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					    % 5 # 4 2 2 ) ' & #            © © ¥ £ ¡
#$" ! %¨3$"10( %$" ! ¥§¨¦¤¢                   "  ¥ ¡
                                                               $A@#$9786£¤¢                       " C    5 B B
                                                                                                2$ F$" @#¤92$ E CD66B




                                                 !                  "
              "                   "                                                "
              "                                  "                  "                              "
                                                                    "
              "
                                                                    "
              "                   "              "
                                  "
              "                                                                    "               "                "
                                  "


              "                                  "                                     %           "%                   %
                %




                  ×

!         "           −      + # = $(        −   )(    −       )=   $       = %$   =       +

                      ( )=    $       ( )=       &    ( )=          ( )
                      ( )=    &       ( )
#             '              (              & ) **
                                             )                                 *           *      (       +,
              ,                                 .
                                               - )/0

1                 )                                            +        +     =

              -                              %
                                                 −!        ≥
                                                      !
                                                 ≥                  ≥




Page 1 of 7                                                                                    Courtesy : www.gateforum.com
    % 5 # 4 2 2 ) ' & #            © © ¥ £ ¡
#$" ! %¨3$"10( %$" ! ¥§¨¦¤¢                               "  ¥ ¡
                                                                           $A@#$9786£¤¢                             " C    5 B B
                                                                                                                  2$ F$" @#¤92$ E CD66B


                          =           $               =        $       =−


2         "           =       =

              ∴         =             &                   & 3           &

                                      !                                            ω      !
4         "         =             =                   =        ×        $ =           =
                                              −#                                    π   π

              5         &678%                 =           Ω$               =        =             =           ω
                                                                               !        !×


          "             * .           -               9                        (


    !
                  :           :
    #
    1     "
    2     "
    4            7
              + 0; -                      (               .    %


              ∴



              ∴         <         +

              =           -<          <           (        +       )
          "
                                  ∞                       ∞                    ∞
                  ( )         =           ( )=                             =
                                                                                    !
                                                                                         =            =
                                                                                                          !
                                  −                       =                    =              −
                                                                                                  !


                  2               !                   2 +!             #! + #
                              +               =                    =                =!

    !
          "       &        3                  -                                (             (        )       &)                               -
                          (.                                           (          -
                                                                               . *-

    #           )                 )                       >ω<              *ω<∞
                                          +
    1
    2


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    % 5 # 4 2 2 ) ' & #            © © ¥ £ ¡
#$" ! %¨3$"10( %$" ! ¥§¨¦¤¢                                                    "  ¥ ¡
                                                                                                $A@#$9786£¤¢                   " C    5 B B
                                                                                                                             2$ F$" @#¤92$ E CD66B


                       =                   (ω              β       + φ)
               ω =             ×       !
                                            β
                                           % =                             !
                           ω                   ×           !
                       =     =                                     =                   ×       1
                                                                                                       ;
                           β                               !
                                   ,                   ?3              %                   @%              &            3 × *(
                           ,                   *) 3 .                                  ,           (ω      −β   )   - ?3     *(            &

              ∴A <                                 ×           1
                                                                   (;


 4        "


                                                               ×           2
                                                                                           ×       2
                               &               <                                   =                   =   ×    2
                                                                                                                    = λ
                                                                   η
              ∴λ =                 µ


                   &           3                               !%
              8 -* &                               3                           λB                      <
                λ+!                    −
                                                                       =
                   −!              λ−

              - λ<!%2                              <               %!                  <                                    )
                                                                                                                    !

                                                                           −
              - λ<                     %           <                                                   →

                       −
                               =


                   −                                                               #
                           =                                   =
                               #

                                                                                       1
                   +           =           +               =                   =
                                   #           #                   #
 !            8)                       &                       -C                                          )(             *3           !
                                   ∞
                                       −
                                           (   −µ)
                                                   σ                   =
               σ           π   −∞
               =                µ
                               - = %

              B<
                                               *                   ( )     =

                                                       ∞
                                                               −
                           <                                       2               =
                                               π




Page 3 of 7                                                                                                                 Courtesy : www.gateforum.com
    % 5 # 4 2 2 ) ' & #            © © ¥ £ ¡
#$" ! %¨3$"10( %$" ! ¥§¨¦¤¢                                "  ¥ ¡
                                                                            $A@#$9786£¤¢        " C    5 B B
                                                                                              2$ F$" @#¤92$ E CD66B

              ∴                  <B<
                         −                         −
                                 =−                                 *
                                                                   * -

    #


                                                                                    !
                                 !
                                          !                             −               !
    1                    =                                     = $          =




