Maths Past Paper PDF

The line representing 4𝑥 + 3𝑦 = 24 1. intersects the x-axis at point..... o A. (3, 0) o B. (0, 4) o C. (6, 0) o D. (0, 8) 6+ 6 + 6 +... 2. is: o A. 4 o B. 3...

The line representing 4𝑥 + 3𝑦 = 24 1. intersects the x-axis at point..... o A. (3, 0) o B. (0, 4) o C. (6, 0) o D. (0, 8) 6+ 6 + 6 +... 2. is: o A. 4 o B. 3 o C. -2 o D. 3.5 For a given AP, 𝑎𝑛 = 8𝑛 + 3 3.. Then, the 20th term of that AP is..... o A. 155 o B. 149 o C. 163 o D. 157 4. If P (2, 4), Q (0, 3), R (3, 6), and S (5, y) are vertices of parallelogram PQRS, then (y =..... o A. 7 o B. 5 o C. -7 o D. -8 If 𝑎𝑐𝑜𝑠⁡θ + 𝑏𝑠𝑖𝑛⁡θ = 4 and 𝑎𝑠𝑖𝑛⁡θ − 𝑏𝑐𝑜𝑠⁡θ = 3 2 2 , then 𝑎 + 𝑏 = 5.......... o A. 7 o B. 12 o C. 25  o D. 1 6. The mean of 20 observation is 38. 6 is added to each observation and then each result is divided by 4. Then, the mean of new observation so obtained is......... o A. 44 o B. 11 o C. 9.5 o D. 40 ( 9 − 7)( 9 + 7) 7. is........ number. (rational, irrational, negative integer) For a given graph of 𝑥 = 𝑝(𝑦) , the number of zeroes of 𝑝(𝑦) 8. is......... (1, 2, 4) 9. The probability of a certain event is......... (0, 1, -1) 1 2 −1= 𝑠𝑖𝑛 ⁡θ 10.......... (tan² θ, cosec² θ, cot² θ) 11. Point A lies in the exterior of a circle with point P and a tangent from A touches the circle at B. If PA = 29 cm and AB = 21 cm, then the diameter of the circle is........ cm. (20, 40, 50) For a given frequency distribution, if 𝑀 = 15 and 𝑥‾ = 18 , then 𝑍 = 12.......... (9, 15, 36) 13. HCF (32, 81) = 1. 2 6 is one of the zeroes of the polynomial 𝑝(𝑥) = 𝑥 − 17𝑥 + 66 14.. If (3, a) is one of the solutions of equation 4𝑥 − 𝑦 = 10 , then 𝑎 = 2 15.. 16. If the probability that Rayna wins the match is 0.48, then the probability that Rayna does not win the match is 0.52. 17. Find the 20th term of the AP 11, 16, 21,.....  18. If tangents PA and PB from point P to a circle with centre O are inclined to each other at an angle of 80°, then find ∠POA. If 𝑃(𝐴): 𝑃(𝐴‾) = 2: 7 , then find 𝑃(𝐴‾) 19.. 5𝑛 If the mean of first n natural numbers is 9 20. , find n. 4 4 𝑐𝑜𝑠 ⁡θ − 𝑠𝑖𝑛 ⁡θ 21. is: A. 1 B. 0 2 2 C. 𝑐𝑜𝑠 ⁡θ − 𝑠𝑖𝑛 ⁡θ 2 2 D. 𝑐𝑜𝑠 ⁡θ + 𝑠𝑖𝑛 ⁡θ For some given data, if 𝑍 + 𝑥 = 98 and 𝑍 − 𝑥 = 12 , then 𝑀 = 22........ by the inter-relationship of mean, median, and mode: A. 55 B. 43 C. 47 D. 45 If 𝐻𝐶𝐹(65, 117) = 3𝑘 − 2 , then 𝑘 = 23........... (5, 4, 3) 2 If the product of the zeroes of the polynomial 𝑝(𝑥) = 6𝑥 − 𝑥 + 𝑘 1 is − 3 , then 𝑘 = 24........... (2, -2, 6) In an 80-mark test of Mathematics, the probability of Rayna scoring 80 out of 80 marks 1 is.......... ( 80  1 , 81 25. ) 2 2 𝑡𝑎𝑛 ⁡θ − 𝑠𝑒𝑐 ⁡θ = 26........... (0, -1, 1) Point P lies in the exterior of a circle with centre O. Tangents PA and PB drawn from point P are inclined to each other at 58°. Then ∠𝑃𝑂𝐴 = 27........... (122°, 58°, 61°) For a given frequency distribution, if Σ𝑓𝑖𝑥𝑖 = 245 and Σ𝑓𝑖 = 100 , then 𝑥 = 28........... (245, 2.45, 2450) The LCM of 35 and 42 is 35 × 42 29.. 2 For the quadratic polynomial 𝑝(𝑥) = 𝑥 + 5𝑥 + 4 30. , the sum of the zeroes is greater than the product of the zeroes. The pair of linear equations 5𝑥 − 15𝑦 = 8 24 and 3𝑥 − 9𝑦 = 5 31. has infinitely many solutions. 3 If 𝑃(𝐴) = 4 4 , then 𝑃(𝐴) = 3 32.. 33. Find the common difference of the AP: -5, -1, 3, 7,.... 34. At the most, how many tangents can be drawn parallel to the diameter of a circle? 35. A letter is chosen at random from the English alphabet. Find the probability that the chosen letter is a vowel. If the median of the observations 8, 12, 17, 𝑥 , 25, 28 is 20, find 𝑥 36.. 37. LSA of a cuboid: (a) Perimeter of base × Height (b) Area of base × Height 1 (c) 3 × Area of base × Height 38. Volume of a cone: (a) Perimeter of base × Height (b) Area of base × Height 1 (c) 3 × Area of base × Height 39. Sector: (a) Portion of a circular region enclosed by an arc and two radii (b) Any part of the circumference of a circle (c) Portion of a circular region bounded by an arc and the chord joining the end-points of the arc 40. Segment: (a) Portion of a circular region enclosed by an arc and two radii (b) Any part of the circumference of a circle (c) Portion of a circular region bounded by an arc and the chord joining the end-points of the arc If the pair of equations 2𝑥 + 7𝑦 = 13 and 5𝑥 + 𝑘𝑦 = 32 41. has a unique solution, then........ holds good. A. 𝑘 = 17. 5 B. 𝑘 = 15. 7 C. 𝑘 ≠ 17. 5 D. 𝑘 ≠ 15. 7 5 If 2  2 is one of the roots of the equation 10𝑥 − 29𝑥 + 𝑘 = 0 , then 𝑘 =........ 42.. A. 25 B. -25 C. -10 D. 10 For a given AP, if 𝑑 =− 4 ,𝑛 = 7 and 𝑎𝑛 = 4 , then 𝑎 =........ 43.. A. 6 B. 7 C. 20 D. 28 Point (5, − 12) 44. lies on a circle with the origin as the centre. Then, the radius of that circle is........ units. A. 7 B. 13 C. 13 D. 10 45. Area of the base of a cylinder 2 A. 3π𝑟 2 B. π𝑟 2 C. 2π𝑟 46. Curved surface area of a hemisphere 2 A. 3π𝑟 2 B. π𝑟 2 C. 2π𝑟 47. Length of a minor arc  2 π𝑟 θ A. 360 π𝑟θ B. 360 π𝑟θ C. 180 48. Area of a minor sector 2 π𝑟 θ A. 360 π𝑟θ B. 360 2 π𝑟 θ C. 180 Here are questions 1 to 20 from the image: 