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Enobltivb0. @t heter l`r is aeika mub kertj `t ` spbbm eg 26 dh/j. It h`dbs ` 96e cbgt turk witjeut lj`kaika tjb

spbbm. ]jb lj`kab ik tjb vbcelity eg tjb l`r is `neut

(@) 26 d h/j tew`rms wbst (N*) 16 d h/j tew`rms s eutj-wbst

(L) 16 dh/j tew`rms kertj-wbst (M) zbre

,m bdsWo mdo hdo mj vdso26gmbj-/5d`Wd mj pdy cs td oaj a\@ 4a viuj pdy vigoegr_r oTdrs aq, ld`4j vdso 96 mds.d cs 5dwb

tdrj a\@ mdo ms esx bs` igoer_u a\ &(@) 26gmbj6/5d`WdX ig'dpb mj vdso (N*) 16gmbj6/5d`Wd kg{d.d&ig'pb mj vdso(L) 16gmbj6/5d`WdX h^ro&ig'pb mj vdso (M)'dwR4

\ec. N

Lj`kab ik vbcelity eg tjb l r 8 Wg Wi

8 >> 2626 tew`rms seutj-wbst 8 >26 dh/j

8 16 dh/j tew`rms seutj-wbst

>. Gia. sjews tjb mispc`lbhbkt tihb ar`pj eg ` p`rtilcb hevika ek tjb Z-`xis.

(@) tjb p`rtilcb is lektikueuscy aeika ik pesitivb x mirbltiek

(N) tjb p`rtilcb is `t rbst

(L) tjb vbcelity iklrb`sbs up te ` tihb te, `km tjbk nblehbs lekst`kt.

(M*) tjb p`rtilcb hevbs `t ` lekst`kt vbcelity up te ` tihb te, `km tjbk steps.

Z-v{d ms vuqgk'd xgr'djy m.d md geCGddiu&cb4 ysTddgp8dX gp8d bs `izkg'd_r a\ &

(@)m.d guoRro /dud^bmxgk'dd bs` xgr'djy a\@(N)m.d geodbdeCGdd bs` a\@(L)cb4 t

erm esx l3+rd a\ r^i'pdr~ gu4r ads tdrd a\@

(M*)m.d cb4term gu4r esx cs xgr'djy oard a\X r^i'pdr~ geodbdeCGdd bs` vd tdrd a\@

\ec. M

\cepb eg "x-t" ar pj aivbs vbcelityJ b r b ( t 8 6 t e t 8 t6) scepb is lekst`kt se wb l`k s`y tj`t vbcelity is lekst`kt. ]j`k `gtrbr te, scepb is

zbre. \e vbcelity is zbre. \e vbcelity is zbre.

vbcelityzbre hb`ks p`rtilcb steps.

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cs

r4 mord a\@ vd\cr esx md bdu a\ &

(@)

0 >

> (N) >0 (L*)

>>

00>

(M)

>>

000

\ec. ]et c mispc`lbhbkt 8 >x

]et c tihb t`dbk 8 t0

+ t>

8>0 v

x

v

x

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Lj`ptbr # < ^bst & Hetiek ? Dikbh`tils T0 v

x

v

x

x>

v 8

>0 v

0

v

0

>

v

>8

>0 v

0

v

0

7. @ stekb is rbcb`sbm greh `k bcbv`ter aeika up witj `k `llbcbr`tiek . ]jb `llbcbr`tiek eg tjb stekb `gtbr

tjb rbcb`sb is

(@) upw`rm (N) (a-`) upw`rm (L) (a-`) mewkw`rm (M*) a mewkw`rm

io mj vdso`^eo.d cs xgr'djy gyW cs ,m i^Gdo KdsH+ d tdrd a\@ bqMr mous ms i'pdr~ i^Gdo md ^eo.d a\ &(@) `io mj vdso (N) (a-`)io mj vdso (L) (a-`)ujps mj vdso (M*) aujps mj vdso

\ec. M

\tekb is rbcb`sbm greh `k bcbv`ter

]jb `llbcbr tiek eg tjb stekb `gtbr tjb rbcb`sb is

`\b

8 -a 8 a mewkw`rm

1. @ pbrsek st`kmika kb`t tjb bmab eg tjb tep eg ` nuicmika tjrews twe n`ccs @ `km N. ]jb n`cc @ is tjrewk

vbrtil`ccy mewkw`rm witj tjb s`hb spbbm. ]jb n`cc @ jits tjb areukm witj spbbm@

`km tjb n`cc N jits

tjb areukm witj ` spbbmN

. Qb j`vb ?

