## Karnataka Board Question Paper (Mathematics) SSLC Exam. June 2009

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### June - 2009

General Instructions :
i) The question-cum-answer booklet contains two Parts, Part – A & Part – B.
ii) Part – A consists of 60 questions and Part – B consists of 16 questions.
iii) Space has been provided in the question-cum-answer booklet itself to answer the questions.
iv) Follow the instructions given in Part – A and write the correct choice in full in the space provided below each question.
v) For Part – B enough space for each question is provided. You have to answer the questions in the space provided.
vi) Space for Rough Work has been printed and provided at the bottom of each page.

PART – A

Four alternatives are suggested to each of the following questions / incomplete statements. Choose the most appropriate alternative and write the answer in the space provided below each question.       60 × 1 = 60

1. If U = { 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 } and A = { 0, 1, 3, 5, 7 } , then Al is

(A) { 0, 2, 3, 4, 6, 8, 9 }              (B) { 0, 2, 4, 6, 8 }

(C) { 2, 4, 6, 8 }                          (D) { 2, 4, 6, 8, 9 } .

2. If A and B are disjoint sets, then n ( A B ) is

(A) 0                                   (B) ϕ

(C) { 0 }                               (D) { ϕ } .

3. If A = { 1, 2, 3 } , B = { 0, 1, 3, 4 } and C = { 2, 3, 4 } , then the set A U ( B C )

represents

(A) { 0, 1, 2, 3 }                          (B) { 0, 1, 3, 4 }

(C) { 1, 2, 3, 4 }                           (D) { 2, 3, 4 } .

4. In a progression, if Tn = 2n2 + 1, then S2 is

(A) 9                             (B) 12

(C) 10                           (D) 11.

5. In an A.P., the common difference is 3, first term is 1, then its tenth term is

(A) 27                      (B) 29

(C) 30                       (D) 28.

7. If x, y, z are in H.P., then the harmonic mean is

(A) 2xz/x + z                              (B) 2xy/x + y

(C) 2yz/y + z                              (D) 2xz/x + y

8. If A, G, H are AM, GM and HM of a and b, then

(A) A, G, H are in A.P.

(B) A, G, H are in G.P.

(C) A, G, H are in H.P.

(D) A, G, H are not in any of A.P., G.P. and H.P.

9. In a G.P., T7 : T4 = 8 : 1, then common ratio r is

(A) 1                           (B) 3

(C) 2                           (D) 4.

10. If A is skew symmetric matrix, then which of the following is correct ?

(A) A = AI                                 (B) A = – A

(C) AI = ( AI)I                             (D) A = – AI .

14. nPn-1 is

(A) ( n – 1 ) !                          (B) ( n + 2 ) !

(C) n ! (D)                              ( n + 1 ) !.

15. If 11Pr = 990, then r is

(A) 3                                      (B) 4

(C) 2                                       (D) 5.

16. If nC9 = nC6 , then n is

(A) 3                                        (B) 15

(C) 10                                       (D) 14.

17. How many triangles can be formed by using 10 non-collinear points ?

(A) 100                                       (B) 110

(C) 120                                        (D) 140.

19. If ( 5x – 10 ) and (5x2 – 20) are two expressions, then their H.C.F. is

(A) 5 ( x – 2 )                             (B) ( x – 2 )

(C) ( 5x – 2 )                              (D) x – 10.

20. If A and B are two expressions and their H.C.F. is H, then their L.C.M. can be

calculated by using the formula

(A) L = (H × A)/B                       (B) L = A/(H × B)

(C) L = B/(A × H)                       (D) L = (A × B)/H .

21. H.C.F. and L.C.M. of two expressions are 5x2 y2 and 10x3 y3 respectively. If one

of the expressions is 5x 2 y 3 then other is

(A) 10x3 y3                                (B) 10x2 y2

(C) 10x3 y2                                (D) 5x3 y2.

22. When ∑ notation is used, the expression x2 + y2 + z2 xy yz zx becomes

(A) ∑ x2 + ∑ xy                             (B) ∑ x2 – ∑ xy

(C) ∑ x2 xy                                 (D) ∑ x2 + xy.

23. When ∑ x ( y z ) expanded and simplified, its value is

(A) 0                                         (B) xy yz zx

(C) xy xz                                (D) xy + yz + zx.

24. If one of the factors of a3 b3 is ( a b ), then the other one is

(A) ( a2 + b2 ab)                     (B) (a2 b2 + ab)

(C) (a2 b2ab)                      (D) (a2 + b2 + ab).

25. When a + b + c = 2s, then the value of ( b + c a ) is

(A) 2s a                                 (B) 2 ( s a )

(C) 2 ( s + a )                           (D) 2s + a.

30. In a quadratic equation ax2 + bx + c = 0, if a = 0, then it becomes

(C) simple linear equation

(D) second degree equation.

31. The roots of quadratic equation 3x2 – 3x = 0 are

(A) 0 and 1                               (B) 0 and 3

(C) 1 and 3                               (D) 0 and – 3.

33. The sum of a number and its square is 42. It represents the equation

(A) x2 + x + 42 = 0

(B) x2 + x – 42 = 0

(C) 2x2 + x – 42 = 0

(D) x2 x – 42 = 0.

