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8/3/2019 Sol.Paper-4
1/6
VHRD ZOH]XI^ZGX Z^@FG!K X]@FG * 0
VHRDZOH] LHR I^ZG ^GZ^ ]@]GR!>
0) \hewag hl z}ogrg 1:r
:
>
\hewag hl j{ekingr 1 r2or
z}ogrg1 r
j{ekingr/fk|gi+
oj{ekingr
1 2rj{ekingr
/fk|gi+
oj{ekingr
1 2rz}ogrg
j
z
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j2
j
:z
or
r:
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1
z2
z
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r2r
r:
>
1
2:
>
1 2 3 :
2) Ag`i hl 0z~ 27 127
27z~0hlzwa
:= 127
27z~0hlzwa
zwa hl 0z~ 27 1 := 27 1 67= )))))/k+
ag`i hl rgz~ 27 127
27rgz~hlzwa
zwa hl rgz~ 27 1 :2 27 1 ?== ))))/kk+
^h~`e ag`i 17=
?==67= 1
7=
077=1 :0
:) r 1 2
7
|hewag hl z}ogrg 1 2
7
2
7
:
>
2
7
1
) @rg` hl hl rohabwz 12
0 N
0 N
2
2? 1 2N>2
0
N2
1 0> ja
Ki rkfo~ @ifegn N@HB
x2 1 62 $ >2
x 1 7:
]grkag~gr hl rohabwz 1 >x 1 > 7: ja @iz)
7)
N
@ B
J
7 ja
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02 ja
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x x
b:; ja
A I
` $ b 1 72 :; 1 0: ja )))/kkk+
Ki @NA%
x2 $ `2 1 27 ))))/k+
Ki BJI%
x2 $ b2 1 0>> ))))/kk+
Zwb~r`j~ /k+ lrha /kk+% vg fg~
b2 `2 1 00;/b `+ /` $ b+ 1 00;
]w~~kif |`ewg hl /` $ b+% vg fg~
/b `+ 0: 1 00;
/b `+ 10:
00;))))/k|+
@nnkif /kkk+ , /k|+% vg fg~
2b 10:
00;$ 0:
b 12>
Pwgz) 0 2 : > 7 < 6 ? ; 0= 00 02 0: 0> 07 0< 06 0? 0; 2=
@iz) J N B @ J N J @ B @ J @ J B B @ J @ B @
Pwgz) 20 22 2: 2> 27 2< 26 2? 2; := :0 :2 :: :> :7 :< :6 :? :; >=
@iz) @ B B J B J B B N B @ B @ B J N N N B
Pwgz) >0 >2 >: >> >7 >< >6 >? >; 7= 70 72 7: 7> 77 7< 76 7? 7;
8/3/2019 Sol.Paper-4
2/6
VHRD ZOH]XI^ZGX Z^@FG!K X]@FG * 2
]w~ |`ewg hl b ki gpw`~khi /kkk+% vg fg~
` 1 0: 0:
0>>1
0:
27
Zh% }w~ |`ewg hl ki gpw`~khi /k+
x2 $0 7 7 02 1 :)0> 0== 1 :0> ja2
0:)
N J:= a
:= a
B@ 0= a
`rg` hl ~og zo`ngn rgfkhi 1:
8/3/2019 Sol.Paper-4
3/6
VHRD ZOH]XI^ZGX Z^@FG!K X]@FG * :
0>) Kiigr r`nkwz hl ~og bhve kz r 1 7 ja
^okjdigz hl ~og bhve kz 1 =)27 ja
Zh% k~z hw~gr r`nkwz /R+ 1 7 $ =)27 1 7)27
`in k~z hw~gr j`r|gn zwrl`jg rg` 1
JZ@ 1 2r2
JZ@ 1 2 6
22
>
20
>
20
JZ@ 1002
0;>=>1 06:)27 ja2
07) \hewag hl jwbhkn 1 7 2 7 1 7= ja:
\hewag hl jwbg awz~ bg ki `: lhra % zh lrha
h}~khiz hie{ 7= 2= 1 0=== fk|gz wz lhra hl
}grlgj~ jwbg%zh ih) hl jwbhknz 1 2= /B+
0
8/3/2019 Sol.Paper-4
4/6
VHRD ZOH]XI^ZGX Z^@FG!K X]@FG * >
2>)x l lx
> : 02
7 2 0=
< : 0?