,m Jdeu ms io gmudos io TdH+d E4gMr kds xs`ks@ ,e` NPs`mrd a\@ xs`k@ h/ed_/do io mj vdso rGdd xs`k Nh/ed_/do ujps mjvdso cbdu pdy cs Ps`mj x4j a\@ xs`k@ tbju cs

@pdy cs Wmodrj a\ rGdd xs`k Ntbju cs

Npdy cs Wmodrj a\@ ab ma

cmrs a\ gm &(@)

@;

N (N)

@3

N (*L)

@8

N

(M) tjb rbc`tiek nbtwbbk @ `km N mbpbkms ek jbiajt eg tjb nuicmika `nevb tjb areukm.

v@

rGddvNbs` c`l`/d Jdeu mj tbju cs pdn_ io guJd_o mord a\@

\ec. L

@gtbr lehb n`ld `t cbvbc 0 vbcelityeg tjb n cc '@' is s`hb `km bqu c te n cc 'N'.v> 8 u> + >`s

N cc@ + N cc N tr vbcs tjb s`hb jbiajt se wb l`k s`y tj`t

uN

8 u@

:. Ik ` preoblticb hetiek tjb vbcelity {dsi.d xgr bs` esx(@) is `cw`ys pbrpbkmiluc`r te tjb `llbcbr`tiek

abs'dd ^eo.d ms yBler~ adsrd a\@(N) is kbvbr pbrpbkmiluc`r te tjb `llbcbr`tiek

mJdj Jdj ^eo.d ms yBler~ uaj` ads cmrd@(L*) is pbrpbkmiluc`r te tjb `llbcbr`tiek ger ekb ikst`kt ekcy

,m {d.d ms gy, ^eo.d ms yBler~ adsrd a\@(M) is pbrpbkmiluc`r te tjb `llbcbr`tiek ger twe ikst`kts.

kds ldo ^eo.d ms yBler~ adsrd a\@\ec. L

Ik ` preoblticb hetiek

`t h`xihuh jbiajt, y lehpekbkt eg tjb vbcelity is zbre. Ekcy ikst`kt vbcelity is pbrpbkmiluc`r te tjb

`llbcbr`tiek.

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9. ]we nuccbts `rb girbm sihuct`kbeuscy, jerizekt`ccy `km witj miggbrbkt spbbm greh tjb s`hb pc`lb. Qjilj

nuccbt wicc jit tjb areukm girst5

(@) tjb g`stbr ekb (N) tjb scewbr ekb

(L*) netj wic c rb`lj sihuct`kbeuscy (M) mbpbkm ek tjb h`ssbs.

{d\grt gk'dd bs` ,m aj CGddu cs ,m cdGd kds xdsgy4d` gJdRu&gJdRu pdyds` cs kdxj x4j a\@ md\ucj xdsyj tbju io iays iaq`psxj &(@)rst xgredyj (N)/djbj xgr edyj(L*)kdsuds` ,m cdGd aj iaq`psxj (M)hums kzE4bduds` io guJd_o mosxd@

\ec. L

Netj nuccbt wicc jittjb areukmsihuct`kbeuscynbl usb mewkw`rm `llbcbr`tiek eg tjbnetj nuccbtis s`hb

& bqu c te a. t girbm `t s`hb pc lb.

\ 8 ut + 0/> `t>

\y8 uy + 0/> `y+ t>\

y8 E + 0/> at>

t 8a

\> y.

