GATE 2012 solved paper

Embed Size (px)

Citation preview

  • 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.

    + + =+ = −

    + =

     

    ! "

    # $ %

    &' !

    ()&' * *

    − → −

     

    ( ) ( )+ + ,!

    -

    = = 

    . /

    0

    − =  

    1 2 ! −=  

    = +   # = +  

    &' #

    ()&' 3 % )

    ( ) ( )

    0 4 4

    ) #/ 4 4

    0 0 0

    − = = =

    = + = +

    = + =

     

    5 ( )   , 4− τ=   )) 66 τ  

      !

    −τ

     

    τ  # +  

    &' !

    ()&' ( )

    ,   4 ! 7 )/ 8 8

    − τ= = + + + +  

    ,

    ,

    9

    / )

    − τ

    − 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

    &'

    ()&'

    :

    : );   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.

    : . ) ) / ) / % ) /

    ) / % ) / "

    . / CC / / %

    %/ $"( >

    () D*((* )

    ! () (EF3 )

    () 3(-- )

    # () G(*$

    &'

    B 5 % /

    ) H ) ) ;>

    H ) ;

    ! H ; H ;

    # H ) ;

    &' #

    = )) 3 .

    )) / % / ) ) ))

    # ! # 9

    . # . 9

    &' !

    ()&' 5 /

    0

    0E

    I3 : E3#

    # # #

    , µ µπ ∆ρ = = =

    π 

    I E 0EI

    ))   # #

    0

    = = = π π

     

    ( )0

    )

    #   ∆ α  

    0   0

    # )#) ) )

    # # 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 ∝  

    &' 

    ()&' 5 % )/ + δ % <

    :

    %)  

    . + ) % * ( )0>   / ) / )

    , ! ,0 0 #

    &' #

    ()&' 5 +/

    ; / ( ) ( )  ( )

    ( )

  • 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  

      ) /

     

    ) )

      ) )

    − = −

     

    ( ) ( )

    0 0

    0 0

     

    π ×   =     =

    π ρ π ρ

      =     = = =     =

     

    9 . " " )) % * * :" *∝   / % % ))/

    % )) #

    :#−   ! #−   # # :#

    &' !

    ()&'

    ::   # I #" *

    H

    ρα     α

    µ  

    : : :: :

    :

    # I # I # H

    H

    −ρ   α     α ρµ

     

    5 % %/ #−∴ α  

    A . K'' / ' )

    ' %)' % ' )/

    -) %) ! 3 )

    - %) # -

    &' ! 

    ()&' 

    ∴  )

     

     

    ( )<  

    ( )0  

    ( )  ( )  

    ( )  

    5  

    ( )

    ( )

    ( )

    ( )

    ( )

    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 *

    &' !

    B '   )

    $

    ! $

    $

    # /

    &' #

    ()&' 5   /

    +

    − =  

    ( ) ( )

    $

      + + +

    + +−

      − =     =     − = −  

    5 / 1 , $

    =  

    ( ) ( )

    + H

    −− + − + +   − = +     − = +

     

    ( )( )

    <

    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

    &'

    ) / / ) D$ %

    D C C D$ C

    ! 3 C D$ C C

    D$ C C C C

    # 3 C CD$ C

    &'

    ) ) -*/ ) ) ;-/ )

    3 =D- ) J =D- )

    -*43 =D-4 J=D-4 ;- ! ;-4 -*4 3=D-4 J=D-

    -*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

     © 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.

  • 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

     © 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%/ J

  • 8/19/2019 GATE 2012 solved paper

    11/20

     © 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 5

    0*

    π= = = =

    π 

    ( )0 0

    / 5 = σ −  

    5

    0∴ =  

    0 J =

    ( )

  • 8/19/2019 GATE 2012 solved paper

    12/20

     © 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.

    !

    ! !

    ; ;

    H ; H ; H ;∝

    + + +  !

    ( ) !

    ! !

    ; ;

    H ; H ; H ;∝

    + + + 

    ( )

    !

    <

    ! !

    ; ;

    H ; H ; H ;∝

    + + +  # !

    ; ;

    ;∝  

    &' !

    A )

  • 8/19/2019 GATE 2012 solved paper

    13/20

     © 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.

    " 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

     © 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.

    ) ) ) % 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

     © 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: % ! +,

    0

  • 8/19/2019 GATE 2012 solved paper

    17/20

     © 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.

  • 8/19/2019 GATE 2012 solved paper

    18/20

     © 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.

  • 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 # ;=

    &

    9

    ;& A A

    E& A A %

    *& #

    -& # % %

    ;/ E ! E/ * ;/ * # */ -

    &

    ()&' ; *

    ( ) V/ / / 0W +

    # / D / 5H / M; / $I

    +   +   0+