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2022 QP Solutions
48. Choose the correct option and write it : HCF of (91, 21) is - (a) 91 (b) 21 (c) 13 (d) 12
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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 = ________
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50. Match the correct column : (i) sec (90°– θ) (a) 1
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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
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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.
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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.
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54. Find the L.C.M. of 6.72 and 120 using the prime factorisation method.
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55. Find the zeroes of the quadratic polynomial 6x–3–7x.
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56. Find the quadratic polynomial, the sum and product of whose zeroes are, 1, 1 respectively.
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57. For the A.P. –5, –1, 3, 7.... write the first term a and common difference d.
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58. Which term of the A.P. 21, 18, 15, .... is –81 ?
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59. State whether the following figures are similar or not.
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60. Two polygons of the same number of sides are similar if (i) their corresponding angles are _____ and (ii) their corresponding
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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.
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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.
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63. Find the area of a triangle ABC formed by the A(5, 2), B(4, 7) and C(7, - 4).
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64. Find the value of K if the points A(2, 3), B(4, K) and C(6, –3) are collinear.
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65. If sin A = 3/4, then find the value of cos A and tan A.
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66. In a right angle triangle ABC, right angled at B, if tan A = 1, then verify that 2 sin A . cos A = 1.
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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)
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68. In a circle of radius 21 cm an arc subtends an angle 60° at the centre. Find the length of the arc.
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69. Define impossible event.
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70. Define elementary event.
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71. One card is drawn from a well–shuffled deck of 52 cards. Calculate the probability that the card will not be an ace.
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72. If P(E) = 0.06, what is the probability of "not E" ?
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73. Find the roots of the equation 2x2 +x–6 = 0 by factorisation.
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74. Find the nature of roots of the quadratic equation 2x2–3x+5=0
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75. Which term of the A.P. 3, 8, 13, 18, .... is 78?
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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 ?
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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
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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
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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.
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80. Prove that the tangent at any point of a circle is perpendicular to the radius through the point of contact.
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81. Solve the following pair of linear equations by the elimination method : 3x + y = 10 and 2x + 2y = 12.
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82. Solve the following pair of linear equations by the substitution method :
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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
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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.
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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
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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
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87. Consider the following distribution of doily wages of 50 workers of a factory. Find the mean daily wages of the workers of the
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88. The distribution below shows the number of wickets taken by bowlers in one–day cricket matches. Find the mean number of
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