48. Choose the correct option and write it : HCF of (91, 21) is - (a) 91 (b) 21 (c) 13 (d) 12 2022 49. Fill in the blanks : (i) HCF (a, b) x LCM (a, b) = __________ (ii) In the equation x + y = 8 if x = 3 then y = ________ 2022 50. Match the correct column : (i) sec (90°– θ) (a) 1 2022 51. Write the answer in one word/sentence of each : (i) If a=bq then what is the relation between a and b ? (ii) If a, b and c are real 2022 52. Write True/False in the following : (i) The value of x in x(x–1)= 0 are zero and one. (ii) 10th term of the A.P. 10, 7, 4..... is –17. 2022 53. Show that every positive even integer is of the form 2q and that every positive odd integer is of the form 2q + 1 where y is some integer. 2022 54. Find the L.C.M. of 6.72 and 120 using the prime factorisation method. 2022 55. Find the zeroes of the quadratic polynomial 6x–3–7x. 2022 56. Find the quadratic polynomial, the sum and product of whose zeroes are, 1, 1 respectively. 2022 57. For the A.P. –5, –1, 3, 7.... write the first term a and common difference d. 2022 58. Which term of the A.P. 21, 18, 15, .... is –81 ? 2022 59. State whether the following figures are similar or not. 2022 60. Two polygons of the same number of sides are similar if (i) their corresponding angles are _____ and (ii) their corresponding 2022 61. Find the coordinates of the point which divides the line segment, joining the points (–1, 7) and (4, –3) in the ratio 2 : 3. 2022 62. If the points A(6, 1), B(8, 2), C(9, 4) and D(P, 3) are the vertices of a parallelogram, taken in order, find the value of P. 2022 63. Find the area of a triangle ABC formed by the A(5, 2), B(4, 7) and C(7, - 4). 2022 64. Find the value of K if the points A(2, 3), B(4, K) and C(6, –3) are collinear. 2022 65. If sin A = 3/4, then find the value of cos A and tan A. 2022 66. In a right angle triangle ABC, right angled at B, if tan A = 1, then verify that 2 sin A . cos A = 1. 2022 67. A chord of a circle of radius 10 cm subtends a right angle at the centre. Find the area of the corresponding minor segment. (π = 3.14) 2022 68. In a circle of radius 21 cm an arc subtends an angle 60° at the centre. Find the length of the arc. 2022 69. Define impossible event. 2022 70. Define elementary event. 2022 71. One card is drawn from a well–shuffled deck of 52 cards. Calculate the probability that the card will not be an ace. 2022 72. If P(E) = 0.06, what is the probability of "not E" ? 2022 73. Find the roots of the equation 2x2 +x–6 = 0 by factorisation. 2022 74. Find the nature of roots of the quadratic equation 2x2–3x+5=0 2022 75. Which term of the A.P. 3, 8, 13, 18, .... is 78? 2022 76. If the 3rd and the 9th terms of an A.P. are 4 and 8 respectively, which term of this A.P. is zero ? 2022 77. If a line intersects sides AB and AC of a ∆ABC at D and E respectively and is parallel to BC, then prove that AD/AB = AE/AC 2022 78. Prove that, if a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points, then the other two 2022 79. Prove that if two concentric circles, the chord of the larger circle, which touches the smaller circle, is bisected at the point of contact. 2022 80. Prove that the tangent at any point of a circle is perpendicular to the radius through the point of contact. 2022 81. Solve the following pair of linear equations by the elimination method : 3x + y = 10 and 2x + 2y = 12. 2022 82. Solve the following pair of linear equations by the substitution method : 2022 83. Construct a triangle of sides 4 cm, 5 cm and 6 cm and then a triangle similar to it whose sides are 2/3 of the corresponding sides 2022 84. Construct a triangle similar to a given triangle ABC with its sides equal to 3/4 of the corresponding sides of the triangle ABC. 2022 85. A Juice seller was serving his customers using glasses as shown in fig. The inner diameter of the cylindrical glass was 5 cm but 2022 86. A cone of height 24 cm and radius of base 6 cm is made up of modelling clay. A child reshapes it in the form of a sphere. Find 2022 87. Consider the following distribution of doily wages of 50 workers of a factory. Find the mean daily wages of the workers of the 2022 88. The distribution below shows the number of wickets taken by bowlers in one–day cricket matches. Find the mean number of 2022