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Karnataka SSLC English Medium : KSEEB Mathematics June 2009

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81-E 2 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. 1. If U = { 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 } (A) { (C) { 2, 4, 6, 8 } 0, 2, 3, 4, 6, 8, 9 } 60 1 = 60 and A = { 0, 1, 3, 5, 7 } (B) { 0, 2, 4, 6, 8 } (D) { 2, 4, 6, 8, 9 Ans. : 2. If A and B are disjoint sets, then n ( A I B ) is (A) 0 (B) (C) {0} (D) { }. Ans. : ( SPACE FOR ROUGH WORK ) VIII I-E-9912130 , then A l is }. 3 3. { 1, 2, 3 } , If A = B= 81-E { 0, 1, 3, 4 } and C = { 2, 3, 4 } , then the set A U (B I C) represents (A) { 0, 1, 2, 3 } (B) { 0, 1, 3, 4 } (C) { 1, 2, 3, 4 } (D) { 2, 3, 4 } . Ans. : 4. In a progression, if T n = 2n 2 + 1, then S 2 is (A) 9 (B) 12 (C) 10 (D) 11. Ans. : 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. Ans. : 6. In a G.P., if T n is the n th term and r is the common ratio then T n 1 term can b e determined by (A) T n r (B) T n r (C) T n 2 r (D) T n + 1 r. Ans. : ( SPACE FOR ROUGH WORK ) VIII I-E-9912130 [ Turn over 81-E 7. 4 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 Ans. : 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. Ans. : 9. In a G.P., T 7 : T 4 = 8 : 1, then common ratio r is (A) 1 (B) 3 (C) 2 (D) 4. Ans. : 1 0. If A is skew symmetric matrix, then which of the following is correct ? (A) A = A l (B) A= A (C) A l (D) A = A l . = ( A l ) l Ans. : ( SPACE FOR ROUGH WORK ) VIII I-E-9912130 5 11. 6 + x 0 If I = 81-E 0 is an identity matrix of order 2 2, then the value of x is 1 (A) 5 (B) 6 (C) 5 (D) 1. (B) 5 2 2 (D) 0 1 2 Ans. : 1 2. 1 0 2 If A = , then A A l is 1 (A) 1 0 2 (C) 5 0 2 1 2 1 . 2 Ans. : 1 3. 3x 1 If 2 1 + 2 3 4 1 10 3 = 6 , then the value of x is 4 (A) 2 (B) 3 (C) 4 (D) 5. Ans. : 1 4. n P n 1 i s (A) (n 1)! (B) (n+2)! (C) n! (D) ( n + 1 ) !. Ans. : ( SPACE FOR ROUGH WORK ) VIII I-E-9912130 [ Turn over 81-E 15. 6 If 11 P r = 990, then r is (A) 3 (B) 4 (C) 2 (D) 5. Ans. : 1 6. If n n C 9 = C 6 , then n is (A) 3 (B) 15 (C) 10 (D) 14. Ans. : 1 7. How many triangles can be formed by using 10 non-collinear points ? (A) 100 (B) 110 (C) 120 (D) 140. Ans. : 1 8. The formula to find the coefficient of variation is (A) (C) X X 2 2 100 100 (B) (D) X X 100 100. Ans. : ( SPACE FOR ROUGH WORK ) VIII I-E-9912130 7 19. If ( 5x 10 ) and ( 5x 2 20 ) 81-E are two expressions, then their H.C.F. is (A) 5(x 2) (B) (x 2) (C) ( 5x 2 ) (D) x 10. Ans. : 2 0. If A and B are two expressions and their H.C.F. is H , then their L.C.M. can b e 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 Ans. : 2 1. H.C.F. and L.C.M. of two expressions are 5x 2 y 2 and 10x 3 y 3 respectively. If one of the expressions is 5x 2 y 3 then other is (A) 10x 3 y 3 (B) 10x 2 y 2 (C) 10x 3 y 2 (D) 5 x 3 y 2 . Ans. : 2 2. When notation is used, the expression x 2 + y 2 + z 2 x y y z zx becomes (A) x 2 + x y (B) x 2 x y (C) x 2 x y (D) x 2 + x y . Ans. : ( SPACE FOR ROUGH WORK ) VIII I-E-9912130 [ Turn over 81-E 23. 8 When x ( y z ) expanded and simplified, its value is (A) 0 (B) xy y z z x (C) xy x z (D) xy + y z + z x . Ans. : 2 4. If one of the factors of a 3 b 3 is ( 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 ) . Ans. : 2 5. 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. (B) x y (D) x Ans. : 2 6. The rationalising factor of (A) x+ (C) x + y y x + y is Ans. : ( SPACE FOR ROUGH WORK ) VIII I-E-9912130 y. 9 27. When simplified, the sum of 81-E 50 + 6 2 + 128 will be (A) 19 2 (B) 16 2 (C) 14 2 (D) 15 2 . Ans. : 2 8. Product of (A) (C) 2 and 3 5 will be 6 10 (B) 6 200 (D) 6 100 3 200 . Ans. : 2 9. Subtracting ( 5 a + 3 b ) from ( 8 a + 5 b ) , we get (A) 3 a 2 b (B) 3 a +2 b (C) 2 a 3 b (D) 2 a +3 b . Ans. : 3 0. 