejf`

\aej ft g`atur`s ig ]briuhb Drjmh`s

 A drjmh` truss bas twi oajf strulturae amvaftah`s;

1. ]b` prjoary o`od r girl`s ar axjae eiams3

4. ]b` ip f w`d syst o p rojts tb` us` ig a hr at r iv raee m`ptb

(mu` ti e`ss r m`am eiam) tbaf gir af `qujvae`ft siejm w`d hjrm`r.

Ditb tb s` galtirs e`am ti `lifioy jf oat`rjae afm a r`mul`m

m`am w jhbt.

]b` jflr`as`m m`ptb aesi e`ams ti r`mul`m m ge ltjif.

@lifiojlae gir o`mjuo spafs, a`stb`tjlaeey pe`asjfh.

4>

]yp`s ig Drjmh`s

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^rig. Mr. Qajsar Aej T`jfgirl`m Liflr`t` M`sjhf “ JJ

M`parto`ft ig Ljvje @fhjf``rjfh, Pfjv`rsjty ig @fhjf``rjfh afm ]`lbfieihy ^`sbawar 

  Oajf \trultur` Lijfljmjfh wjtb M`lc ejf`

Hjrm`r drjmh`s ig aee typ`s ar` jfleum`m jf tbjs lat`hiry.

@xaope`s ar ;

\ead (siejm afm vijm`m),

]-d`ao,

J-d`ao,

Xjm`-geafh` d`ao,

Liflr t` dix hjrm`r,

\t``e dix,

\t``e peat` hjrm`r.

41

Liflr`t` Dix Hjrm`r Drjmh`

]yp`s ig Drjmh`s

^rig. Mr. Qajsar Aej T`jfgirl`m Liflr`t` M`sjhf “ JJ

M`parto`ft ig Ljvje @fhjf``rjfh, Pfjv`rsjty ig @fhjf``rjfh afm ]`lbfieihy ^`sbawar 

  Oajf \trultur` Lijfljmjfh wjtb M`lc ejf`

44

Dix Hjrm`r Drjmh`

Hjrm`r Drjmh` Pfm`r Lifstrultjif

]yp`s ig Drjmh`s

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^rig. Mr. Qajsar Aej T`jfgirl`m Liflr`t` M`sjhf “ JJ

M`parto`ft ig Ljvje @fhjf``rjfh, Pfjv`rsjty ig @fhjf``rjfh afm ]`lbfieihy ^`sbawar 

  Oajf \trultur` Lijfljmjfh wjtb M`lc ejf`

4<

]yp`s ig Drjmh`s

^rig. Mr. Qajsar Aej T`jfgirl`m Liflr`t` M`sjhf “ JJ

M`parto`ft ig Ljvje @fhjf``rjfh, Pfjv`rsjty ig @fhjf``rjfh afm ]`lbfieihy ^`sbawar 

Eiams gir Drjmh` M`sjhf

4=

Eiams ti d` lifsjm`r`m jf drjmh` m`sjhf laf d` mjvjm`m

jfti twi driam lat`hirj s;

^`roaf`ft eiams,

]rafsj`ft eiams.

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^rig. Mr. Qajsar Aej T`jfgirl`m Liflr`t` M`sjhf “ JJ

M`parto`ft ig Ljvje @fhjf``rjfh, Pfjv`rsjty ig @fhjf``rjfh afm ]`lbfieihy ^`sbawar 

Eiams gir Drjmh` M`sjhf

 ^`roaf`ft Eiams \`eg w`jhbt ig hjrm rs afm m`lc, w`arjfh surgal , lurds afm

parap ts afm rajejfhs, utjejtj`s afm euojfarj s afm pr ssur`s

grio `artb r`tajfo`fts.

]wi jopirtaft m`am eiams ar`;

ML; M`am eiam ig strulturae liopif`fts afm fif strulturae

attalbo`fts.

MX; M`am eiam ig w arjfh surgal`.

40

^rig. Mr. Qajsar Aej T`jfgirl`m Liflr`t` M`sjhf “ JJ

M`parto`ft ig Ljvje @fhjf``rjfh, Pfjv`rsjty ig @fhjf``rjfh afm ]`lbfieihy ^`sbawar 

 ^`roaf`ft Eiams

Oat rjae ^rip`rtj s gir ^av`o`ft

 μdjtuo`f ? 440> ch/o< ? 44.1 cF/o< (1=> ed/ g <)

 μliflr`t` ? 4=>> ch/o< ? 4<.7 cF/o< (10> ed/ g <)

Eiam galtirs gir ^av`o`ft M`am Eiams

]b` oaxjouo eiam galtir gir ML ? 1.40

]b` oaxjouo eiam galtir gir MX ? 1.0

47

Eiams gir Drjmh` M`sjhf

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^rig. Mr. Qajsar Aej T`jfgirl`m Liflr`t` M`sjhf “ JJ

M`parto`ft ig Ljvje @fhjf``rjfh, Pfjv`rsjty ig @fhjf``rjfh afm ]`lbfieihy ^`sbawar 

48

Eiams gir Drjmh` M`sjhf

 ]rafsj`ft Eiams Hravjty (Ejv`) eiams mu` ti v`bjluear, rajeway afm p`m`strjaf

traggjl.

]b` autioidje` js if` ig tb` oist liooif v`bjluear ejv`

eiam if oist drjmh`s3 jt js tb` trulc tbat laus`s tb` lrjtjlae

eiam `gg`lts.

Eat`rae eiams mu` ti wat`r, wjfm, `artbquac` afm sbjp

lieejsjifs `tl.

^rig. Mr. Qajsar Aej T`jfgirl`m Liflr`t` M`sjhf “ JJ

M`parto`ft ig Ljvje @fhjf``rjfh, Pfjv`rsjty ig @fhjf``rjfh afm ]`lbfieihy ^`sbawar 

42

Eiams gir Drjmh` M`sjhf

 ]rafsj`ft Eiams

Gieeiwjfh `gg`lts laus`m dy Ejv` eiam ar` aesi v`ry

jopirtaft afm oust d` lifsjm`r m jf tb` m`sjhf ig a drjmh .

Jopalt (myfaojl `gg`lts),

Dracjfh girl`s,

L`ftrjguhae girl`s (jg pr`s`ft) afm

]b` `gg lts ig itb`r trulcs sjouetaf`iusey pr`s`ft.