    2               ∠# − ∠ =                                   ∠4 °

    4     " D ? ? ? ×                                      ×            4
                                                                       <D
!
                                                       ×
                     =       $            =                        =        2
!
                     =−                   2
!
                    =        ! +
                    =        ! +
              - A < %)                            <            Ω
              )      <
                    ! = −!
!         "        -
                   -
               σ                     µ   µ
!!        "          =                 =   =
               σ                     µ   µ
                                                                        −
                             ∈                    1×2 2 ×
!         "             =        =                                 −#
                                                                                =       µ"
                                                           ×
                                      #
!#              $    =               #        −


              A<               A        %
                             1% 8 < # (A B0 <
              B < !4(
!1
!2
!4




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    % 5 # 4 2 2 ) ' & #            © © ¥ £ ¡
#$" ! %¨3$"10( %$" ! ¥§¨¦¤¢                                                    "  ¥ ¡
                                                                                                $A@#$9786£¤¢               " C    5 B B
                                                                                                                         2$ F$" @#¤92$ E CD66B


                   %       =           %        =
                           =! $                     >       %           −


                                            !           ×
          "            −           1=                           $
                                                                        +       $       B       (

              B <                  !(

                       =           $
                                            =! µ
                                   +β
                       =            − & ×α ×                        $   =                   4≈ #
                       −           2
                                       −                    =               1

              E
                                       1
              ∴            =                    =       1

    !          (       +       )(          +        )
               4µ              −                = #µ                        −
                                                                                    (       −   )

                   −           =        (       −       +           )
                   −           = −2 +
               4=
                       =
    #                   F<                  :< G                    E
                        F
                       % <                      <               <
                       F<                       <                               =
    1         ?3               *&               &&              *


                                            E               *E                              &       &


    2              4           2           1

                                       G                    G                           )
                                       G                G                               )
                   )                           *             H                          -
    4
                                                            − ω(                    )+          − ω(        ) +
                   (ω ) − (ω )                                              −                           +         − ω


                       − ω
               =                            +           ω
#




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    % 5 # 4 2 2 ) ' & #            © © ¥ £ ¡
#$" ! %¨3$"10( %$" ! ¥§¨¦¤¢                          "  ¥ ¡
                                                                      $A@#$9786£¤¢                  " C    5 B B
                                                                                                  2$ F$" @#¤92$ E CD66B


               ( (ω )
                         =         −       'ω'
                                                 =       (ω ) =       (ω )    (ω )
#         "    (ω )
              ∴ (ω ) = −               'ω '      + π&

                        *          ) π

                   ( )↔                ×
#         "
                   =

              ∴               )                          - &      "
#         "   = (.                -                         (             )   *. @
#!
#
##            8                        ()                             -       (        ;
               ) = ( %(
                #                      ) ( )=@                    -                &
                         →


              <              =

#1
#2            8) .                                   *.                                 I %
#4                     (                    ( *                 60J
1                (
              " )-                 * -& (                              *.
              "K<                 ? 2            < 2
1
                  ( )= ( − )
                  ( )= ( − )

1
1
1!
               !
                                                                          !
                       ( )=                & =
                                                                      !
                                                                              =        <

               !
                   &
                     # # =
                   !
                                                 !                    !
                                                                 &                     & !                   !
               6                           <         #    (# ) = !            # =
                                                                                       ! !
                                                                                           =
                                                                                               ×!×!
                                                                                                      !! =       =2


1              λ=           =

1#             * = * ×*'                             * = 1 #4 −                   !Ω




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    % 5 # 4 2 2 ) ' & #            © © ¥ £ ¡
#$" ! %¨3$"10( %$" ! ¥§¨¦¤¢                      "  ¥ ¡
                                                                  $A@#$9786£¤¢              " C    5 B B
                                                                                          2$ F$" @#¤92$ E CD66B

               *= +
               !
11        "
               * =
                '           &       & =         &

12

14                  =           −           =    #
                                    2

                                                          ×
               , = ,'               −            =                    −       =   21
2         "                                               2               !
               µ = −, ( -                   )=−       !
2                                                          × 7
                                                          + J% ''
                                                          +×       %
                                                                  , 1              ,
                                                      # 6AB       %                + 1
                                                        5
                                                      2J "6
                                                 <        I       ,       +
                                                 <            I       <
          "                                               ! <! ?                  <#
2
          "

2               "                                         - &                 <


                                                      =               =
                                                !
          "
                                    !       + -               +
2!              "       (
                                =       =             =
                        (                   − -               −

          "

                                                - =           =   #

                                                      * −*
                                                - =        =                  #
                                                      * +*
                                                . =
2                       )- )
          "




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Description: These are the previous question paper for GATE student