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8/19/2019 GATE 2012 solved paper
1/20
© All rights reserved by Gateforum Educational Services Pvt. Ltd. No part of this booklet may be reproduced or utilized in any form without the
written permission.
+ + =+ = −
+ =
! "
# $ %
&' !
()&' * *
−
− → −
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− τ= = + + + +
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9
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− τ
= − + − +
8/19/2019 GATE 2012 solved paper
2/20
© All rights reserved by Gateforum Educational Services Pvt. Ltd. No part of this booklet may be reproduced or utilized in any form without the
written permission.
0 ) 9 .
) / )
9 ! 9 9 # 9
&'
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:
: ); 8
; 9988 988
= =
8/19/2019 GATE 2012 solved paper
3/20
© All rights reserved by Gateforum Educational Services Pvt. Ltd. No part of this booklet may be reproduced or utilized in any form without the
written permission.
: . ) ) / ) / % ) /
) / % ) / "
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# )#) ) )
# # 9 ∆ ∴ ∆ = ∆ = ∆ =
%
; ! I * # $
&'
8/19/2019 GATE 2012 solved paper
4/20
© All rights reserved by Gateforum Educational Services Pvt. Ltd. No part of this booklet may be reproduced or utilized in any form without the
written permission.
5 ' ) ) *
/ + ( )δ %
)
,0δ ∝ ! ,δ ∝ ,δ ∝ # δ ∝
&'
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( )
8/19/2019 GATE 2012 solved paper
5/20
© All rights reserved by Gateforum Educational Services Pvt. Ltd. No part of this booklet may be reproduced or utilized in any form without the
written permission.
()&' = +/
;
)
∞
−= −
−
J ( ) 0 & %
= π = ρ = ρ π
) /
) )
) )
− = −
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3 )
-
K %)
I)
0 - %)
< -) %)
=
=
=
=
=
8/19/2019 GATE 2012 solved paper
6/20
© All rights reserved by Gateforum Educational Services Pvt. Ltd. No part of this booklet may be reproduced or utilized in any form without the
written permission.
: 5 / ) ) ' >
; %
E %
* ' '
- ' '
; L E ! ; L * ; L - # E L *
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B ' )
$
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−− + − + + − = + − = +
( )( )
<
H
− −− =
−
( )( )
<
+
− −−=
−
& + + ! → →
! ' % + + : +M,/ )% ? !/ )
-* ) ! ;5* )
-* ) # ;5* )
&' !
8/19/2019 GATE 2012 solved paper
7/20
© All rights reserved by Gateforum Educational Services Pvt. Ltd. No part of this booklet may be reproduced or utilized in any form without the
written permission.
()&' 5 % /
! !
H H
= −
H H ! → →
: :0 :0
!H H
× ×− −× ×= −
∴ J )
!
. ) %
; ")
! ;
D
# 3
&'
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D C C D$ C
! 3 C D$ C C
D$ C C C C
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-*4 J=D-4 3=D-4 ;- # ;-4 J=D-4 3=D-4 -*
&'
0 N )) 1 /
8/19/2019 GATE 2012 solved paper
8/20
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written permission.
8/19/2019 GATE 2012 solved paper
9/20
© All rights reserved by Gateforum Educational Services Pvt. Ltd. No part of this booklet may be reproduced or utilized in any form without the
written permission.
: "'*)
( ) = − π ≤ ≤
.
8/19/2019 GATE 2012 solved paper
10/20
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written permission.
&' #
()&' D%/ J
8/19/2019 GATE 2012 solved paper
11/20
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written permission.
&'
()&'( )( )
* 5 5
0*
π= = = =
π
( )0 0
/ 5 = σ −
5
0∴ =
0 J =
( )
8/19/2019 GATE 2012 solved paper
12/20
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written permission.
!
! !
; ;
H ; H ; H ;∝
+ + + !
( ) !
! !
; ;
H ; H ; H ;∝
+ + +
( )
!
<
! !
; ;
H ; H ; H ;∝
+ + + # !
; ;
;∝
&' !
A )
8/19/2019 GATE 2012 solved paper
13/20
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written permission.
" R 1( )
( ) ( )
>
∴ =
0 % ')
! +
'/ ' )
) ? %/ % ) G
! #
&' !
0 + ))
H
)
τ +
τ +
*+
−
+
+
.
F
G
G
G
G
*
( )
( )
9
B H
B 9 H
B
+
× − +
8/19/2019 GATE 2012 solved paper
14/20
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written permission.
) ) ) % H )%
) ) F1/ ) : τ = τ =
0 !
8/19/2019 GATE 2012 solved paper
15/20
© All rights reserved by Gateforum Educational Services Pvt. Ltd. No part of this booklet may be reproduced or utilized in any form without the
written permission.
&' !
()&'( )
( )
( )
( )
9
) < <*
<
+ × × += =
+ − + −
( ) ( ) :A
8/19/2019 GATE 2012 solved paper
16/20
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written permission.
0: % ! +,
0
8/19/2019 GATE 2012 solved paper
17/20
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written permission.
8/19/2019 GATE 2012 solved paper
18/20
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written permission.
8/19/2019 GATE 2012 solved paper
19/20
© All rights reserved by Gateforum Educational Services Pvt. Ltd. No part of this booklet may be reproduced or utilized in any form without the
written permission.
9 #33 &
% + % J)
! 7 ) !
+ 5 3+ )/
# 7 ) %
& #
9 ) + )) S T
S )) 9@ T )) 0@ + +
R ) $ S7 + / B9@ $ T7 + / A@
) + / /
T :: ! 0 99A # A
& !
()&'
-)) 9@ 0@
* B9@ A@
$%
8/19/2019 GATE 2012 solved paper
20/20
© All rights reserved by Gateforum Educational Services Pvt. Ltd. No part of this booklet may be reproduced or utilized in any form without the
written permission.
D'
! S)
" + ) %
# " '
&
()&'D % !
90 D% / # D 5H M;/
$I ! $= ;I # ;=
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9
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