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. Ans. : ( SPACE FOR ROUGH WORK ) VIII I-E-9912130 [ Turn over 81-E 31. 10 The roots of quadratic equation 3x 2 3x = 0 are (A) 0 and 1 (B) 0 and 3 (C) 1 and 3 (D) 0 and 3. (B) 3 (D) 5. Ans. : If 7y = 35 y (A) 7 (C) 3 2. then the values of y are 5 7 Ans. : 3 3. 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. Ans. : 3 4. When 2m 2 = 2 m is written in the standard form, then quadratic equation becomes (A) 2m 2 + m 2 = 0 (B) 2m 2 m 2 = 0 (C) 2m 2 m + 2 = 0 (D) 2 m 2 + m + 2 = 0. Ans. : ( SPACE FOR ROUGH WORK ) VIII I-E-9912130 11 35. 81-E The roots of a quadratic equation 2k 2 2 k 5 = 0, when the values of the coefficient a, b and c are being substituted in the formula, are (A) k= ( 2 ) ( 2 ) 2 4 ( 2 ) ( 5 ) 2 (B) k= 2 ( 2 ) 2 4 ( 2 ) ( 5 ) 2 ( 2 ) (C) k= 2 ( 2 ) 2 4 ( 2 ) ( 5 ) 2 ( 2 ) (D) k= 2 ( 2 ) 2 4 ( 2 ) ( 5 ) . 2 ( 2 ) Ans. : 3 6. In a quadratic equation when b 2 = 4ac, then the roots are (A) real and equal (B) real and distinct (C) imaginary (D) imaginary and equal. Ans. : 3 7. If m and n are roots of a quadratic equation, then the standard form of quadratic equation is (A) x 2 + ( m + n ) x + m n = 0 (B) x 2 ( m + n ) x m n = 0 (C) x 2 + ( m n ) x + m n = 0 (D) x 2 ( m + n ) x + m n = 0. Ans. : ( SPACE FOR ROUGH WORK ) VIII I-E-9912130 [ Turn over 81-E 38. 12 If m and n are roots of equation 2x 2 6x + 1 = 0, then the value of m 2 n + m n 2 is (A) 3 2 (C) (B) (D) 3 2 2 3 1 . 2 Ans. : 3 9. 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. Ans. : 4 0. If y y 1 ( mod 3 ), then the value of y is (A) 1 (B) 3 (C) 6 (D) 2. Ans. : 4 1. The sum of ( 3 7 6 ) 7 5 is (A) 5 (B) 2 (C) 0 (D) 7. Ans. : ( SPACE FOR ROUGH WORK ) VIII I-E-9912130 13 42. 81-E O is the centre of a circle, AB is a chord. From the figure ACB is C O . A B (A) 90 (B) less than 90 (C) greater than 90 (D) 180 . Ans. : 4 3. Two circles when touch externally, the number of transverse common tangnets that can be drawn, is (A) 0 (B) 1 (C) 2 (D) 3. Ans. : 4 4. In a ABC, if XY BC then AX BX = A X Y B (A) (C) AY XY AY CY C (B) (D) AX XY CY . AY Ans. : ( SPACE FOR ROUGH WORK ) VIII I-E-9912130 [ Turn over 81-E 45. 14 A BC 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. Ans. : 4 6. 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. Ans. : 4 7. The length of a diagonal of a square of side 5 cm is (A) 5 2 cm (B) 2 5 cm (C) 10 cm (D) 10 2 cm. Ans. : ( SPACE FOR ROUGH WORK ) VIII I-E-9912130 15 48. 81-E From the figure, the length of AD is A 11 cm E D 12 cm 6 cm B C 12 cm (A) 12 cm (B) 14 cm (C) 11 cm (D) 13 cm. Ans. : 4 9. Which one of the following is Pythagorian Triplet ? (A) 8, 15, 16 (B) 8, 15, 18 (C) 8, 15, 17 (D) 8, 15, 19. Ans. : 5 0. 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. Ans. : ( SPACE FOR ROUGH WORK ) VIII I-E-9912130 [ Turn over 81-E 51. 16 PA and P B are tangents drawn from point P to a circle of centre O. If APO = 30 then AOB is A 30 O. P B (A) 60 (B) 120 (C) 110 (D) 100 . Ans. : 5 2. In a circle of radius 10 cm, O is the centre, OP A B . If OP = 6 cm, then the length of chord AB is O A B P (A) 8 cm (B) 12 cm (C) 20 cm (D) 16 cm. Ans. : ( SPACE FOR ROUGH WORK ) VIII I-E-9912130 17 53. 81-E In the figure, XP, XQ and XR are tangents to the circles. If the length of X Q = 9 cm then the length of tangent XR is Q R . A B . X P (A) 18 cm (B) 10 cm (C) 9 cm (D) 12 cm. Ans. : 5 4. 