2014 jee main paper -2 code m

Post on 19-Nov-2015

14 Views

Category:

Documents

0 Downloads

Preview:

Click to see full reader

DESCRIPTION

2014 Jee Main B Arch Paper 2

TRANSCRIPT

  • !"#$

    !" # ! " ! ! #$

    ! %$ "

    !! &''(

    !

    ! ( (

    #$

    ) !''&

    !

    * +, - (

    #$ !"# $ %&'( ) ! "# "*+, ./

    0

    !"# $

    1 0-%2"0-%2)!# #$%$#

    $3 (# $ % $ 0$3( ( # $ %$

    !"#$%& !'$&& () *+ !,-$!%& ! '$& ()# !&()$.()/$&$0$ 1'# !"#$$"& !'##*+ ! &21.345 !&& *+&6$. !%' #()!"!"#$#!"#$!$#(*+$*+),$5#'#71()/$&+1 !8$+ '#7

    !$& () !#*()1(()$'!(91+5'

    * !*$$ ! $: 8;+#

    #()/## !

  • !

    " # $%

    &!!'

    &!'

    &!!'

    ! &!'

    () * *+) + ) ")

    )))

    2 2 2 22 31x x x p=

    1 2 3

    1 1 1 1x x x p

    =

    22 2 22 31

    1 1 1 1

    x x x p=

    ! 3 3 3 32 31

    1 1 1 1

    x x x p=

    !" #$%% & %% %%%! %%%

    ' %( )' *# ##+,-./$01%( 23 &!!'

    &!'

    &!!'

    ! &!'

    456*#45 #27+8'*+ 6#++3 9: '7+* 4,019:663

    2 2 2 22 31x x x p=

    1 2 3

    1 1 1 1x x x p

    =

    22 2 22 31

    1 1 1 1

    x x x p=

    ! 3 3 3 32 31

    1 1 1 1

    x x x p=

  • "'()

    %

    ,'

    #

    !!

    ! &'

    " 2

    5 2 51 5

    f (x)sin xdx C

    cos x sin x cos x=

    !

    "10 1k

    kS

    =

    -..

    ( /

    /

    .

    2 n kS 2 1n kS 2 1n kS !

    2n kS

    ! 0 %' " -!

    &!

    $

    &

    ! &

    ' '-2 ;' %4 +3 0

    ;'3

    ,'

    #

    !!

    ! &'

    '2

    5 2 51 5

    f (x)sin xdx C

    cos x sin x cos x=

    0

    663

    !

    '

  • " 1 ( 2 ()

    !

    # " 2 4

    = = 1 1 3

    yx z

    2 = =

    1 2 4yx z

    $

    #

    #

    !

    $ 12

    1 > 2

    2

    if xxf (x)

    a bx if x

    =

    (

    3 1

    = and = 4 16

    a b

    3 1

    = and = 4 16

    a b

    1 1

    = and = 4 16

    a b

    !

    1 1

    = and = 4 16

    a b

    " 0 ,= %&>%% 2

    2

    xxf (x)

    a bx x

    =

    0#% '0'3

    3 1

    = = 4 16

    a b

    3 1

    = = 4 16

    a b

    1 1

    = = 4 16

    a b

    !

    1 1

    = = 4 16

    a b

  • 2(( ( )2%)

    245 4

    147 4

    45 4

    ! 137 4

    1()% ) $&!! )# )32

    16 9

    , 5 5

    143 1

    , 3 4

    8 77

    , 9 3

    !

    4 3

    , 2 2

    /)) 4 5 ( 6 )) 4 ( 5 52( (( ,! &! !,'! &''

    %6 4@-./0*A&!6B!'6C&!-./D%!7'E3

    245 4

    147 4

    45 4

    ! 137 4

    4F+6, @7%($&!! @7 %(

    6* 4 !7+7*3#- $G

    + # 2 6 0

    7+3

    16 9

    , 5 5

    143 1

    , 3 4

    8 77

    , 9 3

    !

    4 3

    , 2 2

    :3%H7'0,$5,I0 J )'%:3 6 #$05,K%6 4 0, ' 6 %H7' ,01

  • " ) # )3) !' ' % !

    7 '

    1

    0 ,e

    1

    1,e

    !

    "1

    x

    xe

    f (x)e

    =

    (a)

    1( a)

    { (1 )} andf

    f

    I x g x x dx=

    (a)

    2( a)

    { (1 )} f

    f

    I g x x dx=

    2

    2

    1

    II

    12

    !

    '6#*,3#-

    *# !' ' 9: 6, 03

    !

    7' , # BL0%3

    1

    0 ,e

    1

    1,e

    !

    '1

    x

    xe

    f (x)e

    =

    (a)

    1( a)

    { (1 )} f

    f

    I x g x x dx=

    (a)

    2( a)

    { (1 )} f

    f

    I g x x dx=

    0

    ,=G/ 0 21

    II

    3

    12

    !

  • !

    ! ))( )-()8( " 8 ( )- )

    2 2

    a cos cot

    2 2

    a sin tan

    2 2

    a cos tan

    ! 2 2

    a sin cot

    " 13

    < < 4

    21

    2 = K cot cotsin

    9%

    '

    ! 1 2

    ! .M'%%( '7 61;%7$*I6*C, #?' 68 2# ', %8%( '72# 0*I& N=473

    2 2

    a cos cot

    2 2

    a sin tan

    2 2

    a cos tan

    ! 2 2

    a sin cot

    " 3 < < 4

    21

    2 = K cot cotsin

    0

    9663

    '

    ! 1 2

    http://www.iitscholars.com

  • "

    # : , a , b c

    )

    d))

    " ( ) ( ) 1 1 1 6 3 3

    a b c d i j k

    ( a b

    '

    c

    2 2

    3i j k

    2 2

    3i j k

    2

    3i j k

    !