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^rig. Mr. Qajsar Aej T`jfgirl`m Liflr`t` M`sjhf “ JJ

M`parto`ft ig Ljvje @fhjf``rjfh, Pfjv`rsjty ig @fhjf``rjfh afm ]`lbfieihy ^`sbawar 

  W`bjluear M`sjhf Eiams ]b` AA\B]I m`sjhf eiams oim e lifsjsts ig tbr`` mjstjfltey

mjgg r`ft eiams;

M`sjhf ]rulc,

M`sjhf ]afm`o,

M`sjhf Eaf .

4:

Eiams gir Drjmh` M`sjhf

^rig. Mr. Qajsar Aej T`jfgirl`m Liflr`t` M`sjhf “ JJ

M`parto`ft ig Ljvje @fhjf``rjfh, Pfjv`rsjty ig @fhjf``rjfh afm ]`lbfieihy ^`sbawar 

  W`bjluear M`sjhf Eiams

M`sjhf ]rulc

^r`vjiusey B\4> was us`m as M`sjhf trulc. ]b` B m`fit`s

bjhbway afm \ m`fit`s \`oj traltir afm 4> js tb` w`jhbt ig  

traltir jf tifs (P\L ufjts).

]b` f`w v`bjle liodjfatjif as m`slrjd`m jf AA\B]I (1::=)

ETGM Drjmh` sp`ljgjlatjifs ar` m`sjhfat`m as BE-:< gir  

Bjhbway Eiamjfh all`pt`m jf 1::<.

<>

Eiams gir Drjmh` M`sjhf

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^rig. Mr. Qajsar Aej T`jfgirl`m Liflr`t` M`sjhf “ JJ

M`parto`ft ig Ljvje @fhjf``rjfh, Pfjv`rsjty ig @fhjf``rjfh afm ]`lbfieihy ^`sbawar 

  W`bjluear M`sjhf Eiams

<1

BE-:< ]rulc Eiam

1=0 cF

(<4 cjps)

(1=.0 tifs)

1=0 cF

(<4 cjps)

(1=.0 tifs)

<0 cF

(2 cjps)

(<.0 tifs)

=.< o ti :.> o

(1= gt ti <> gt)

=.< o

(1= gt)

Eiams gir Drjmh` M`sjhf

^rig. Mr. Qajsar Aej T`jfgirl`m Liflr`t` M`sjhf “ JJ

M`parto`ft ig Ljvje @fhjf``rjfh, Pfjv`rsjty ig @fhjf``rjfh afm ]`lbfieihy ^`sbawar 

  W`bjluear M`sjhf Eiams

M`sjhf ]afm`o

<4

11> cF

(4= cjps)

(11 tifs)

11> cF

(4= cjps)

(11 tifs)

1.4 o

(= gt)

Eiams gir Drjmh` M`sjhf

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^rig. Mr. Qajsar Aej T`jfgirl`m Liflr`t` M`sjhf “ JJ

M`parto`ft ig Ljvje @fhjf``rjfh, Pfjv`rsjty ig @fhjf``rjfh afm ]`lbfieihy ^`sbawar 

  W`bjluear M`sjhf Eiams M`sjhf Eaf` Eiam

]b` AA\B]I m`sjhf eaf` eiamjfh js ejc` a laravaf ig trulcs.

Jt js :.< cF/o afm js assuo`m ti illupy a r hjif ig <.> o (1> gt).

Jt js appej`m as <.1 cF/o4 ir >.>7= c/gt4 (7= ed/gt4) igpr`ssur` tia wjmtb ig <.> o ir 1> gt

iv r tb``ftjr e`fhtbig drjmh`gir G@O.

<<

<.> o (1> gt)Drjmh`

:.< cF/o

(>.7= cjp/ gt)

Eiams gir Drjmh` M`sjhf

^rig. Mr. Qajsar Aej T`jfgirl`m Liflr`t` M`sjhf “ JJ

M`parto`ft ig Ljvje @fhjf``rjfh, Pfjv`rsjty ig @fhjf``rjfh afm ]`lbfieihy ^`sbawar 

  W`bjluear M`sjhf Eiams

Jf suooary tbr`` m`sjhf eiams sbiuem d` lifsjm`r`m; tb`

m`sjhf trulc, m`sjhf tafm`o, afm tb` m`sjhf eaf .

]b`s` eiams ar` sup`rjopis`m dy twi ways ti yj`em tb` ejv`

eiam `gg`lts, wbjlb ar liodjf`m wjtb tb` itb r eiam `gg`lts.

]b` twi ways ig sup rpisjtjif ar ; ]rulc + eaf ,

]afm`o + eaf ,

<=

Eiams gir Drjmh` M`sjhf

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^rig. Mr. Qajsar Aej T`jfgirl`m Liflr`t` M`sjhf “ JJ

M`parto`ft ig Ljvje @fhjf``rjfh, Pfjv`rsjty ig @fhjf``rjfh afm ]`lbfieihy ^`sbawar 

 Eiam Oimjgj`r   A galtir alliuftjfh gir multjejty, r`mufmafly afm tb`

ip`ratjifae jopirtafl` ig tb` drjmh`.

Jt js tac`f as 1.>0 gir sjopey suppirt`m drjmh`s afm js

appej`m if aer`amy galtir m vaeu`s ig d`fmjfh oio`fts.

<0

Eiams gir Drjmh` M`sjhf

^rig. Mr. Qajsar Aej T`jfgirl`m Liflr`t` M`sjhf “ JJ

M`parto`ft ig Ljvje @fhjf``rjfh, Pfjv`rsjty ig @fhjf``rjfh afm ]`lbfieihy ^`sbawar 

Afaeysjs afm M`sjhf ig \jopey\uppirt`m TL \ead Drjmh`s

<7

  \jopey \uppirt`m TL \ead Drjmh`

]bjs typ` ig drjmh` lifsjst ig ifey sead (wjtbiut afy itb`r suppirtjfh

o`od r sulb as hjrm`rs).

]bjs giro ig drjmh js wjm ey us`m wb`f tb` drjmh` lriss s a ojfir riam ir 

soaee rjv r.