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. Ans. : 5 5. The total surface area of a cylinder is (A) 2 rh (B) 2 r ( r + h ) (C) rh (D) rl . Ans. : 5 6. 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 . Ans. : ( SPACE FOR ROUGH WORK ) VIII I-E-9912130 [ Turn over 81-E 57. 18 In the graph, the order of a node C is C A B (A) 2 (B) 4 (C) 3 (D) 5. Ans. : 5 8. 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. Ans. : 5 9. The one which is not a platonic solid is (A) Tetrahedron (B) Hexahedron (C) Square based pyramid (D) Octahedron. Ans. : 6 0. The number of edges of an octahedron is (A) 12 (B) 14 (C) 8 (D) 6. Ans. : ( SPACE FOR ROUGH WORK ) VIII I-E-9912130 19 81-E PART B 61. If U = { 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 show that ( A U B ) l = A l I B l } ,A= { 1, 4, 9 } . and B = { 2, 4, 6, 8 } , then 2 ( SPACE FOR ROUGH WORK ) VIII I-E-9912130 [ Turn over 81-E 62. 20 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. ( SPACE FOR ROUGH WORK ) VIII I-E-9912130 2 21 63. Find the sum of the following geometric series : 81-E 2 2 + 4 + 8 + + 256. ( SPACE FOR ROUGH WORK ) VIII I-E-9912130 [ Turn over 81-E 64. 22 How many 3-digit even numbers can be formed using the digits 2, 3, 4, 5 and 6 without repetition ? 2 ( SPACE FOR ROUGH WORK ) VIII I-E-9912130 23 65. 81-E Find the H.C.F. of expressions x 3 7x 2 + 14x 8 and x 3 6x 2 + 11x 6. 2 ( SPACE FOR ROUGH WORK ) VIII I-E-9912130 [ Turn over 81-E 66. 24 If a + b + c = 2s , prove that a 2 + b 2 c 2 + 2ab a 2 b 2 + c 2 + 2ac = ( SPACE FOR ROUGH WORK ) VIII I-E-9912130 ( s c ) . ( s b ) 2 25 67. Rationalise the denominator and simplify : 2 3 2 + 81-E 2 3 3 + 2 ( SPACE FOR ROUGH WORK ) VIII I-E-9912130 [ Turn over 81-E 68. 26 Solve the quadratic equation x 2 8x + 1 = 0, by using the formula. ( SPACE FOR ROUGH WORK ) VIII I-E-9912130 2 27 69. 81-E Construct two tangents to a circle of radius 5 cm from an external point 12 cm away from the centre. 2 ( SPACE FOR ROUGH WORK ) VIII I-E-9912130 [ Turn over 81-E 70. 28 The sides of a quadrilateral ABCD are tangents to the circle with centre O. Then show that AB + CD = AD + BC. 2 D R S O . A P C Q B ( SPACE FOR ROUGH WORK ) VIII I-E-9912130 29 71. 81-E The surface area of a sphere is 154 cm 2 . Find the diameter of the sphere. 2 ( SPACE FOR ROUGH WORK ) VIII I-E-9912130 [ Turn over 81-E 72. 30 Draw a plan from the following notes of the field book : To D ( in m ) 250 150 To E 100 100 to C 100 50 50 to B From A ( SPACE FOR ROUGH WORK ) VIII I-E-9912130 2 31 73. 81-E Calculate the arithmetic mean and standard deviation for the given frequency distribution : 4 Class-Interval frequency ( f ) 1 5 4 6 10 6 11 15 8 16 20 2 N = 20 ( SPACE FOR ROUGH WORK ) VIII I-E-9912130 [ Turn over 81-E 74. 32 Construct a transverse common tangent to two circles of radii 4 cm and 2 cm whose centres are 10 cm apart. 4 ( SPACE FOR ROUGH WORK ) VIII I-E-9912130 33 75. 81-E Prove that If two triangles are equiangular, then their corresponding sides are proportional. 4 ( SPACE FOR ROUGH WORK ) VIII I-E-9912130 [ Turn over 81-E 76. 34 Draw the graph of y = x 2 and y = 2x + 3 and hence solve the equation x 2 2 x 3 = 0. 4 ( SPACE FOR ROUGH WORK ) VIII I-E-9912130 35 81-E graph ( SPACE FOR ROUGH WORK ) VIII I-E-9912130 [ Turn over 81-E 36 ( SPACE FOR ROUGH WORK ) VIII I-E-9912130

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Additional Info : Karnataka SSLC (Secondary School Leaving Certificate) English Medium - Karnataka Secondary Education Examination Board (KSEEB)
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