EE 2012 Solved

8/20/2019 EE 2012 Solved

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© All rights reserved by Gateforum Educational Services Pvt. Ltd. No part of this booklet may be reproduced or utilized in any form without thewritten permission.

!

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% " " " # ( ) ( ) & '= ω − φ

( ) ( )% % & = ω − φ φ (

%

−φ %

φ ( )% ) %π − φ ( )% ) %π + φ

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1

2

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=

1

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−

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8 / 1

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π$";' %

4 % /"#$

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< <

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< <

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<

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+ 1

1 %

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1 %

2,# @ 1

%

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> < >

< <

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A & ( ) ( ) B'9'? %'1'4'8 '=

B9'B9 B9'B9?'B9?

B9?'B9?'B9 B9?'B9?'B9?'B9?

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+ C + C= +

0 " ( ) ( ) ( )( ) ( ) ( )

% . %D

1 4

+ +=

+ + + + ( ) ω

$ @

) ω = % ) ω =

1 ) ω = 4 ) ω =

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%

% % %

. 4D /= .= -1)

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/

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+

−

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( ) ( ) ( )

%

7

7 8/&2 8/

& &

7 7 /; // & .. =

$//// //& // // //& ////

// &%//// //& &%//// %//

&7 // & .. // & //

%//

= = = Ω

= − = + +

= + × = +

− = = − = −

− = + + = +

8/&

=

/ & " "'

%

:+

:

−+

:+

/

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<

& /

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E% E %

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:Ω

/

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Ω

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%

& &

@ @ @ @ @

% % @ @ 1

= −

π π + +

%

%

@ @-$1

@ C & @ /@ 1

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@

= −

= =+

∴ = = − =+

% " B 9

FE' G +FB' 9G )%

1)4 .)> )4 %)1

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%

= =

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% % % % %

1 1 .+

% % 4 4 >− −

≤ = = ≤ ≤ ≤ ≤ =

= = × =

1 I " ' +

( ) ( ) ( ) ( ) ( ) ( ) ( ) 1 1 1 8 * * 1 & & 1 & 8 = ω + ω = ω − φ + ω − φ + ω

" !

* & % φ

1 1 8

* & * & * &

%φ + φ +

1 1 1

* & * &

%φ + φ

1

* & * &

%φ + φ

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1 1 15

* * & %

= φ + φ

4 & + = − ' ++

)%−π )%π +

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*+#$ ( )

+ D' +- $= + −

= − =

( ) ( )

%

)% )%

! ;" % %

πθ

π −π

π π= θ + θ = + =

∴ = =

8 %/

8/ %/ / /8

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> $ $ 2$< &

α

"

%

α −

π

%

α

π

α

π

"#$

A ( "#

@& :8'& :/8' & := = − = −

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*+#$ %λ = λ

%

<

<

%

<

% < % %

/'/// = %8//

/'///4 %8//

5 5 5

5

/'/// %8// 5 %8// %8// 8

5 // %/6!

8

/8 /85 /8 // %6!

8 %8 %8

5 5 5 5 4/ %/ 5 % 5 %%6!

λ = λ =

= =∂ − −

−∂

− = =

= × =

= = = × =

= + − = + − =

.

& '

, "

8/20/2019 EE 2012 Solved

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%/ 9 %$ " %$

%$ " '

4 > 0 /

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/ / /

L C C = + =

% $ " /A

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>%

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%

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?

+

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2 - /=

∴

/

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/

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/

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C

( ) ( ) / /

C

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%1 " ( )4 :1− Ω

( )8 // // π +

44% ! 8/ ! >%8 ! %8 !

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% %

<

5 & 2 8 4 8/!

% %= = × × =

%4 %%/ 7' 8 ;!' /// " /%8 Ω '

>0 %%

+ ( >// " " 8%0 0

00O 00O

1>1>O 1>1>O

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8/20/2019 EE 2012 Solved

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*+#$ %

% %

*3

3 *

φ= ×

φ

%2 /%8 = & > %% >80=& 8%0 0 8= = − = = − =

%

/// %%/ >80 /%8

>// %%/ 8 /%8

φ− × = × − × φ

%

/>1>4φ

=φ

O - % %

// // φ − φ φ

× = − × φ φ

1>1>O =

%A & "' " // ;@ "

8/O D ∆ > ;$$; &/ 8 ' ;

>>

8/

80

4%

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5; - & 8 80% %

∆+ = + =

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8

86! ) 67−

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818 >/% A/0 A.>

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+

8 5

8

×= =

5 /8=

, , + , +5 5 0/ 1/ = 0/ 0/ 8/= δ = δ = − =

( ) / %0/ +− δ = δ π − +

, /8 8/ A.>1

− π = π − + =

P

* 8

+

=

=

= µ

/8

8/20/2019 EE 2012 Solved

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2< 1& 7 = θ

1> /48& %%4

8

×= =

5 7& 1> %%4 /48= θ = × × A8/ !≅

% % %%

= =

%. I " "' %

+ "