06. ]jb r`kab eg preoblticb girbm `t `k `kacb eg 02e is 26 h. Ig it is girbm witj tjb s`hb spbbm `t `k `kacb eg

=2e, its r`kab wicc nb

(@) >2 h (N) 2bj- (N) siku>

26 8a

.......... (0)

a

u >

8 066 .......... (>)

Aivbk girbm witj tjb s`hb spbbm `teh `kacb eg =2

^' 8a

=2>siku > 8

a

u >

sik96 { sik96 8 0}

^' 8a

u >

8 06 h

00. ]we preoblticbs @ `km N `rb preobltbm witj `kacb eg preobltiek 02e ger tjb preoblticb @ `km =2 e ger tjb

preobltiek N. Ig @

`km ^N

nb tjb jerizekt`c r`kab ger tjb twe preoblticbs, tjbk

(@) ^@3 ^N (N) ^@8 ^N (L) ^@; ^N(M*) tjb ikgerh`tiek is iksuggilibkt te mblimb tjb rbc`tiek eg @

witj ^N

.

iz{dsI4@, 02e mds.d io rGdd iz{dsI4N, =2e mds.d io iz{dsgir gm4s x4s a\@ 4gk@

rGdd^Nnu kdsuds` mj {dsgrt iodc a\X rds &

(@) @

3 ^N

(N) @

8 ^N

(L) @

; ^N

(M*) @

rGdd^Nms b/4 c`l`/d cqgug'pr mous ms gy4s cwpud vi4d_Ir a\@

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\ec. M

^ 8a

>siku>

`kacb's `rb aivbk nut ket aivbk tjbikgerh`tiek `neut 'u'.

0>. @ rivbr is gcewika greh wbst te b`st `t spbbm eg 2 hbtrbs pbr hikutb. @ h`k ek tjb seutj n`kd eg tjb

rivbr, l`p`ncb eg swihhika `t 06 hbtrbs pbr hikutb ik sticc w`tbr, w`kts te swih `lress tjb rivbr ik tjb

sjertbst tihb. Jb sjeucm swih ik ` mirbltiek.

(@*) mub kertj (N)

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ENOBL]IWB - II0. Leksimbr tjb hetiek eg tjb trip eg tjb hikutb j`km eg ` lceld. Ik ekb jeur

( @*) tjb mispc`lbh bkt is zbre ( N) tjb mist`klb levbrbm is zbre

( L) tjb vbr`ab spbbm is zbr e ( M*) tjb vbr `ab vbcelity is zbre

5dH+j mj gbuW edyj cqn_ mj udsm mj xgr io gepdo mgo4s@ ,m 5d`Ws bs` &(@*)geCGddiu 'dwR4 a\@ (N)r4 mj xn_ kwoj 'dwR4 a\@

(L)vd\cr pdy 'dwR4 a\@ (M*)vd\cr esx 'dwR4 a\@\ec. @M

Hikutb j`km lehpcbtb ekb ret tiek ik 0 jeur.

\e Mispc`lbhbkt is zbre.

Mist`klb 8 >r 6

`vbr`ab spbbm 8t`dbktihb]et`c

Mist`klb6

`vbr`ab vbcelity 8t`dbktihb]et`c

ktMispc`lbhb8 6

>. @ p`rtilcb hevbs `ceka tjb Z-`xis `s

x 8 ut(t>s) + `(t>s)>

(@) tjb ikiti`c vbcelity eg tjb p`rtilcb is u (N) tjb `llbcbr`tiek eg tjb p`rtilcb is `

(L) tjb `llbcbr`tiek eg tjb p`rtilcb is >` (M*) `t t 8>s p`rtilcb is `t tjb eriaik.

Z-v{d mj vdso xgr'djy ,m m.d ms gy4sx 8 ut(t>s) + `(t>s)>

(@)m.d md vdogBJdm esxua\@ (N)m.d md ^eo.d`a\@(L)m.d md ^eo.d>`a\@ (M*)cb4t 8 6cs- io m.d bwy glRkq io a\@

\ec. `t t 8 > sblekm

x 8 6 i.b. p`rtilcb is `t eriaik.

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(n) Cbt otsikitlesv

mt

vm

8 otlesitsik

\Emt

vm

6

v 8 tsiktles >> 8 0

mt

vm

8 6

(l) Cbt tjb p`tj eg tjb p`rtilcb is

Mispc lbhbkt 8 6

@vbr`ab vbcelity 8 6

Nut ikst`kt`kbeus vbcelityis kbvbr zbre ik tjb iktbrv`c.

(m) Ik tjb str`iajtcikbhetiek

Mispc lbhbkt 8 6

@vbr`ab vbcelity 8 6Nut ik tjis hetiek `t ekb peikt ikst`kt kbeus vbcelity is zbre.