Jf sulb las`s, tb` spaf js r eatjv ey soaee afm ouetjpe` spafs ar jfg`asjde`

ir/afm uff`l`ssary.

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^rig. Mr. Qajsar Aej T`jfgirl`m Liflr`t` M`sjhf “ JJ

M`parto`ft ig Ljvje @fhjf``rjfh, Pfjv`rsjty ig @fhjf``rjfh afm ]`lbfieihy ^`sbawar 

<8

Afaeysjs afm M`sjhf ig \jopey

\uppirt`m TL \ead Drjmh`s

@ @ @ @@

  Afaeysjs ig \ead Drjmh`

\ead drjmh`s laf d` afaeyz m as <M, 4M afm 1M oim es.

Jg jt js ti d` afaeyz`m as 1M oim`e (ejf` afaeysjs), tb drjmh` wjmtb wjee d`

mjvjm`m jfti varjius strjps ig sp`ljgjl wjmtb (@). ]b`s` strjps ar` laee`m

m`sjhf eaf`s.

^rig. Mr. Qajsar Aej T`jfgirl`m Liflr`t` M`sjhf “ JJ

M`parto`ft ig Ljvje @fhjf``rjfh, Pfjv`rsjty ig @fhjf``rjfh afm ]`lbfieihy ^`sbawar 

<2

Afaeysjs afm M`sjhf ig \jopey\uppirt`m TL \ead Drjmh`s

Oio`ft Idtajf`m grio 1M afaeysjs

O/@ O/@ O/@ O/@O/@

• M`sjhf eaf` wjmtbs laf d` laelueat`m usjfh quatjifs hjv`f if f`xt sejm`

  Afaeysjs ig \ead Drjmh`

]b` m`sjhf eaf`s ar` tb`f

trafsgiro`m ti ejf` `e`o`fts (1M

oim e) gir ejf` afaeysjs. ]b` oio`ft

ar` laelueat`m grio ejf` afaeysjs.

]b s` oio`fts (O) ar tb`f mjvjm m

dy tb` m`sjhf eaf` wjmtb (@) ti h`t

oio`ft p r giit (O/@) gir tb` sead.

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^rig. Mr. Qajsar Aej T`jfgirl`m Liflr`t` M`sjhf “ JJ

M`parto`ft ig Ljvje @fhjf``rjfh, Pfjv`rsjty ig @fhjf``rjfh afm ]`lbfieihy ^`sbawar 

<:

X

X1

\

Afaeysjs afm M`sjhf ig \jopey

\uppirt`m TL \ead Drjmh`s

 M`sjhf Eaf`s M`sjhf Eaf` Xjmtb

  Gir sjfhe` eaf` eiam`m;

@ (jflb`s) ? 1>.> + 0.> ∛ (E1X1)

E1 ? Oimjgj m spaf e`fhtb ? Ojfjouo ig (\) afm 7> gt

X1 ? Oimjgj`m `mh` ti `mh` wjmtb ? Ojfjouo ig (Iv`raee wjmtb ig  

drjmh , X1) ir <> gt

^rig. Mr. Qajsar Aej T`jfgirl`m Liflr`t` M`sjhf “ JJ

M`parto`ft ig Ljvje @fhjf``rjfh, Pfjv`rsjty ig @fhjf``rjfh afm ]`lbfieihy ^`sbawar 

=>

X

X1

\

Afaeysjs afm M`sjhf ig \jopey\uppirt`m TL \ead Drjmh`s

 M`sjhf Eaf`s

M`sjhf Eaf` Xjmtb

  Gir ouetjeaf` eiam`m;

@ (jflb`s) ? 2= + 1.==∛ (E1X1) ≭ X1/FE

E1 ? \ao` as sjfhe eaf eiam m las` ? Ojfjouo ig (\) afm 7> gt

X1 ? Ojfjouo ig (iv raee wjmtb ig drjmh , X1) ir 7> gt

FE ? Fi. ig m`sjhf eaf s? JF] (X/14)

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^rig. Mr. Qajsar Aej T`jfgirl`m Liflr`t` M`sjhf “ JJ

M`parto`ft ig Ljvje @fhjf``rjfh, Pfjv`rsjty ig @fhjf``rjfh afm ]`lbfieihy ^`sbawar 

  Ouetjpe` ^r`s`fl` Galtir  Ouetjpe` pr s`fl` galtirs oimjgy tb` v`bjluear ejv` eiams gir tb` pridadjejty

tbat v`bjluear ejv` eiams illur tih tb`r jf a gueey eiam`m stat`.

]b`s` galtirs sbiuem d` appej`m d gir` afaeysjs ir m`sjhf ifey wb`f mijfh

tbr``-mjo fsjifae oim`ejfh, wircjfh wjtb sudstrultur s.

 A galtir ig 1.4 js aesi us`m jf tb` ejf` afaeysjs ig `mh` strjp ig a sead drjmh`.

=1

Afaeysjs afm M`sjhf ig \jopey

\uppirt`m TL \ead Drjmh`s

^rig. Mr. Qajsar Aej T`jfgirl`m Liflr`t` M`sjhf “ JJ

M`parto`ft ig Ljvje @fhjf``rjfh, Pfjv`rsjty ig @fhjf``rjfh afm ]`lbfieihy ^`sbawar 

=4

\

Afaeysjs afm M`sjhf ig \jopey\uppirt`m TL \ead Drjmh`s

  Ojfjouo \ead M`ptb gir \ead Drjmh`

Ojfjouo m`ptb gir T.L.L \eads (b);

b? 1.4(\ + 1>)/<> (wb`r`  ‒\‚  js jf gt.)

Xb`r \ ? spaf ig drjmh` (l/l ig d`arjfh).

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^rig. Mr. Qajsar Aej T`jfgirl`m Liflr`t` M`sjhf “ JJ

M`parto`ft ig Ljvje @fhjf``rjfh, Pfjv`rsjty ig @fhjf``rjfh afm ]`lbfieihy ^`sbawar 

M`sjhf \t`ps gir \jopey \uppirt`m TL

\ead Drjmh`

  \t`p >1; \jz`s

Ojfjouo m`ptb gir T.L.L \eads;

M ptb, b (gt) ? 1.4(\ + 1>)/<>

Xb`r \ ? spaf ig drjmh .