% &%

7 '= 72 ( )D%K

%

/% /%>0 /1% /4

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D %

8/20/2019 EE 2012 Solved

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( )

1

%

8/20/2019 EE 2012 Solved

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"#$

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/ / /

/ / /

11

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*

*

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//; TT%;%> %> = @ %>; = 4%

& %>@ C//; %%

@ C @ TT %% = 4% 4% @ C 2 %% /;

/

+ − − = = µ = β = =

∴ = = Ω = β = Ω ∴ = =

= = Ω = = + + +

≈

K /= K =

/=

/=

= =

/;

//;

−

//; %;

7

8/20/2019 EE 2012 Solved

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14 &

7 7 >7' 7 7− = −

E87 %7 17 >7

"#$

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7 7 >& 1= ";

% % 7 7 & - 1

−= = =

−

7 % 1 7 8 7 = 7 7 87= + + = + − = −

18 + ( ) 1 % + + .+ %4+ 8= − + + F' >G

% %8 4 4>

"#$

*B5#$ ( ) 1 %D' + + .+ %4+ 8= − + +

( )( ) ( ) ( )

( )

%

1 %

C + / 1+ 0+ %4 / +-%'4

U + >+ 0= U % % 0 /= U 4 %4 0 /

+ + +-%

+ % . % %4 % 8 %8

" + '

= − + = = − = − < = − >

∴ − × + × + =

( ) 1 % > > > . > %4 > 8 4 ∴ = − × + × + =

1> D 18 1 /

& ' % / /

− − = =

8 %&+ . 1/&+ A 8&+ A %&+

"#$

−

+/7

2%Ω2

2

2

+ −

87 7 7

2

2

Ω

%

2

7

7

7 7

Ω

%

7

Ω+−

7

%7

1

≡

8/20/2019 EE 2012 Solved

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*+#$ $8 $1

D# - =% /

( ) ( )

( ) ( )

%

% 1 % %

1

1

8 1 ( $& / /

% /8 > / 8 > /

8 > 8 > 8 8 > > 8 >

%8 > 1/ . 1/* + ( . 1/&

− − λ −λ = =

− λ − − λ −λ + = λ + λ + =

λ = − λ − λ = − λ − λ = − − λ − − λ λ = − λ −

λ = λ − λ + = λ +∴ = +

1A / ;7' 8/ @ " ;7 " " /8

88 !' ('

" %

; " & % ;7 8/ @

' "' '

/A ' AA0 ! /A ' 88> !

' / ! ' %%/ !

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% = 5 % = 5 % 88 88!∝ = = × =

( )1

%

%

% % % %

% %

88 & % & % % /88

///88

& //88=///

6@ ' & & & /8 //88 /4.>.

2 /// %///3" 2 = %% % 3 % 3

φ

= × = =

= =

= − = − =

= φ = φ = = φπ π

φ =

( )

%

%

%

%%

& 3 & 3 %& 3= %

2 2 22

& %& %& % /4.>. /A/%2

φ φ φ

φ φ φ

= = φ = φ =

∴ = = = × =

10 ; 1$' 8 ;!' 4$' %1/ 7' 8/

@ 8/ 3 @

' + ; " " %1> 7' 8A @

808 48/ 48A 88>

"#$

*+#$ % % % %%% %

% % % %% %

* * * *& -

@ B ∝ = × =

8/20/2019 EE 2012 Solved

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1. + ! %/; 'Ω 44/ 7 $" 0/;Ω 18% 7 I

4/;Ω '

1A 7 101 7 1.4 7 4/> 7

"#$

*+#$

8/20/2019 EE 2012 Solved

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*+#$ ( ) ( ) ( ND /=

( )( ) ( )1 %

1 %

; /= ; % ; /

%

++ = + + + + + =

+ + +

( ) ( )

1

%

/

; %

; ; % ;

+

++ − +

( )

( )

% % %

% %

; /= -: = = %

; /= ; = 4-;N= I ' ;-%' -/A8

+ + = ω = −ω ω =

− ω + + = ω = +

4% I ( ) ( ) ( ) ( ) : % % )ω = ω ω ω

/

)4 )% %

"#$

*+#$

41

8/20/2019 EE 2012 Solved

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%

%

%

1

/ /

K / / = & ; K 1 +' K

/ /

/

/ K /

/

= = =

≠

≠ ≠

=

44 ' 2 "+ "

/0 Ω 4 Ω % Ω %0 Ω

"#$

*+#$ ( )

%

A > /2 4% A/25" - 7&-

2N% 2 % 2 %

+ + = + +

( ) ( ) ( ) ( )

( )

