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  • CCE PF CCE PR

    PF+PR-7021 [ Turn over

    560 003

    KARNATAKA SECONDARY EDUCATION EXAMINATION BOARD, MALLESWARAM, BANGALORE 560 003

    2016

    S. S. L. C. EXAMINATION, MARCH/APRIL, 2016

    MODEL ANSWERS

    : 04. 04. 2016 ] : 81-K

    Date : 04. 04. 2016 ] CODE NO. : 81-K

    Subject : MATHEMATICS

    ( / New Syllabus )

    ( + / Private Fresh + Private Repeater )

    / Kannada Version

    [ : 100

    [ Max. Marks : 100

    I. 1. C 12 1

    2. A 5 1

    3. C 07 1

    4. D 3 1

    5. B 5 1

    6. D 3 1

    7. B 3

    5

    1

    8. A 12 1

  • 81-K 2 CCE PF+PR

    PF+PR-7021

    3

    II.

    9. Al = U A

    A l = { 1, 2, 3, 4, 5 } { 2, 4, 5 }

    A l = { 1, 3 } 1

    10. ( a, b ) = .H.C.F),( ba

    ba

    = 6

    1812

    = 36 1

    11. f ( x ) = 22x + 3x + 2

    f ( 2 ) = 2 ( 2 ) 2 + 3 ( 2 ) + 2

    = 8 + 6 + 2

    = 16 1

    12. d = 10 d = 4

    R = 2

    10 = 5 r =

    2

    4 = 2

    d = R + r

    d = 5 + 2 = 7 1

    13.

    1

    14. = 2 r ( r + h ) 1

    III. 15.

    n = 8 = 2

    Cn n

    = 2

    8C 8

    = 2

    8

    2

    1P 8

    = 82

    78

    = 2

    56 8.

    = 28 8.

    = 20 2

  • CCE PF+PR 3 81-K

    PF+PR-7021 [ Turn over

    4

    10

    1

    n = 8

    = nCn 2

    = 2

    )3( nn

    = 2

    )38(8

    = 2

    58

    = 20. 2

    16. 2 + 5

    2 + 5 = q

    p p, q z, q 0

    2 q

    p = 5

    52

    q

    pq

    5

    q

    pq 2

    5

    2 + 5

    2 + 5 2

    17. n ( S ) = 500

    n ( A ) = 50

    P ( A ) = )(

    )(

    Sn

    An

    P ( A ) = 500

    50

    = 10

    1

    500

    50

    2

  • 81-K 4 CCE PF+PR

    PF+PR-7021

    3

    2

    18. 3

    2 3 = 6

    6

    6

    2

    1

    33

    = 3 6/3 = =

    6/26

    6

    3

    1

    22 =

    36 427

    = 6 108 2

    19. 23

    23

    23

    23

    49

    4669

    23

    2623

    1

    625

    2

    23

    23

    23

    23

    22

    2

    )2()3(

    )23(

    23

    2623

    5 + 62 . 2

  • CCE PF+PR 5 81-K

    PF+PR-7021 [ Turn over

    20. 83

    6541

    2

    23

    xx

    xxxx

    x 3 + 1x 2

    () ()

    + 3x 2 5x + 6

    + 3x 2 + 3x

    () ()

    8x + 6

    8x 8

    (+) (+)

    14

    q ( x ) = x 2 + 3x 8

    R ( x ) = 14. 2

    1 1 4 5 6

    0 1 3 8

    1 3 8 14

    R ( x ) = 14

    q ( x ) = x2 + 3x 8 2

    1

  • 81-K 6 CCE PF+PR

    PF+PR-7021

    1

    12232

    2

    2342

    x

    xxxxxx

    x 4 + 2x 3 3x2

    () () (+)

    x 2 + x 1

    x 2 + 2x 3

    () () (+)

    x + 2

    r ( x ) = x + 2 { r ( x ) } = x 2

    ( x 2 ) P ( x )

    g ( x ) 2

    21. ABC DE || AB

    CB

    CE

    CA

    CD

    1812

    5 CE

    12 CE = 5 18

    CE = 2

    15

    12

    185

    CE = 75 2

    22. 1tan3

    tan = 3

    1

    tan 30 = 3

    1 = 30

    sin 3 = sin 3 ( 30 )

    sin 3 = sin 90 = 1. 2

  • CCE PF+PR 7 81-K

    PF+PR-7021 [ Turn over

    23. )3,2(),( 11 yx )7,4(),( 22 yx

    =

    2,

    2

    2121yyxx

    =

    2

    73,

    2

    42

    =

    2

    10,

    2

    6

    = ( 3, 5 ). 2

    24. r = 7 l = 10

    = rl

    = 1077

    22 +

    = 220 2

    = hr2

    = 10777

    22

    = 22 70

    = 1540 2

    25. 2x 4x + 2 = 0

    a = 1, b = 4, c = 2

    x = a

    acbb

    2

    42

    x = )1(2

    )2()1(4)4()4( 2

    x = 2

    8164

    x = 2

    84

    x = 2

    224

    = 2

    )22(2

    x = 22 . 2

  • 81-K 8 CCE PF+PR

    PF+PR-7021

    26.