=. @k enoblt h`y j`vb

(@) v`ryika spbbm witjeut j`vika v`ryika vbcelity

(N*) v`ryika vbcelity witjeut j`vika v`ryika spbbm

(L) kekzbre `llbcbr`tiek witjeut j`vika v`ryika vbcelity

(M*) kekzbre `llbcbr`tiek witjeut j`vika v`ryika spbbm.

,m eCrq ms gy4s cBJde a\ &(@)igoer_u'djy esx ms glud igoer_u'djy pdy(N*)igoer_u'djy pdy ms glud igoer_u'djy esx

(L)igoer_u'djy esx ms glud v'dwR4 ^eo.d(M*)igoer_u'djy pdy ms gludX v'dwR4 ^eo.d

\ec. NM

( ) \pbbm iklrb sb, tj`t l`usbs h`akitumb eg vbcelity iklrb`sbs.

(n) H`akitumb eg vbcelityis lekst`kt nut mirbltiek is lektikueus lj`kabs.

(l) @llbcbr tiek 8 r tb eg lj`kab eg vbcelity

(m) H`y nb pessincb tj`t `llbcbr tiek lj`kab tjb mirbltiek eg tjb p rtilcb nut ket lj`kab tjb h`akitumb eg

tjb vbcelity.

2. H`rd tjb lerrblt st`tbhbkts ger ` p`rtilcb aeika ek ` str`iajt cikb?

,m coy osTdd bs` xgr mo oas m.d ms gy, caj mGdu md p4u mjgt, &

(@) Ig tjb vbcelity `km `llbcbr`tiek j`vb eppesitb siak, tjb enoblt is scewika mewk.4gk esx e ^eo.d md gpRa geigor ads rds eCrq bgkr ads oaj a\@(N) Ig tjb pesitiek `km vbcelity j`vb eppesitb siak, tjb p`rtilcb is hevika tew`rms tjb eriaik.

4gk gCGdgr e esx md gpRa geiojr ads rds m.d bwy glRkq mj vdso xgr mo oad a\@(L) Ig tjb vbcelity is zbre `t `k ikst`kt, tjb `llbcbr`tiek sjeucm `cse nb zbre `t tj`t ikst`kt.

4gkgmcj {d.d esx'dwR4 ads rds hc {d.d ^eo.d Jdj 'dwR4 adsud pdga,@(M) Ig tjb vbcelity is zbre ger ` tihb iktbrv c, tjb `llbcbr tiek is zbre `t `ky ikst`kt witjik tjb tihb iktbrv c.

4gk gmcj cb4 vRrody bs` esx 'dwR4 ads nc cb4 vRrody bs` ^eo.d 'dwR4 adsxd@\ec. (@), (N), (M)

Murika rbt rm`tiek, `llbcbr`tiek eppesbs vbcelity. b`ku ms kd\oduX ^eo.d esx md grods/d mord a\@Wbcelity ihpcibs tjb mirbltiek eg hetiek eg ` nemy. esx eCrq mj xgrmj gk'dd k'dd_rj a\@

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7. ]jb vbcelity eg ` p`rtilcb is zbre `t t 8 6

(@) ]jb `llbcbr`tiek `t t 8 6 hust nb zbre

(N*) ]jb `llbcbr`tiek `t t 8 6 h`y nb zbre.

(L*) Ig tjb `llbcbr`tiek is zbre greh t 8 6 te t 8 06 s, tjb spbbm is `cse zbre ik tjis iktbrv`c.

(M*) Ig tjb spbbm is zbre greh t 8 6 te t 8 06 s tjb `llbcbr`tiek is `cse ik tjb iktbrv`c.

t 8 6io m.d md esx 'dwR4 a\ &(@) t 8 6io ^eo.d gug'pr ?i cs 'dwR4 adsxd@(N*) t 8 6io ^eo.d 'dwR4 ads cmrd a\@(L*) t 8 6cs t 8 06cs- ms b/4 ^eo.d 'dwR4 a\X nc cb4dRro bs` pdy J dj 'dwR4 adsxj@(M*)4gk t 8 6cs t 8 06cs- ms b/4 pdy 'dwR4 a\ rds nc cb4dRro bs` ^eo.d Jdj 'dwR4 adsxd@

\ec. NLM

(`) Grbb g`ccika nemy t 8 6 v 8 6 & ` 8 a

(n) Nemy `t rbst

(l) Greh t 8 6 tet 8 06s, tjb spbbm is `cse zbre iktjis iktbrv`c.Nbl`usb (v 8 u + `t)

(m) Ig nemy is rbst ik tjb iktbrv`c eg t 8 6 te t 8 06s.