    2 2

    3i j k

    $ 1.( (..; .

  • #

    1 ;

  • $

    ( )(( )'=)=))")(( (%

    2 5 )%

    2 3

    1 2

    13

    ! 1 4

    "

    48 47 46 2 1

    2 3 3 4 4 5 48 49 49 50. . . . .

    51 1 1 1K 1

    2 2 3 50

    9%

    12

    !

    #& J0 , 4( # ')'=)=061:,0,6 64(#,'1:! '

  • " ( ))>?

    !

    ! / ' )()

    !

    " ")( )

    (1 )(1 )

    z zz z

    22 cos 2

    1 cos 2

    1 sin 2

    ! 22 sin 2

    ' 0 , =%%

  • # 1( ))

    %%&'%

    %%&'%

    /

    8

    8

    ! /

    $ " 80 11 01

    a b

    c a

    b c

    =

    80

    3 3

    2

    94

    54

    !

    # 7;'

    OJ

    G%&

    #G'G'

    G'

    #G'

    ! G'#G'

    $ 80 0 ' 11 01

    a b

    c a

    b c

    = 0

    803

    3 3

    2

    94

    54

    !

  • ! !" # #" $%

    $ !

    &'# !"'#"

    !

    !

    !

    ( # " )! ! * +! )" ! !" #

    #$% %&&'()*'

    &'# !"'#"

    !

  • &'# !"'#"

    !

    ! !" #" #! # %

    +%#!,-*!

    &'#" !"'#"

    !

    ! !"# " )" $, # # !#%

    $,&+.!&'# !"'#"

    !

    !

    "

    !

  • '!# !## *)!"! #

    #$%%+/0-*'

    &'#

    #

    ' !

    $

    & ! # ! @

    # ! !

    ! # !

  • &'#

    # & ! !

    # & ! !

    -!

    "!!" # ! ! #! !! ." !%

    )*12'.)%*'

    &'# !"'#"

    !

    !

  • !

    ( # " )" * /

    0! ! ! " ! )! ! !" #

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

    &'# !"'#"

    !

    !

    "

    !

  • "

    '! ## ! #)!"1

    )#3*"'

    #

    !

    $

    !

    !

    !

    ( $,# " )"!*+! )" ! !" #

    $,*#$%&'(.)*'

    &'# !"'#"

    !

  • #

    &'# !"'#"

    !

    !

    ( # " )" ! * +! )! ! !" #

    0! ! ! "

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

    &'# !"'#"

    !

    !

    !

  • $

    2"!!#!# ! # " # %

    )+*.!

    &'#

    "

    , $ ! '

    #

    ' ! $

    ( $, # " )" ! * +! ! )" ! !" #

    0! ! ! "

    $,*#$%*&'&%*. %&)*'

    &'# !"'#"

    $

    !

    !

  • &'# !"'#"

    !

    !

    2"! !# ! ! #)! "%

    )45%-%+/!

    &'#

    ! !

    $ ! '

    http://www.iitscholars.com

  • A ( ( (B 8 - )! *

    ! A ( C.B 8 .

    2(

    2 ) - -

    ! 2 3

    " 6)/-(( / D D -(! E

    # A

    B EF 3D EE30 0F 31-! 2) 3/

    !$ A B 6( 2 D! G

    #!#!2 !!" &5 !6 6! ! !

    ! 6C #H!+ +1(+18J'!'," J'5'71(+

    55'7 P,+

    %6*

    ! 6:'+

    " / 6'3 +,= ,! #6! '

    # 38' *"

    !#5*Q, !#Q4>7 C#5*QP*! + 22)Q+

    !$ Q0;%% 77"

    C 7 BC! =4

  • ! 8-

    /)

    1

    ! G

    ! AB

    2 -

    ))

    ! 1

    ! A ( B

    G

    6

    8

    ! 1

    ! A B

    >5>

    HE

    46E

    ! EC0

    ! A B

    I 3'F/

    /63GG8

    A3AE

    ! I )34))>

    ! 6@=" ! ! ,%

    ! )'5J'" ,* #5

    ! #! !!7!7*=

    ! % 6 0 I7# 5# '," !B R+ 6SB! *DBBE

    ! 3% "

    ,% P, T/T! / P,U?BVJB

    ! I38' *"

    !CQ'CN!BV B /Q!SC!B6, %+!BQ)BN! WQ '

  • ! 12)F(( 4 D D! 8

    !! A B

    :)31-

    /( 34

    J 3G

    ! D) 30

    !" G) (

    G

    "

    "

    ! "

    !# A

    B

    2 3*I%-

    F 30

    *C 3:J

    ! /-0) 3I%-

    "$ A %- B

    2((

    >00

    1((-(

    ! /(

    3'3

    ! S B?6'" '5' ,'! 6'

    !! IQ8' *"

    1'QX ?6Q!% %2 Q@B! ,'Q

    !" %G',J'3 #9:! #I&*47 ''7%2#5! '4

    !# I8' *"

    Q! '&5 %Q#2Q,%'%7 #P, Q'5T% T2! $% 'B CQ&5

    "$ I=43&5%$"

    C /6 #T T T/=4 &% FB % ! B /6

    3'3

    http://www.iitscholars.com

top related