  \t`p >4; Eiams

M t`rojf` eiam ML, XML ? bμliflr`t`

M t`rojf` eiam MX, XMX ? bμw`arjfh surgal`

  \t`p ><; Afaeysjs

M t`rojf` sead oio`fts mu` ti m`am eiams;

OML ? XML\4/2

OMX ? XMX\4/2

=<

\

M`am Eiams

^rig. Mr. Qajsar Aej T`jfgirl`m Liflr`t` M`sjhf “ JJ

M`parto`ft ig Ljvje @fhjf``rjfh, Pfjv`rsjty ig @fhjf``rjfh afm ]`lbfieihy ^`sbawar 

  \t`p ><; Afaeysjs (Liftjfu`m)

M t`rojf` sead oio`fts mu` ti ejv` eiams;

1. Oio`ft mu` BE-:< ]rulc eiam, O]rulc

(Oax. oio`ft mu ti trulc eiam laf d` idtajf m dy pealjfh tb ojmme` axe` at ojm spaf ig 

tb drjmh` afm r ar axe` eiam at mjstafl` ig 1= gt grio tb ojmme` axe` eiam)

==

<4 cjps<4 cjps2 cjps

1= gt1= gt

\/4

M`sjhf \t`ps gir \jopey \uppirt`m TL\ead Drjmh`

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^rig. Mr. Qajsar Aej T`jfgirl`m Liflr`t` M`sjhf “ JJ

M`parto`ft ig Ljvje @fhjf``rjfh, Pfjv`rsjty ig @fhjf``rjfh afm ]`lbfieihy ^`sbawar 

  \t`p ><; Afaeysjs (Liftjfu`m)

M t`rojf` sead oio`fts mu` ti ejv` eiams;

4. Oio`ft mu` ]afm`o Eiam, O]afm`o

(Oax. oio`ft mu` ti tafm`o eiam laf d` idtajf`m dy pealjfh tb twi eiams at mjstafl` ig 

4 gt grio tb` ojm spaf)

=0

4= cjps4= cjps

4 gt4 gt

\/4

M`sjhf \t`ps gir \jopey \uppirt`m TL

\ead Drjmh`

^rig. Mr. Qajsar Aej T`jfgirl`m Liflr`t` M`sjhf “ JJ

M`parto`ft ig Ljvje @fhjf``rjfh, Pfjv`rsjty ig @fhjf``rjfh afm ]`lbfieihy ^`sbawar 

  \t`p ><; Afaeysjs (Liftjfu`m)

M t`rojf` sead oio`fts mu` ti ejv` eiams;

<. Oio`ft mu` m`sjhf eaf` eiam, OEaf`

OEaf` ? >.7= \4/2

]ac` hr at`r oio`ft vaeu` aoifh O]afm`o afm O]rulc afm ouetjpey jt dy

jopalt galtir ig 1.<< afm tb`f amm jt wjtb OEaf`

]b`r gir , OEE+JO ? 1.<<(O]afm`o IT O]rulc) + OEaf`

Lifv`rt OEE+JO ti oio`ft/gt, Mjvjm` OEE+JO dy ―@‟ m`sjhf eaf wjmtb.

=7

>.7= cjp/gt

\

M`sjhf \t`ps gir \jopey \uppirt`m TL\ead Drjmh`

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^rig. Mr. Qajsar Aej T`jfgirl`m Liflr`t` M`sjhf “ JJ

M`parto`ft ig Ljvje @fhjf``rjfh, Pfjv`rsjty ig @fhjf``rjfh afm ]`lbfieihy ^`sbawar 

  \t`p ><; Afaeysjs (Liftjfu`m)

Gir Jft`rjir \trjp, \jfhe` Eaf` Eiam`m, ―@‟ js hjv`f dy;

@ (jflb`s) ? 1>.> + 0.> ∛ (E1X1)   (1)

Gir Jft rjir \trjp, Ouetjeaf` eiam`m, ―@‟ js hjv`f dy;

@ (jflb`s) ? 2= + 1.==∛ (E1X1) ≭ X1/FE   (4)

Gjfaeey, M`sjhf Eaf` Xjmtb @, js tb` soaee`st vaeu` ig (1) & (4)

M`t rojf` Ou gir jft rjir strjp;

Ou (jft`rjirstrjp) ? 1.>0 S1.40OML + 1.0OMX + 1.80OEE+JO _ (p`r giit)

=8

M`sjhf \t`ps gir \jopey \uppirt`m TL

\ead Drjmh`

^rig. Mr. Qajsar Aej T`jfgirl`m Liflr`t` M`sjhf “ JJ

M`parto`ft ig Ljvje @fhjf``rjfh, Pfjv`rsjty ig @fhjf``rjfh afm ]`lbfieihy ^`sbawar 

  \t`p ><; Afaeysjs (Liftjfu`m)

Gir @mh` \trjp, ―@‟ js hjv`f dy;

@ ? Darrj`r wjmtb at das` + 1 gt + (1/4) strjp wjmtb ≭ Guee strjp wjmtb ir 7

gt (wbjlb`v`r js e`ss)

D`laus` tb` `mh` strjp wjmtb js ejojt`m ti 7‴ , if`-eaf` eiam`m

(wb``e ejf` ? ¿ eaf` eiam) wjtb a ouetjpe` pr s fl` galtir, o ig 1.4

wjee d` lrjtjlae. B`fl` `mh` strjp oio`ft p r giit wjmtb js `quae ti;

OEE+JO (@mh` strjp) p`r giit ? ¿ Ø (OEE+JO) Ø 1.4/@

M`t rojf` Ou gir @mh` \trjp;

Ou (jft`rjir strjp) ? 1.>0 S1.40OML + 1.0OMX + 1.80OEE+JO _ (p`r giit)

=2

M`sjhf \t`ps gir \jopey \uppirt`m TL\ead Drjmh`

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^rig. Mr. Qajsar Aej T`jfgirl`m Liflr`t` M`sjhf “ JJ

M`parto`ft ig Ljvje @fhjf``rjfh, Pfjv`rsjty ig @fhjf``rjfh afm ]`lbfieihy ^`sbawar 

  \t`p >=; M`sjhfa) M`sjhf gir Jft`rjir \trjp (laelueat` As usjfh Jft rjir \trjp Oio`ft)

d) Mjstrjdutjif r`jfgirl`o`ft gir jft`rjir strjp (dittio trafsv`rs`

r`jfgirl`o`ft) {A0.1=.=.1};