1. H`rd tjb lerrblt st`tbhbkts?

(@*) ]jb h`akitumb eg tjb vbcelity eg ` p`rtilcb is bqu`c te its spbbm.

(N) ]jb h`akitumb eg `vbr`ab vbcelity ik `k iktbrv`c is bqu`c te its `vbr`ab spbbm ik tj`t iktbrv`c.

(L) It is pessincb te j`vb ` situ`tiek ik wjilj tjb spbbm eg ` p`rtilcb is `cw`ys zbre nut tjb `vbr`abspbbm is ket zbre

(M) It is pessincb te j`vb ` situ`tiek ik wjilj tjb spbbm eg tjb p`rtilcb is kbvbr zbre nut tjb `vbr`ab

spbbm ik `k iktbrv`c is zbre.

caj mGduds` md p4u mjgt4s &(@*)gmcj m.d ms esx md igobd.d hcmj pdy ms lodlo a\@(N)gmcj cb4d`rody bs` vd\cr esx md igobd.dX hc cb4d`ro bs` vd\cr pdy ms lodlo a\@(L),m ,scj igogCGdgr cBJde a\ gm gmcj m.d mj pdy ck\e 'dwR4 ads gmRrq vd\cr pdy 'dwR4 uaj` ads@(M),m ,scj igogCGdgr cBJde a\ gm gmcj m.d mj pdy mJdj Jdj 'dwR4 uaj` adsX gmRrq gmcj cb4d`ro bs` vd\cr pdy 'dwR4 ads@

\ec. @

(`) \pbbm 8 v

(n) @vbr`ab vbcelity 8t`dbktihb]et`c

ktMispc`lbhb]et`c

@vbr`ab spbbm 8t`dbktihb]et`c

Mist`klb

|@vbr`ab vbcelity| |@vbr`ab spbbm|

|Mispc`lbhbkt| |Mist`klb|

(l) \pbbm eg ` p rtilcb is `cw`ys zbre hb`ks p rtilcb `t rbst. Mist`klb tr`vbccbm ny tjb p rtilcb is zbre. \e

`vbr`ab spbbm 8 6

(m) \pbbm eg ` p rtilcb is kbvbr zbre hb`ks, p rtilcb tr vbccbm sehb mist klb.

\e `vbr`ab spbbm 8tihb

Mist`kb6

:. ]jb vbcelity-tihb pcet ger ` p`rtilcb hevika ek ` str`iajt cikb is sjewk ik gia.

,m coy osTdd bs` xgr'djy m.d md esx&cb4 xdzP k'dd_rd a\(@) ]jb p`rtilcb j`s lekst kt `llbcbr`tiek

m.d md eo.d gu4r a\@(N) ]jb p rtilcb j`s kbvbr turkbm `reukm.

m.d mJdj Jdj uaj` bqH+rd@

(L) ]jb p`rtilcb j`s zbre mispc lbhbktm.d md geCGddiu'dwR4 a\@(M) ]jb `vbr`ab spbbm ik tjb iktbrv`c 6 te 06s is tjb s`hb `s tjb `vbr`ab spbbm ik tjb iktbrv`c 06s te >6s.

6cs 06sbs` vd\cr pdy bs` rGdd06scs >6sbs` vd\cr pdy md bdu cbdu a\@

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\ec. (@), (M)

\cepb eg aivbk v-t ar`pj (i.b. `llbcbr`tiek) is lekst`kt.

Greh 6 te 06sblekms, vbcelityis ikpesitivb`km tjbk kba tivb. ]j`t hb`ks tjb p rtilcb tr ks `reukm

`t t 8 06 sbl.

]jb pesitivb `km kba tivb `rb`s rb ket bqu c, \e mispc`lbhbkt is ket zbre.

@rb` eg v-t ar`pj greh t 8 6 te t 8 06 sbl is s`hb `s tj`t greh t 8 06 te >6 sbl.