49. If 33x + 27y = 147 and 27x + 33y = 153, the x + y =.......... A. 6 B. 5 C. -5 D. -6 50. If the equation 2x² - kx + k = 0 has equal roots, then k =.......... A. 0 B. 4 C. 8 D. 0 or 8 51. The 10th term of the AP √3, √12, √27,... is.......... A. √363 B. √243 C. √300 D. √342 52. The distance of point P (m, n) from the origin is.......... A. m² + n² B. √(m² + n²) C. m + n D. √(m² - n²) 𝑐𝑜𝑠⁡θ 𝑠𝑖𝑛⁡θ + 𝑠𝑖𝑛⁡θ 53. is.......... A. 𝑡𝑎𝑛⁡θ B. 𝑐𝑜𝑡⁡θ C. 𝑠𝑒𝑐⁡θ D. 𝑐𝑜𝑠⁡θ 54. Some observations arranged in ascending order as 12, 18, 27, x + 3, x + 9, 40, 42, 50. If the median of the data is 35, then x =.......... A. 35 B. 30 C. 29 D. 28 55. LCM (220, 60) =.......... A. 20 B. 660 C. 1320 The sum of zeroes of the polynomial 𝑝(𝑥) = 𝑥² + 2𝑥 − 899 56. is.......... A. 2 B. -2 C. -899 57. In the experiment of rolling a balanced die once, the probability of receiving a multiple of 3 is.......... A. 1/3 B. 1/2 C. 2/3 2𝑡𝑎𝑛⁡30° 1+𝑡𝑎𝑛⁡²30° 58. is.......... A. 3 o B. 1/2 C. 3/2 59. Point P lies in the exterior of a circle and two tangents from P touch the circle at A and B. If ∠PAB = 45°, then ∠PBA =.......... o A. 90° o B. 45° o C. 135° 60. If the mean of 6, 7, x, 8, y, 14 is 9, then x + y =..........  o A. 9 o B. 19 o C. 14 61. For any two positive integers a and b, HCF (a, b) × LCM (a, b) = a × b. The graph of the quadratic polynomial 𝑝(𝑥) = 𝑎𝑥² + 𝑏𝑥 + 𝑐 62. intersects the x-axis at two points at least. The graph of 4𝑥 + 7𝑦 = 0 63. is a line passing through the origin. 64. A number is selected at random from the single-digit natural numbers. The probability of that number being even is 1/2. 65. Find the sum of the first 15 multiples of 12. 66. The common point of a circle and its tangent is known as.......... o A. the point of tangency If 𝑃(𝐴): 𝑃(𝐴) = 8: 7 , find 𝑃(𝐴) 67.. For a given data, if 𝑍 = 15 and 𝑥 = 15 68. , then find M. If (1, 0) is one of the solutions of equation 8𝑥 + 3𝑦 + 5𝑘 = 18 , then 𝑘 = 69........... A. 8 B. 4 C. 2 D. 5 2 The discriminant of the equation 𝑥 − 4𝑥 + 7 = 0 70. is.......... A. 12 B. -12 C. 44  D. -44 The sum of first 𝑛 terms of the AP 𝑘, 3𝑘, 5𝑘,... is.......... (𝑘 ≠ 0 71. ) A. 𝑛𝑘 B. (2𝑛 − 1)𝑘 C. (𝑛 + 1)𝑘 2 D. 𝑛 𝑘 72. The perpendicular distance of the point (-3, 8) from the y-axis is.......... A. 3 B. 8 C. 11 D. 5 4 2 𝑠𝑒𝑐 ⁡θ − 𝑠𝑒𝑐 ⁡θ = 73........... 2 4 A. 𝑡𝑎𝑛 ⁡θ − 𝑡𝑎𝑛 ⁡θ 4 2 B. 𝑡𝑎𝑛 ⁡θ − 𝑡𝑎𝑛 ⁡θ 4 2 C. 𝑡𝑎𝑛 ⁡θ + 𝑡𝑎𝑛 ⁡θ 2 4 D. 