    OP

    P 2

    27. 20 = 1

    40 = 2

    80 = 4

    120 = 6

    160 = 8

    60 = 3

    2

    1

  • CCE PF+PR 9 81-K

    PF+PR-7021 [ Turn over

    4 2 2

    28. n ( M ) = 12, n ( D ) = 15, n ( M D ) = 7

    n ( M D ) = ?

    n ( M ) + n ( D ) = n ( M D ) + n ( M D )

    n (M D ) = n ( M ) + n ( D ) n (M D )

    = 12 + 15 7

    = 27 7

    n (M D ) = 20

    = 20 2

    29. =

    313

    2r = hr 2

    2

    3

    2 12 12 12 = 6 6 h

    32 = h

    h = 32

    = 32 2

    30. 4 + 7 + 10 + ......

    a = 4, d = 7 4

    = 3 20

    S = ?

    2

    nS

    n [ 2a + ( n 1 ) d ]

    ]3)120(42[2

    2020

    S

    = 10 [ 8 + 57 ]

    = 10 65

    20S = 650

    20 = 650 2

  • 81-K 10 CCE PF+PR

    PF+PR-7021

    31. A ( B C ) = { 1, 2, 3, 4 } { 5 } 1

    = { 1, 2, 3, 4, 5 } 1 2

    32. 6

    1,

    4

    1,

    2

    1 ..... H.P.

    2, 4, 6 ..... AP.

    a = 2, d = 4 2 = 2 10

    T = ?

    nT = a + ( n 1 ) d

    10T = 2 + ( 10 1 ) 2

    = 2 + 18

    10T = 20

    10

    T = 20

    1

    2

    a = 2, d = 2, 10T = ?

    dnaTn )1(

    1

    2)110(21

    10 T

    = 182

    1

    = 20

    1.

    2

    33. 1 + toup...9

    1

    3

    1

    a = 1, 3

    1r

    S = ?

    r

    aS

    1

    3

    11

    1

    S

    3/2

    1

    S

    2

    31

    S

    2

    3

    S .

    2

  • CCE PF+PR 11 81-K

    PF+PR-7021 [ Turn over

    34. 28875634

    = 74875794

    = 71675712

    = ( 12 + 5 16 ) 7

    = 7 . 2

    35. S = { ( HH ) ( TT ) ( HT ) ( TH ) }

    n ( S ) = 4

    ( A ) = ( HT ) ( TH )

    n ( A ) = 2

    P ( A ) = )(

    )(

    Sn

    An

    P ( A ) = 2

    1

    4

    2

    2

    1

    2

    36. = 36

    = 12036036

    12

    = 16036036

    16

    = 8036036

    8

    1

    2

  • 81-K 12 CCE PF+PR

    PF+PR-7021

    37. m = 5, n = 7

    m + n = 5 + 7 = 12

    mn = 5 7 = 35

    2x x ( m + n ) + mn = 0

    2x x ( 12 ) + 35 = 0

    2x 12x + 35 = 0 2

    38. k = 2

    2

    1mv

    kmv 22

    m

    kv

    22

    v = m

    k2

    v = 2

    1002

    = 100

    v = 10 . 2

    39. ABC, B = 90, BD AC

    2BD = AD CD

    28 = 4 CD

    4CD = 64

    CD = 4

    64 = 16

    2

    40. r = 7

    = 24 r

    = 777

    224

    = 88 7

    = 616 2

  • CCE PF+PR 13 81-K

    PF+PR-7021 [ Turn over

    IV. 41.

    A B P

    A, P B

    XPY

    APX = 90 (i) ( AP XY )

    BPX = 90 (ii) ( BP XY )

    (i) (ii)

    APX + BPX = 180

    APB = 180

    APB

    A, P, B 3 42. f x fx x x = D 2D

    2Df

    1 5 4 3 12 5 25 100

    6 10 3 8 24 0 00 00

    11 15 2 13 26 5 25 50

    16 20 1 18 18 10 100 100

    N = 10 fx = 80 f 2D = 250 1

    10

    80

    N

    fxx = 8

    2510

    2502

    N

    Df = 5 1

    3

  • 81-K 14 CCE PF+PR

    PF+PR-7021

    43. 1, 2, 3, 4, 5, 6

    a) 4- 46P

    345646 P

    46P = 360

    b) 5000

    14P

    1

    5P

    14P

    1

    3P

    13P

    14P

    15P

    14P

    = 13P 1

    4P 1

    5P 1

    4P

    = 3 4 5 4

    5000 = 240. 3

    16 31

    313 PP nn

    16 . n ( n 1 ) ( n 2 ) = 13 ( n + 1 ) n ( n 1 )

    16 ( n 2 ) = 13 ( n + 1 )

    16n 32 = 13n + 13

    16n 13n = 13 + 32

    3n = 45

    n = 3

    45

    n = 15. 3

  • CCE PF+PR 15 81-K

    PF+PR-7021 [ Turn over

    44. = )90(cos1

    cos

    sin1

    )90(sin

    =

    sin1

    cos

    sin1

    cos

    =

    2sin1

    )sin1(cos)sin1(cos

    =

    2sin1

    sin.coscossin.coscos

    =

    2cos

    cos2

    = cos

    2

    = 2 sec

    = 3

    = cos ( A + B )

    = cos ( 60 + 30 )

    = cos 90

    = 0

    = cos A . cos B sin A . sin B

    = cos 60 . cos 30 sin 60 . sin 30

    =

    2

    1

    2

    3

    2

    3

    2

    1

    = 4

    3

    4

    3

    = 0

    = 3

  • 81-K 16 CCE PF+PR

    PF+PR-7021

    45. = x

    = 1000

    = x

    1000

    10

    = x 10

    = 1000

    = 10

    1000

    x

    5

    10

    1000

    x

    x

    1000 = 5