 Atrafsv`rs` ? (1>>/∛\ ir 0> %) ig As (wbjlb v`r js e`ss, Dut Jt sbiuem fit d` e`ss

tbaf As(\brjfcah`)

 Astojo (sbrjfcah`)? >.>>12Ah

l) M`sjhf gir @mh` \trjp (Laelueat` As usjfh @mh \trjp Oio`ft)

m) Mjstrjdutjif T`jfgirl`o`ft gir @mh` \trjp ( \ao` ^ril`mur` as Adiv`)

`) \brjfcah` afm t`op`ratur` r`jfgirl`o`ft jf tip gal` ig sead (eifh afmtrafsv`rs` ditb); Gir hram` 7> st` e,

•  Ast ? >.>>12Ah

=:

M`sjhf \t`ps gir \jopey \uppirt`m TL

\ead Drjmh`

^rig. Mr. Qajsar Aej T`jfgirl`m Liflr`t` M`sjhf “ JJ

M`parto`ft ig Ljvje @fhjf``rjfh, Pfjv`rsjty ig @fhjf``rjfh afm ]`lbfieihy ^`sbawar 

  T`jfgirl`o`ft M`taje jf \ead Drjmh`;

 As, Oajf r`jfgirl`o`ft

(ti d` m`sjhf`m)

]rafsv`rs` Dittio r`jfgirl`o`ft

(e`ast ig 1>>/∛\ % ir 0> %) ig As

 As p`r sbrjfcah` afm

t`op ratur r`jfgirl`o`ft

r`qujr`o`fts

M`sjhf \t`ps gir \jopey \uppirt`m TL\ead Drjmh`

A

A‴ 

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^rig. Mr. Qajsar Aej T`jfgirl`m Liflr`t` M`sjhf “ JJ

M`parto`ft ig Ljvje @fhjf``rjfh, Pfjv`rsjty ig @fhjf``rjfh afm ]`lbfieihy ^`sbawar 

  T`jfgirl`o`ft M`taje jf \ead Drjmh`;

Drjmh` T`jfgirl`o`ft Afjoatjif

01

M`sjhf \t`ps gir \jopey \uppirt`m TL

\ead Drjmh`

^rig. Mr. Qajsar Aej T`jfgirl`m Liflr`t` M`sjhf “ JJ

M`parto`ft ig Ljvje @fhjf``rjfh, Pfjv`rsjty ig @fhjf``rjfh afm ]`lbfieihy ^`sbawar 

@xaope`

  M`sjhf ^ride o; M`sjhf ig 

sjopey suppirt m sead drjmh`

gir BE-:< ejv` eiam.

\paf e`fhtb ig <0 gt l`ftr` ti

l`ftr` ig d`arjfhs.

Tiamway wjmtb js == gt lurd ti

lurd.

 Aeeiw gir a gutur` w`arjfh

surgal` ig < jflb tbjlc

djtuojfius iv`reay.

Ps` g  l‴  ? =>>> psj afm g  y ? 7>

csj.

04

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^rig. Mr. Qajsar Aej T`jfgirl`m Liflr`t` M`sjhf “ JJ

M`parto`ft ig Ljvje @fhjf``rjfh, Pfjv`rsjty ig @fhjf``rjfh afm ]`lbfieihy ^`sbawar 

@xaope`

 \ieutjif;   \t`p Fi 1; \jz`s.

\paf e`fhtb ig drjmh` (\) ? <0 gt l/l

Le ar riamway wjmtb (X) ? == gt (lurd ti lurd)

Gir a lurd wjmtb ig 10 jflb`s, titae wjmtb ig tb` drjmh` (X1) ?

== + (4 Ø 10/14) ? =7.0 gt

Ojfjouo tbjlcf`ss ig drjmh` sead js hjv`f dy girouea;

bojf ? 1.4(\ + 1>)/<> ? 1.4 (<0 + 1>)/<> ? 1.2 gt ? 41.7‼ ≂ 44‼

0<

^rig. Mr. Qajsar Aej T`jfgirl`m Liflr`t` M`sjhf “ JJ

M`parto`ft ig Ljvje @fhjf``rjfh, Pfjv`rsjty ig @fhjf``rjfh afm ]`lbfieihy ^`sbawar 

@xaope`

 \ieutjif;

  \t`p Fi 4; Eiams.

\ead eiam (wML) ? bμlifl

? (44/14) Ø >.10 ? >.480 csg 

X`arjfh surgal` eiam (wMX) ? bμw`arjfh surgal`

? (</14) Ø >.1= ? >.><0 csg 

0=

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^rig. Mr. Qajsar Aej T`jfgirl`m Liflr`t` M`sjhf “ JJ

M`parto`ft ig Ljvje @fhjf``rjfh, Pfjv`rsjty ig @fhjf``rjfh afm ]`lbfieihy ^`sbawar 

@xaope`

 \ieutjif;   \t`p Fi <; Afaeysjs.

M`am eiam oio`fts;

\ead oio`fts (OML) ? wML\4/2

? >.480 Ø (<04)/2 ? =4 gt-cjp/gt

X`arjfh surgal` oio`ft (OMX) ? wMX\4/2

? >.><0 Ø <04/2 ? 0.< gt-cjp/gt

00

^rig. Mr. Qajsar Aej T`jfgirl`m Liflr`t` M`sjhf “ JJ

M`parto`ft ig Ljvje @fhjf``rjfh, Pfjv`rsjty ig @fhjf``rjfh afm ]`lbfieihy ^`sbawar 

07

@xaope`

 \ieutjif;

  \t`p Fi <; Afaeysjs.

Ejv` eiam oio`fts;

]rulc Eiam oio`fts;

O]rulc ? <0> gt-cjp

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^rig. Mr. Qajsar Aej T`jfgirl`m Liflr`t` M`sjhf “ JJ

M`parto`ft ig Ljvje @fhjf``rjfh, Pfjv`rsjty ig @fhjf``rjfh afm ]`lbfieihy ^`sbawar 

@xaope`

 \ieutjif;   \t`p Fi <; Afaeysjs.