34. When 2m2 = 2 – m is written in the standard form, then quadratic equation becomes

(A) 2m2 + m – 2 = 0                  (B) 2m2 m – 2 = 0

(C) 2m2 m + 2 = 0                  (D) 2m2 + m + 2 = 0.

36. In a quadratic equation when b2 = 4ac, then the roots are

(A) real and equal                     (B) real and distinct

(C) imaginary                             (D) imaginary and equal.

37. If m and n are roots of a quadratic equation, then the standard form of quadratic equation is

(A) x2 + ( m + n ) x + mn = 0

(B) x2 – ( m + n ) x mn = 0

(C) x2 + ( m n ) x + mn = 0

(D) x2 – ( m + n ) x + mn = 0.

38. If m and n are roots of equation 2x2 – 6x + 1 = 0, then the value of m2 n + mn2 is

(A)3/2                                       (B) 2/3

(C) –3/2                                     (D) 1/2.

39. The graph of y = x2 and y = 2 – x intersects at ( 1, 1 ) and ( – 2, 4 ). Then the

roots of required quadratic equation are

(A) 2 and 2                                (B) 1 and – 2

(C) 0 and – 2                               (D) 0 and 4.

43. Two circles when touch externally, the number of transverse common tangnets that

can be drawn, is

(A) 0                                           (B) 1

(C) 2                                           (D) 3.

45.ABC ||| ∆ DEF, the area of ∆ ABC is 45 cm 2 and the area of ∆ DEF is 20 cm2 ,

one side of ∆ ABC is 3·6 cm then the length of corresponding side of ∆ DEF is

(A) 3·4 cm                         (B) 2·4 cm

(C) 1·4 cm                         (D) 4·4 cm.

46. “If the square on one side of a triangle is equal to the sum of the squares on the other two sides, then those two sides contain a right angle.” This statement refers to

(A) Pythagoras theorem

(B) Thales theorem

(C) Converse of Thales Theorem

(D) Converse of Pythagoras theorem.

49. Which one of the following is Pythagorian Triplet ?

(A) 8, 15, 16                        (B) 8, 15, 18

(C) 8, 15, 17                        (D) 8, 15, 19.

50. If two circles of radii 4·5 cm and 3·5 cm are touching externally then distance

between their centres is

(A) 8·0 cm (B) 1·0 cm

(C) 7·0 cm (D) 7·5 cm.

54. The revolution of a right angled triangle about one of the sides containing the right

angle generates a solid called

(A) cone                                            (B) cylinder

(C) sphere                                          (D) cube.

55. The total surface area of a cylinder is

(A) 2 πrh                                           (B) 2 πr ( r + h )

(C) πrh                                              (D) πrl .

56. The surface area of a sphere whose radius is 7 cm, is

(A) 516 cm2                                 (B) 416 cm2

(C) 88 cm2                                   (D) 616 cm2 .

58. Euler discovered that a graph is not traversable if it has

(A) all even nodes

(B) two odd nodes and two even nodes

(C) only two nodes

(D) more than two odd nodes.

59. The one which is not a platonic solid is

(A) Tetrahedron                                   (B) Hexahedron

(C) Square based pyramid                     (D) Octahedron.

60. The number of edges of an octahedron is

(A) 12                                   (B) 14

(C) 8                                     (D) 6.

PART – B

61. If U = { 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 } , A = { 1, 4, 9 } and B = { 2, 4, 6, 8 }, then show that ( A U B )’ = A’ B’ .     2

62. The fourth and eighth terms of an A.P. are in the ratio of 1 : 2 and tenth term is 30. Find the common difference.                                                 2

63. Find the sum of the following geometric series :                   2

2 + 4 + 8 + …… + 256.

64. How many 3-digit even numbers can be formed using the digits 2, 3, 4, 5 and 6 without repetition ?      2

65. Find the H.C.F. of expressions x3 – 7x2 + 14x – 8 and x3 – 6x2 + 11x – 6. 2

68. Solve the quadratic equation x2 – 8x + 1 = 0, by using the formula.                           2

69. Construct two tangents to a circle of radius 5 cm from an external point 12 cm away from the centre.       2

71. The surface area of a sphere is 154 cm2 . Find the diameter of the sphere.                2

74. Construct a transverse common tangent to two circles of radii 4 cm and 2 cm whose centres are 10 cm apart.        4

75. Prove that

“If two triangles are equiangular, then their corresponding sides are proportional.”                       4

76. Draw the graph of y = x2 and y = 2x + 3 and hence solve the equation X2 – 2x – 3 = 0.                 4

PART – A

1. D,           2. A,         3. C,         4. B,          5. D,

6. B,            7. A,        8. B,          9. B,        10. D,

11. A,         12. B        13. B,        14. C,        15. A,

16. B,         17. C,       18. D         19. A,        20. D,

21. C,          22. B,      23. A,        24. D,        25. B,

26. C,          27. A,      28. C,        29. B,        30. C ,

31. A,          32. D,      33. B,        34. A,        35. C,

36. A,         37. D,      38. A,        39. B,        40. D,

41. C,          42. B,      43. B,        44. C,         45. B,

46. D,         47. A,      48. D,       49. C,         50. A,

51. B,           52. D      53. C,        54. A,         55. B,

56. D,           57. B,     58. D,        59. C,         60. A

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