%

4

/ 1 A A2 > /2& = 7-1N&2-1N

% 2 % 2 %N2 % 2

2 % A/ 4% A/2 % 2 %5/

2 2 %

− + = = = + + +

+ − + += =

+

( ) ( ) ( ) ( ) ( )%

A/ 2 % 4% A/2 % 2 % = 8 2N% % 1 8282 / > /2= 4-82= 2-/0

+ = + + = ++ = + Ω

48 (

( ) ( )( ) ( ) ( )

%

% / /

% " % /

−= =+ + = δ = − =

/

+=

E% E /

+

−17/7

+

−

%Ω 2

:− Ω

/7

+

−

%

+

−

7

2

+

−

17

&

≡

8/20/2019 EE 2012 Solved

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"#$

*+#$ ( ) ( )

( ) ( )%

%

%

+ + = δ

( ) ( ) ( ) ( ) ( ) ( )

( )

( )( )

%

%

%

'

/ C / % /

% % 4

1 %

%

−

− − + − + =

+ + + + =

− −=

+ +

I

( ) ( )

( )

( )

/

%

%

%

+

− −

− − −

=

= − −

= + −

= − =

4> " ' " % % % % ; " + @= = + + ; "

/∇ =

E% % /

"#$

*+#$ ( )% %

! ;" '

∂∇ =

∂

( )%

%

3"'

∂

∇ = ∂

( ) ( )

( )

( )

%

% %

;; %

; %

I' /' % / %

+

+

∂= = +

∂

= +

∴ ∇ = + = = −

4A ( '

)1 )% %)1 1)4

"#$ *+#$ ( ) ( ) ( ) ( )5 5 5 5 = + + +

1 8 % 4

%

% % % % % %

4 %

% 4 4 % % 1 1

4

= + + + = + + +

= + + + = = × = −

8/20/2019 EE 2012 Solved

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!" #"$% &

! /7 "$ ";" "' " " #

Ω " 1

%8 Ω " %

40 I ";' " >7 ' Ω " A)1 & 0 7 '

>7 A7 07 .7

"#$

4. ! /7 ' " AΩ

1)A 8)A .)A

"#$

!" #"$% &

& 1$ "'

0/ $ "

8/

/> 7 44 7 %%% 7 %0%0 7

"#$

*+#$ <

%26 - 7 7

1=

<

7 % %26 - 7 1// 44%7

1 11= = × =

8/20/2019 EE 2012 Solved

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8 &

7 1//7'= " 1$

8 ;! %/ ;! %8 ;! 1/ ;!

"#$

*+#$ ( )

%%

7 44%5 1 1 1///!

2 %/= ⋅ = × =

'$( ) #"$% "

*""" + '$( ) #"$% &

& "' %

7 %%/7'7 %%7'= =

17 1>7=

8% "

/48 /8/ /88 />/

"#$

*+#$ % % % % % %

% 1

%

%%/ %% 1> /48

% % %% 1>

− − − −θ = = =

× ×

81 &<

2 8 '= Ω + "

A// ! A8/ ! 0// ! 08/ !

"#$

*+#$ <2 8

= /48- @ @ @

θ = =

% %1< <

7 1>& %%4= 5 & 2 %%4 8 A8/!

@ = = = = = × =

*""" + '$( ) #"$% &

( )

D

+=

+

84 ( )D

' %= = 1' %= = 1' = − = − 1' = =

8/20/2019 EE 2012 Solved

22/25


"#$

*+#$

− −ω ωφ = −β

φ +

− −ω ω

> β

<

" @

2 $

,

88 +

% ) 1 ) > ) ) 1 )

"#$ *+#$ ( )I ' W ' 25

+ = -' -%' % )∴ ω = =

8> ! " " "X

'"$"#(

* I

6"#$

8A "

" #

,+ " "$( -($ "( " -$ (. ///////// " "" #" " 0-

; ;

; " ;

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80 , ' ' ' " *22,2! " ,11X

, 2#"( "" " #-( 0 3$4 " ($4$3 "" "( $"( +"

(

"

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8/20/2019 EE 2012 Solved

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8. " " " #

5$4 " $# + " $"#"$ "" ( " +. $ // $6$4

:

"#$

>/ & ( ) ( ) ( )%8. %/>% 11%

// 18% // A08' //= = =

%%1 4%1 1A %A>4

"#$

*+#$ // - +

%8. %/>%

11% %8. %/>%

+ 18% + A08

+ + + 18% +A08 %A>4

= =

= = =

> " @

"3 )#" 718

I 4///

%//

2 %///

8//

, + 0//

+

/O 4O 0O 0>O

"#$

*+#$ - /'8//

*+ - .///

'9000

86%10500

=

>% 2: 4 ; 2%/ 2

/ 2%1/ 2 / 2:

8 > . /

8/20/2019 EE 2012 Solved

24/25


"#$

*+#$

8/20/2019 EE 2012 Solved

25/25

© All rights reserved by Gateforum Educational Services Pvt Ltd No part of this booklet may be reproduced or utilized in any form without the

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Documents

EE 2012 Solved