Ejv` eiam oio`fts;

]afm`o oio`ft;

Otafm`o ? <84 gt-cjp

Eaf` oio`ft;

Oeaf` ? 7=> Ø <04/2 ? :2>>> gt-ed ? :2 gt-cjp

08

^rig. Mr. Qajsar Aej T`jfgirl`m Liflr`t` M`sjhf “ JJ

M`parto`ft ig Ljvje @fhjf``rjfh, Pfjv`rsjty ig @fhjf``rjfh afm ]`lbfieihy ^`sbawar 

@xaope`

02

 \ieutjif;

  \t`p Fi <; Afaeysjs.

Ejv` eiam oio`fts;

Otafm`o 6 Otrulc, tb`r gir w` wjee us` Otafm`o

OEE+JO (Jfleumjfh jopalt) ? 1.<<Otafm`o + Oeaf`

? 1.<< Ø <84 + :2 ? 0:< gt-cjp

]i lifv`rt OEE+JO ti oio`ft/gt, Mjvjm` OEE+JO dy ―@‟ m`sjhf eaf` wjmtb.

]b` AA\B]I lim` r`lioo`fms s`parat` laelueatjif ig @ afm r suetjfh

d`fmjfh oio`ft ―O‟ gir af jft`rjir afm `mh` strjps ig a TL sead drjmh`.

B`fl` f`xt sejm`s mjsluss`s jft rjir afm `mh strjps s`parat`ey.

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^rig. Mr. Qajsar Aej T`jfgirl`m Liflr`t` M`sjhf “ JJ

M`parto`ft ig Ljvje @fhjf``rjfh, Pfjv`rsjty ig @fhjf``rjfh afm ]`lbfieihy ^`sbawar 

@xaope`

 \ieutjif;   \t`p Fi <; Afaeysjs.

M`sjhf Eaf` wjmtb ―@‟ gir jft rjir strjp;

Gir sjfhe` eaf` eiam`m;

@ (jflb`s) ? 1>.> + 0.> ∛ (E1X1)

E1 ? Oimjgj`m spaf e`fhtb ? Ojfjouo ig (\ ? <0 gt) afm 7> gt ? <0 gt

X1 ? Oimjgj`m `mh` ti `mh` wjmtb ? Ojfjouo ig (X1 ? =7.0 gt) ir <>

gt ? <> gt

]b`r gir , @ ? 1>.>> + 0.>∛ (<0 Ø <>.>>) ? 184 jf ? 1=.< gt

0:

^rig. Mr. Qajsar Aej T`jfgirl`m Liflr`t` M`sjhf “ JJ

M`parto`ft ig Ljvje @fhjf``rjfh, Pfjv`rsjty ig @fhjf``rjfh afm ]`lbfieihy ^`sbawar 

@xaope`

7>

 \ieutjif;

  \t`p Fi <; Afaeysjs.

M`sjhf Eaf` wjmtb ―@‟ gir jft rjir strjp;

Gir ouetjeaf` eiam`m;

@ (jflb`s) ? 2= + 1.==∛ (E1X1) ≭ X1/FE

E1 ? <0 gt

X1 ? Ojfjouo ig (X1 ? =7.0 gt) ir 7> gt ? =7.0 gt

FE ? Fi. ig m`sjhf eaf`s.? JF] (X/14) ?JF] (==/14) ? <

@ ? 2= + 1.== ∛ (<0 Ø =7.0) ≭ =7.0/<

? 1=4 jflb ir 11.2= gt ≭ 10.0

]b`r`gir`, @ ? 11.2= gt (E`ast ig aee)

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^rig. Mr. Qajsar Aej T`jfgirl`m Liflr`t` M`sjhf “ JJ

M`parto`ft ig Ljvje @fhjf``rjfh, Pfjv`rsjty ig @fhjf``rjfh afm ]`lbfieihy ^`sbawar 

@xaope`

 \ieutjif;   \t`p Fi <; Afaeysjs.

Jft rjir \trjp Oio`ft (p`r giit)

OEE +JO (Jft rjir strjp) p r giit ? 0:</11.2= ? 0> gt-cjp/gt

Fiw,

Ou (jft`rjirstrjp) ? 1.>0 S1.40OML + 1.0OMX + 1.80OEE+JO (p r giit)_

Ou (jft rjirstrjp) ? 1.>0 (1.40 Ø =4 + 1.0 Ø 0.<< + 1.80 Ø 0>)

Ou (jft`rjirstrjp) ? 100.< gt-cjp/gt ? 127<.7 jf-cjp/gt

71

^rig. Mr. Qajsar Aej T`jfgirl`m Liflr`t` M`sjhf “ JJ

M`parto`ft ig Ljvje @fhjf``rjfh, Pfjv`rsjty ig @fhjf``rjfh afm ]`lbfieihy ^`sbawar 

@xaope`

 \ieutjif;

  \t`p Fi <; Afaeysjs.

M`sjhf eaf` wjmtb gir `mh` strjp; Allirmjfh ti AA\B]I ETGM

lim` A=.7.4.1.=,

@ ? Darrj`r wjmtb at das` + 1 gt + (1/4) strjp wjmtb ≭ Guee strjp wjmtb

ir 7 gt (wbjlb`v r js e`ss)

@ ? 1.40 gt + 1 gt + (1/4) Ø 11.2= ≭ 11.2= gt ir 7gt

@ ? 2.18 gt 6 7 gt

]b`r`gir @ ? 7 gt

74

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^rig. Mr. Qajsar Aej T`jfgirl`m Liflr`t` M`sjhf “ JJ

M`parto`ft ig Ljvje @fhjf``rjfh, Pfjv`rsjty ig @fhjf``rjfh afm ]`lbfieihy ^`sbawar 

@xaope`

 \ieutjif;   \t`p Fi <; Afaeysjs.

