**Karnataka Board SSLC Exam Question Paper**

**Mathematics**

**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 A^{l} *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 *T _{n}*

*= 2*

*n*+ 1, then

^{2}*S*is

_{2}(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., *T _{7} *:

*T*= 8 : 1, then common ratio

_{4}*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 *= *A ^{I}* (B)

*A*= –

*A*

(C) *A ^{I} *= (

*A*)

^{I}^{I}(D)

*A*= –

*A*.

^{I}

**14.** ^{n}P_{n-1} is

(A) ( *n *– 1 ) ! (B) ( *n *+ 2 ) !

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

**15.** If ^{11}*P _{r} *= 990, then

*r*is

(A) 3 (B) 4

(C) 2 (D) 5.

**16.** If ^{n}*C _{9} *=

^{n}

*C*, then

_{6}*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 ( 5*x *– 10 ) and (5x^{2} – 20) are two expressions, then their H.C.F. is

(A) 5 ( *x *– 2 ) (B) ( *x *– 2 )

(C) ( 5*x *– 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 5*x ^{2}*

*y*and 10

^{2}*x*

^{3}*y*respectively. If one

^{3}of the expressions is 5*x *2 *y *3 then other is

(A) 10*x ^{3}*

*y*(B) 10

^{3}*x*

^{2}y^{2}(C) 10*x ^{3} y^{2}* (D) 5

*x*.

^{3}y^{2}**22.** When ∑ notation is used, the expression *x ^{2} *+

*y*+

^{2}*z*–

^{2}*xy*–

*yz*–

*zx*becomes

(A) ∑ *x ^{2} *+ ∑

*xy*(B) ∑

*x*– ∑

^{2}*xy*

(C) ∑ *x ^{2} *–

*xy*(D) ∑

*x*+

^{2}*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 *a ^{3} *–

*b*is (

^{3}*a*–

*b*), then the other one is

(A) ( *a ^{2} *+

*b*–

^{2}*ab)*(B) (

*a*–

^{2}*b*+

^{2}*ab)*

(C) (*a ^{2} *–

*b*–

^{2}*ab)*(D) (

*a*+

^{2}*b*+

^{2}*ab*).

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

(A) 2*s *– *a *(B) 2 ( *s *– *a *)

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

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**30.** In a quadratic equation *ax ^{2} *+

*bx*+

*c*= 0, if

*a*= 0, then it becomes

(A) pure quadratic equation

(B) adfected quadratic equation

(C) simple linear equation

(D) second degree equation.

**31.** The roots of quadratic equation 3*x ^{2} *– 3

*x*= 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) *x ^{2} *+

*x*+ 42 = 0

(B) *x ^{2} *+

*x*– 42 = 0

(C) 2*x ^{2} *+

*x*– 42 = 0

(D) *x ^{2} *–

*x*– 42 = 0.

**34.** When 2*m ^{2} *= 2 –

*m*is written in the standard form, then quadratic equation becomes

(A) 2*m ^{2} *+

*m*– 2 = 0 (B) 2

*m*–

^{2}*m*– 2 = 0

(C) 2*m ^{2} *–

*m*+ 2 = 0 (D) 2

*m*+

^{2}*m*+ 2 = 0.

**36.** In a quadratic equation when *b ^{2} *= 4

*ac*, 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) *x ^{2} *+ (

*m*+

*n*)

*x*+

*mn*= 0

(B) *x ^{2} *– (

*m*+

*n*)

*x*–

*mn*= 0

(C) *x ^{2} *+ (

*m*–

*n*)

*x*+

*mn*= 0

(D) *x ^{2} *– (

*m*+

*n*)

*x*+

*mn*= 0.

**38.** If *m *and *n *are roots of equation 2*x ^{2} *– 6

*x*+ 1 = 0, then the value of m

^{2}*n*+

*mn*is

^{2}(A)3/2 (B) 2/3

(C) –3/2 (D) 1/2.

**39.** The graph of *y *= *x ^{2} *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 cm^{2} ,

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.

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**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 π*rh *(B) 2 π*r *( *r *+ *h *)

(C) π*rh *(D) π*rl *.

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

(A) 516 cm^{2} (B) 416 cm^{2}

(C) 88 cm^{2} (D) 616 cm^{2} .

**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 *x ^{3} *– 7

*x*+ 14

^{2}*x*– 8 and

*x*– 6

^{3}*x*+ 11

^{2}*x*– 6. 2

**68.** Solve the quadratic equation *x ^{2} *– 8

*x*+ 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 cm^{2} . 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 *= *x ^{2} *and

*y*= 2

*x*+ 3 and hence solve the equation

*X*– 2

^{2}*x*– 3 = 0. 4

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**Answers**

**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