Jbklb `vbr`ab spbbm is s`hb.

ay (@), (M)

gk, x, v-t xzdP md 3dy (i.b. ^eo.d) gu4ra\@ 6 cs 06 c\m.H rmesx /dud^bm a\@ r^i'pdr~esx U.dd^bm a\@ ncmd rd^i4_ a\ gm m.d tr ks `reukm`t t 8 06 sbl U.dd^bm e U.dd^bm {ds8dPy cbdu uaj` a\@ vr% geCGddiu 'dwR4uaj`a\@ v-txzdP mdt 8 6cst 8 06 sblrm et 8 06cs>6 sbl.rm {ds8dPy cbiu a\@ vr% vd\cr pdy cbdu a\@vr%vd\cr pdy cbdu a\@

9. Gia. sjews tjb pesitiek eg ` p`rtilcb hevika ek Z-`xis `s gukl`tiek eg tihb.

gp8d bs`Z-v{d ms vuqgk'd xgr'djy m.d mj gCGdgrX cb4 ms Pyu ms ?i bs` E4Mr mj xn_ a \ &

(@*) ]jb p`rtilcb j`s lehb te rbst 7 tihbs

m.d 7ldo geodbdeCGdd bs` vdrd a\@(N) ]jb h`xihuh spbbm is `t t 8 7 s

t 8 7cs- io vg/dmrb pdy a\@(L) ]jb vbcelity rbh`iks pesitivb ger t 8 6 te t 8 7 s

t 8 6cs t 8 7csm.H ms b/4 esx /dud^bm oard a\@(M) ]jb `vbr`ab vbcelity ger tjb tet`c pbriem sjews is kba`tivb.

izkg'd_r cBiw.d_ cb4d`ro bs` vd\cr esx U.dd^bm a\@\ec. @

( ) \cepb eg x-t ar`pj aivbs tjb vbcelity.

Jbrb 7 tihbs scepb is zbre. \e wb l`k s`y tj`t tjb p`rtilcb j`s lehb te rbst 7 tihbs.

(n) Oust `gtbrt 8 7 sblscepb eg x-t ar`pj is zbre. ]jbk vb. \ewb b`sicy l`ks`y tj`t spbbm isket h xihuh

`t t 8 7s.

(l) \cepb eg x-t ar`pj sehb tihb +vb & sehb tihbvb er zbre. \e wb l`k s`y tj`t ikiktbrv`c eg t 8 6 te

t 8 7s sehb tihb vbcelityis +vb,vb er zbre.

(m) @vbr ab vbcelity8 t`dbktihb]et`c

ktMispc`lbhb]et`c

8 t

xxig

8 t

x8 +vb

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06. ]jb `llbcbr`tieks eg ` p`rtilcb `s sbbk greh twe gr`hbs \0`km \

>j`vb bqu`c h`akitumb = h/s>.

(@) ]jb gr`hbs hust nb `t tjb rbst witj rbspblt te b`lj etjbr.

(N) ]jb gr`hbs h`y nb hevika witj rbspblt te b`lj etjbr nut kbitjbr sjeucm nb `llbcbr`tbm witj

rbspblt te tjb etjbr.

(L) ]jb `llbcbr`tiek eg \>witj rbspblt te \

0h`y bitjbr nb zbre er : h/s>.

(M*) ]jb `llbcbr`tiek eg \>witj rbspblt te \

0h`y nb `kytjika nbtwbbk zbre `km : h/s>.

kds guks_'d r`8dds`\0rGdd\

>cs gmcj m.d ms ^eo.d md izsg{dr bdu ,m cbdu=bj-/cs> a\ &

(@)guks_'d r`8d gug'pr ?i cs ,m kwcos ms cdis{d gCGdo a\@

(N)guksz'd r`8d ,m kwcos ms cdis{d xgr'djy ads cmrs a\X gmRrq mdsn_ Jdj kwcos ms cdis{d ^egor uaj ` ads cmrd a\@(L) \

0ms cdis{d\

>md ^eo.d 'dwR4 vGded :bj-/cs> ads cmrd a\@

(M*) \0ms cdis{d\

>md ^eo.d 'dwR4 rGdd:bj/cs-> ms b/4 mqK Jdj ads cmrd a\@

\ec.0>ss

`

8 ps>`

+0ps

`

0>ss`

8 les.=.=.>== >>

Jbklb0>ss

` h`y cib nbtwbbk 6 & : mbpbkmika upek v`cub eg.