@mh` \trjp Oio`ft (p`r giit);

D`laus` tb` `mh` strjp wjmtb js ejojt`m ti 7‴ , if`-eaf` eiam`m

(wb``e ejf` ? ¿ eaf` eiam) wjtb a ouetjpe` pr`s fl` galtir, o ig 

1.4 wjee d` lrjtjlae. B`fl` `mh` strjp oio`ft p`r giit wjmtb js

`quae ti (T`g r`fl ; lbapt`r =, Darc r afm ^ulc tt) ;

OEE+JO (@mh` strjp) p r giit ? ¿ Ø (0:<) Ø 1.4/7 ? 0:.< gt-cjp/gt

Ou (`mh` strjp) ? 1.>0 S1.40OML + 1.0OMX + 1.80OEE+JO (p r giit)_

Ou (`mh` strjp) ? 1.>0 (1.40 Ø =4 + 1.0 Ø 0.<< + 1.80 Ø 0:.<)

Ou (`mh strjp) ? 184.=2 gt-cjp/gt ? 4>7:.8: jf-cjp/gt

7<

^rig. Mr. Qajsar Aej T`jfgirl`m Liflr`t` M`sjhf “ JJ

M`parto`ft ig Ljvje @fhjf``rjfh, Pfjv`rsjty ig @fhjf``rjfh afm ]`lbfieihy ^`sbawar 

@xaope`

7=

 \ieutjif;

  \t`p Fi =; M`sjhf.

(a) M`sjhf gir Jft`rjir strjp;

Jft`rjir strjp oio`ft (Ou) ? 100.< gt-cjp/gt ? 127<.7 jf-cjp/gt

@gg`ltjv` m`ptb ig drjmh` sead (m) ? b “ liv`r  “ ¿ Ø Mja ig dar  

us`m

Psjfh #2 dar, `gg`ltjv` m`ptb js dittio liv`r gir sead js tac`f

`quae ti 1‼.

m ? 44 “ 1 “ ¿ Ø 1 ? 4>.0 jflb

 Asojf ? >.>>12 Ø 14 Ø 44 ? >.=8 jf4

 As ? Ou/{Χg y (m “ a/4)}

 Agt`r trjaes, As ? 1.2> jf4,(#2 N 0 jflb`s l/l)

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^rig. Mr. Qajsar Aej T`jfgirl`m Liflr`t` M`sjhf “ JJ

M`parto`ft ig Ljvje @fhjf``rjfh, Pfjv`rsjty ig @fhjf``rjfh afm ]`lbfieihy ^`sbawar 

70

 \ieutjif;   \t`p Fi =; M`sjhf.

(d) Mjstrjdutjif r`jfgirl`o`ft gir jft`rjir strjp (dittio

trafsv`rs` r`jfgirl`o`ft) {A0.1=.=.1};

]b` aoiuft ig dittio trafsv`rs` r jfgirl`o`ft oay d` tac f as

a p`rl`ftah` ig tb` oajf r`jfgirl`o`ft r`qujr`m gir pisjtjv`

oio`ft as gieeiws dut fit e`ss tbaf \brjfcah` r jfgirl`o`ft;

 Atrafsv`rs` ? (1>>/∛\ ir 0> %) ig As (wbjlb`v`r js e`ss)

1>>/∛E ? 1>>/∛<0 ? 17.: % 5 0> %

]b r`gir , Atrafsv`rs` ? >.17: Ø 1.2> ? >.<>= jf4

 Astojo (sbrjfcah`)? >.>>12Ah ? >.>>12 Ø 14 Ø 44 ? >.=8 jf4 (#0 N

2 jflb`s l/l)

@xaope`

^rig. Mr. Qajsar Aej T`jfgirl`m Liflr`t` M`sjhf “ JJ

M`parto`ft ig Ljvje @fhjf``rjfh, Pfjv`rsjty ig @fhjf``rjfh afm ]`lbfieihy ^`sbawar 

@xaope`

 \ieutjif;

  \t`p Fi =; M`sjhf.

(d) Mjstrjdutjif r jfgirl`o`ft gir jft`rjir strjp (dittio trafsv`rs`

r`jfgirl`o`ft) {A0.1=.=.1};

Oaxjouo spaljfh gir t`op`ratur st e r`jfgirl`o`ft jf if` way

sead allirmjfh ti ALJ 8.14.4.4 js ojfjouo ig;

<bg ?< Ø 44 ? 77‼

12‼

]b`r gir #0 N 2 jflb`s l/l js IC.

77

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^rig. Mr. Qajsar Aej T`jfgirl`m Liflr`t` M`sjhf “ JJ

M`parto`ft ig Ljvje @fhjf``rjfh, Pfjv`rsjty ig @fhjf``rjfh afm ]`lbfieihy ^`sbawar 

@xaope`

78

 \ieutjif;   \t`p Fi =; M`sjhf.

(l) M`sjhf gir @mh` strjp;

@mh` strjp oio`ft (Ou) ? 184.=2 gt-cjp/gt ? 4>7:.8: jf-cjp/gt

@gg`ltjv` m`ptb ig drjmh` sead (m) ? b “ liv`r  “ ¿ Ø Mja ig dar  us`m

Psjfh #2 dar, `gg`ltjv` m`ptb js dittio liv`r gir sead js tac`f`quae ti 1‼.

m ? 44 “ 1 “ ¿ Ø 1 ? 4>.0 jflb

 Asojf ? >.>>12 Ø 14 Ø 44 ? >.=8 jf4

 As ? Ou/{Χg y (m  “ a/4)}3 Agt`r trjaes As ? 4.>1= jf4, (#2 N =.8jflb`s)

Gjfaeey us` #2 N = jflb`s l/l ditb gir jft`rjir as w`ee as `mh`strjps

^rig. Mr. Qajsar Aej T`jfgirl`m Liflr`t` M`sjhf “ JJ

M`parto`ft ig Ljvje @fhjf``rjfh, Pfjv`rsjty ig @fhjf``rjfh afm ]`lbfieihy ^`sbawar 

@xaope`

72

 \ieutjif;

  \t`p Fi =; M`sjhf.

(m) Mjstrjdutjif r jfgirl`o`ft gir `mh` strjp;

 Atrafsv`rs` ? >.17: Ø 4.>1= ? >.<= jf4

 Astojo (sbrjfcah`)? >.>>12Ah ? >.>>12 Ø 14 Ø 44 ? >.=8 jf4 (#0 N

2 jflb`s l/l)

Oaxjouo spaljfh gir t`op`ratur` st e r jfgirl`o`ft jf if` way

sead allirmjfh ti ALJ 8.14.4.4 js ojfjouo ig;

<bg ? < Ø 44 ? 77‼

12‼

Ps` #0 N 2 jflb`s l/l as dittio trafsv`rs r`jfgirl`o`ft

`v`rywb`r`.

