Karanataka CET 1987 Mathematics

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KARNATAKA COMMON ENTRANCE TEST Question Paper

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1987

1. The vertex of the parabola is the point1) (3, -1) 2) (3,4) 3) (-3, -1) 4) -3,

+1)

2. The length of latus rectum of the parabola is1) 2) 3) 4

4) 8

3. The distance between the foci of the ellipse is1) 2 2) 2 3) 4

4) 4

4. The major axis of an ellipse is three times the minor axis, then the eccentricity is1) 2) 3) 4)

5. The tangent to the hyperbola at the point (3, -2) is1) 2)

3) 4) none of these

6. + =

1) 2) 3) 4)

7. (1 + i) (1 + 2i) (1 - 3i) =

1)1 - 6i 2) 8 - 6i 3) 6 8i 4) 6 + 8i

8. if =

1) 2 2) 0 3) 32 4) none of these

9.

1) 1 + i 2) 1 3) 1 - i 4) -1

10. The G.C.D. of 364 and 462 is

1) 3 2)11 3) 14 4) 7

11. The congruence has the solution

1) x 2) x 3) x 4) none of

these


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1) (3,1) 2) (3, -1) 3) (-3, 1) 4)

(-3, -1)

33. In a triangle ABC if A = 300

, C= 1050

, b = 3 then a =

1) 2) 3 3) 2 4)

34. In a 450

, c= 2

1) 2) 6 3) 4)

35. If

1) 4 2) 9 3) 16 4) 25

36. The equation of the circle with centre (2, -3) and touching the y axis is

1) 2)

3) 4) none of these

37. The length of the tangent from (-1, 2) to the circle is

1) 24 2) 3) 6 4)

38. The radius of the circle

1) 2) 3)1 4) 4

39. if the circle

1) -2 2) 2 3) 1 4) -1

40. The eccentricity of the hyperbola

1) 2) 3) 4)

41. =

1) 1 2) 2 3) 3 4) 8

42. =


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1) 1 2) -2 3) 4) -1/2

43.

1) 2) 4 3) 4) 2

44.

1) 2/3 2) 3/2 3) 2 4)

45. If x =(

1) 2) 3) 4)

46.

1) -4/3 2) 4/3 3) 3/4 4) -3/4

47. If y = + , then =

1) 12 2) 12y/ 3) 4) none of these

48. If x = is

1) -3 2) 3 3) 4 4)

49. The slope of the normal to the curve

1) 2) - 3) 4) none of these

50.

1) 2) 3 3) 4)

51. =

1) 2) 3) 4)

none of these

52.

1) 2) 3) 4)


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53.

1) 1 2) 0 3) -1 4) none of

these

54.

1) 2) 3) 4)

55. If is the angle between the vectors +

1) 2) 3) 4) none of these

56. If + = + = x =

1) 0 2) 2 3)4 4) -4

57. , = =

1) 2) + 3) 4)

58. = + = = , = then

=

1) 15 2) 17 3) 0 4) none of

these

59. =

1) 0 2) 12 3)-12 4)16

60. The roots of the equation = o are

1) (0,1) 2) (0, 2) 3) (0, -1) 4) (0,-2)

61. =

1) 0 2) (

3) 3) none of these


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62. =

1) 2 2) 20 3) -2 3) -20

63. If A = B = , then 3A 2B =

1) 2)

3) 4) none of these

64. If A + 2B = , 2A B = , then B =

1) 2)

3) 4) none of these

65. The angle between the curves

1) 300

2) 600

3) 4) none of

these

66. The length of the sub tangent to the curve

1) -2 2) 3) -3 4) 4

67. The distance moved by a particle in time t is given by

s=

1) 42 2) -42 3) 48 4) -48

68.

1) 2)

3) 4) none of these

69.

1) 2) 3) 4)

70.


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1) 2) 3) 4)

71.

1) 3/2 2) 3 3) 2/3 4) 1/3

72. If y = =

1) 2) 3) 4) none of

these

73. If =

1) 2) 3)

4)

74. if y =

1) 2) 3) 4) none of these

75. sin

1) 2) 3) 4)

Answer Key

Q.No 1

2 3 4 5 6 7 8 9 10 11 12 13 14 15

Ans 4 1 3 1 2 2 3 2 4 3 3 2 4 4 2

Q.No 16

17 18 19 20 21 22 23 24 25 26 27 28 29 30

Ans 1 2 3 1 2 2 4 1 2 2 3 3 1 3 4

Q.No 31

32 33 34 35 36 37 38 39 40 41 42 43 44 45

Ans 1 2 2 4 2 3 4 1 1 4 3 2 1 4 4


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Q.No 46

47 48 49 50 51 52 53 54 55 56 57 58 59 60

Ans 1 2 2 4 1 2 4 1 1 3 3 2 2 1 3

Q.No 61

62 63 64 65 66 67 68 69 70 71 72 73 74 75

Ans 2 4 2 3 3 1 2 3 4 3 2 1 4 3 1

Karanataka CET 1987 Mathematics

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