6 7 :7
? 2 0< {g`rz
2?) x 1 i
x
6)2 10=
`70=0=000=?:><
62 1 ===)Ihv%
Jhrrgj~ |`ewg hl kx 1 >=== ?: $ 7:1 :;6= Jhrrgj~ ag`i
1i
xhl|`ewgjhrrgj~k
1 0==:;6=
1 :;)6
Zh% ~og jhrrgj~ ag`i kz :;)6)
8/3/2019 Sol.Paper-4
5/6
VHRD ZOH]XI^ZGX Z^@FG!K X]@FG * 7
:=) Fk|gi x 1 02)7?
J`ejwe`~khi hl Ag`i 3
xk lk lkxk
7 2 0=
? 7 >=
0= ? ?=
02 22 2
] 6 6]
2= > ?=
27 2 7=
7=lk ]672>xl kk
k
kk
l
xlx
02)7? 17=
]672>
$ 6]
6] 1 0=7
] 1 07)
:0) ki ~og }rgijg hl v`~gr% ~og kfik~khi ~ga}gr`~wrg
hl ~og }`}gr j`i ih~ bg rg`jogn
:2) /0+ /b+% /2+ /`+% /:+/j+
::) Fr`}ok~g nkllgrz lrha nk`ahin `z fr`}ok~g kz
zek}}gr{ ~h ~hwjo vokeg nk`ahin kz o`rn ,
fr`}ok~g kz fhhn jhinwj~hr hl gegj~rkjk~{ vokeg
nk`ahin kz ih~)
:>) zwf`r jo`rjh`e
:7) JiO2i 2:6) o{nrhfgi in ik~rhfgi
:?) o{nrhfgi
:;) ^og `ahwi~ hl j`rbhi ki ]g`~% Ekfik~g%
Bk~wakihwz in @i~or`jk~g kz =) `%/kk+ 4 b% /k|+ 4 j /k+ 4 n% /kkk+
>2) }rgzgijg hl lrgg gegj~rhiz
>:) /`p+JHHOOJ`jkn@jg~kj
: $ I`OJH:
gbkj`rbhi`~Zhnkwa:JHHI`OJ $ O2H $ JH2
>>) O{nrhjoehrkj `jkn
>7) Z`}hiki kz wzgn ki lh`a ~{}g lkrg gx~kifwkzogrz
~h z~`bkeksg lh`a)
>?) hw~gr shig)
>;) J`rbhi ~g~r` joehrkng kz og`|kgr ~o`i kr) Zh% k~
j`i jw~ hll ~og `kr zw}}e{ ~h ~og bwrikif
zwbz~`ijg)
7=) J`a}ohr kz v`x{% vok~g hr ~r`iz}`rgi~ zhekn
vk~o z~rhif rha`~kj hnhwr) K~ lhraz le`ag
hi bwrikif) Krhi% `ewakikwa `in jo`rjh`e nhih~ lhra le`ag bgj`wzg ~og{ nhi~ |`}hwrkzg)
72) Fgig
7:) Joehrhlewhrhj`rbhiz
7>) W)\ r`nk`~khiz
77) Z}kngr
7
8/3/2019 Sol.Paper-4
6/6
VHRD ZOH]XI^ZGX Z^@FG!K X]@FG * ) ^og ah|gagi~ hl @ lrha _ ~h S /_ ~h [% [ ~h S+
`in ~og ah|gagi~ hl B lrha _ ~h N% _ ~h J% J
~h N `z zohvi ki lkfwrg) Jeg`re{% rgpwkrgn
nkz~`ijg SN 1 /[N $ [S+ 1 /_J $ [S+ 1 /7 $
>+ 1 ; daz)
N
J7 da
: da : da
[ > da
S
_
;;) @ee ~og rrhv nk|kngz ~og rgj~`ifeg ki ~vh gpw`e
}`r~z gxjg}~ /N+
0==) @ee eg~~gr rg |hvgez gxjg}~ /J+)