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^rig. Mr. Qajsar Aej T`jfgirl`m Liflr`t` M`sjhf “ JJ

M`parto`ft ig Ljvje @fhjf``rjfh, Pfjv`rsjty ig @fhjf``rjfh afm ]`lbfieihy ^`sbawar 

@xaope`

 \ieutjif;   \t`p Fi =; M`sjhf.

( ) \brjfcah` afm t`op`ratur r jfgirl`o`ft jf tip gal` ig sead

(eifh afm trafsv`rs` ditb); Gir hram` 7> st e,

 Ast ? >.>>12Ah ? >.>>12 Ø 14 Ø 44 ? >.=8 jf4 (#0 N 2 jflb`s l/l)

Gjfaeey us` #0 N 2 jflb`s l/l.

 Gjfae T`lioo`fmatjif;

Oajf st``e (dittio) ? #2 N =‼ l/l gir jft rjir as w`ee as `xt rjir.

]rafsv rs` dittio r jfgirl`o`ft ? #0 N 2‼ l/l tbriuhbiut.

]ip st e (eifh afm trafsv rs ) ? #0 N 2‼ l/l.

7:

^rig. Mr. Qajsar Aej T`jfgirl`m Liflr`t` M`sjhf “ JJ

M`parto`ft ig Ljvje @fhjf``rjfh, Pfjv`rsjty ig @fhjf``rjfh afm ]`lbfieihy ^`sbawar 

@xaope`

 \ieutjif;

  \t`p Fi 0; Mragtjfh

8>

(Oajf r`jfgirl`o`ft)

(Dittio trafsv`rs` r`jfgirl`o`ft)

(\brjfcah` r`jfgirl`o`ft)

(\brjfcah` r`jfgirl`o`ft)

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^rig. Mr. Qajsar Aej T`jfgirl`m Liflr`t` M`sjhf “ JJ

M`parto`ft ig Ljvje @fhjf``rjfh, Pfjv`rsjty ig @fhjf``rjfh afm ]`lbfieihy ^`sbawar 

\io` Gaoius Drjmh`s

 Eifh`st Drjmh`

Mafyafh “Cufsbaf Hrafm Drjmh` jf Lbjfa (17=2>> o)

81

^rig. Mr. Qajsar Aej T`jfgirl`m Liflr`t` M`sjhf “ JJ

M`parto`ft ig Ljvje @fhjf``rjfh, Pfjv`rsjty ig @fhjf``rjfh afm ]`lbfieihy ^`sbawar 

\io` Gaoius Drjmh`s

 Eifh`st \paf

 Acasbj Cajcyŏ Drjmh , Kapaf (1::1 o)

84

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^rig. Mr. Qajsar Aej T`jfgirl`m Liflr`t` M`sjhf “ JJ

M`parto`ft ig Ljvje @fhjf``rjfh, Pfjv`rsjty ig @fhjf``rjfh afm ]`lbfieihy ^`sbawar 

\io` Gaoius Drjmh`s

 Bjhb`st Drjmh`

\j Mu Tjv r Drjmh` (=84 o bjhb)

8<

^rig. Mr. Qajsar Aej T`jfgirl`m Liflr`t` M`sjhf “ JJ

M`parto`ft ig Ljvje @fhjf``rjfh, Pfjv`rsjty ig @fhjf``rjfh afm ]`lbfieihy ^`sbawar 

Drjmh`s jf ^acjstaf

  Eafsmiwf` Drjmh`, \uccur 

8=

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^rig. Mr. Qajsar Aej T`jfgirl`m Liflr`t` M`sjhf “ JJ

M`parto`ft ig Ljvje @fhjf``rjfh, Pfjv`rsjty ig @fhjf``rjfh afm ]`lbfieihy ^`sbawar 

Drjmh`s jf ^acjstaf

  Kaosbiri Drjmh`, Kaosbiri

80

^rig. Mr. Qajsar Aej T`jfgirl`m Liflr`t` M`sjhf “ JJ

M`parto`ft ig Ljvje @fhjf``rjfh, Pfjv`rsjty ig @fhjf``rjfh afm ]`lbfieihy ^`sbawar 

Drjmh`s jf ^acjstaf

 Attilc Drjmh`, Attilc

87

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^rig. Mr. Qajsar Aej T`jfgirl`m Liflr`t` M`sjhf “ JJ

M`parto`ft ig Ljvje @fhjf``rjfh, Pfjv`rsjty ig @fhjf``rjfh afm ]`lbfieihy ^`sbawar 

Drjmh`s jf ^acjstaf

  Oaejr Drjmh`, Caralbj

Eifh`st Drjmh` jf ^acjstaf (0>>> o)

88

^rig. Mr. Qajsar Aej T`jfgirl`m Liflr`t` M`sjhf “ JJ

M`parto`ft ig Ljvje @fhjf``rjfh, Pfjv`rsjty ig @fhjf``rjfh afm ]`lbfieihy ^`sbawar 

Drjmh`s jf ^acjstaf

  Lbjfjit Tajeway Drjmh`

Lifstrult m jf 1288.

82

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^rig. Mr. Qajsar Aej T`jfgirl`m Liflr`t` M`sjhf “ JJ

M`parto`ft ig Ljvje @fhjf``rjfh, Pfjv`rsjty ig @fhjf``rjfh afm ]`lbfieihy ^`sbawar 

Drjmh`s jf ^acjstaf

  Drjmh` if O4 Oitirway

If` ig tb` bjhb`st jf Asja.

8:

^rig. Mr. Qajsar Aej T`jfgirl`m Liflr`t` M`sjhf “ JJ

M`parto`ft ig Ljvje @fhjf``rjfh, Pfjv`rsjty ig @fhjf``rjfh afm ]`lbfieihy ^`sbawar 

T`g`r`fl`s

  M`sjhf ig Bjhbway Drjmh`s dy Tjlbarm O. Darc r.

  ALJ <12

2>

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^rig. Mr. Qajsar Aej T`jfgirl`m Liflr`t` M`sjhf “ JJ

M`parto`ft ig Ljvje @fhjf``rjfh, Pfjv`rsjty ig @fhjf``rjfh afm ]`lbfieihy ^`sbawar 

]B@ @FM

21