𝑐𝑜𝑠 ⁡θ − 𝑐𝑜𝑠 ⁡θ 74. If the mode of a frequency distribution exceeds its mean by 12, then the mode exceeds its median by.......... A. 4 B. 8 C. 6 D. 10 2 The HCF of 20α 𝑏 2 and 30α𝑏 75. is.......... 2 2 A. 10α 𝑏 B. 10α𝑏 2 2 C. 60α 𝑏 The zeroes of the polynomial 𝑝(𝑥) = 3𝑥 − 7 76. is.......... 7 A. 3 7 B. 3 3 C. 7 If 5𝑃(𝐴) = 3𝑃(𝐴) , then 𝑃(𝐴) = 77........... 5 A. 8 3 B. 8 3 C. 5 5 D. 8 If 𝑠𝑖𝑛⁡θ = 𝑡 , then 𝑐𝑜𝑠⁡θ = 78........... 2 A. 1 − 𝑡 2 B. 1 + 𝑡 2 C. 1 −𝑡 79. A tangent of a circle intersects the circle at........ point(s). o A. one o B. two o C. three If the mode of the observations is 15, 17, 23, 28, 23, 25, 19, 28, 𝑥 is 23, then 𝑥 + 7 = 80........... o A. 30 o B. 35 o C. 32 For two positive integers 𝑎 and 𝑏 , it is possible that HCF(𝑎, 𝑏 ) = 15 and LCM(𝑎, 𝑏 81. ) = 162. 2 The sum of the zeroes of the quadratic polynomial 3𝑥 + 5𝑥 − 2 5 is 3 82.. 83. A pair of linear equations in two variables having no solution is not a consistent pair of linear equations. 3 The probability of having 53 Mondays in the year 2020 is 7 84.. For a given AP, 𝑎25 − 𝑎15 = 24 85.. Find the common difference of the AP. ◦ In cyclic quadrilateral ABCD, ∠𝐴 = ∠𝐶 − 40. Find ∠𝐴 86.. 87. The probability of getting a defective shirt in a lot of 400 shirts is 0.035. Find the number of defective shirts. 88. Find the algebraic sum of the deviations of all the observations from their mean. 89. Volume of a cone 1 2 A. 3 π𝑟 ℎ 1 2 B. 2 π𝑟 ℎ 2 2 C. 3 π𝑟 ℎ 90. Volume of a sphere 4 3 A. 3 π𝑟 3 B. π𝑟 2 3 C. 3 π𝑟 91. Angle formed at the center by the minute hand when it revolves for 20 minutes  ◦ A. 120 ◦ B. 60 ◦ C. 180 92. Angle formed at the center by the minute hand when it revolves for 45 minutes ◦ A. 270 ◦ B. 180 ◦ C. 360 93. Curved Surface Area of Sphere: 2 A. π𝑟 ℎ B. 2π𝑟ℎ 2 C. 4π𝑟 94. Curved Surface Area of Cylinder: 2 A. π𝑟 ℎ B. 2π𝑟ℎ 2 C. 4π𝑟 Area of a sector of a circle with radius 𝑟 formed by an arc of length 𝑙 95. : A. π𝑟𝑙 1 B. 2 𝑟𝑙 C. 2π𝑟 96. Circumference of a circle: A. π𝑟𝑙 1 B. 2 𝑟𝑙 C. 2π𝑟 The sum of the numerator and the denominator of a fraction is 16. If 5 is added to its 1 denominator, it reduces to 2 97.. Then, that fraction is......... 9 A. 7 4 B. 12  7 C. 9 12 D. 4 2 If the roots of the equation 6𝑥 − 13𝑥 + 𝑘 = 0 are reciprocal of each other, then 𝑘 = 98.......... A. -13 B. -6 C. 6 D. 78 For a given AP, if 𝑑 = 5 , then 𝑎18 − 𝑎13 = 99.......... A. 5 B. 20 C. 25 D. 30 100. The midpoint of the line segment joining (1, 1) and (3, 3) is......... A. (1, 1) B. ( 2 3 , 2 3 ) C. ( ) 3 3 2 , 2 D. (2, 2) 1 2 = 1+𝑡𝑎𝑛 ⁡θ 101.......... 2 A. 𝑠𝑖𝑛 ⁡θ 2 B. 𝑐𝑜𝑠 ⁡θ 2 C. 𝑡𝑎𝑛 ⁡θ 2 D. 𝑐𝑜𝑡 ⁡θ Usually, for any frequency distribution, Mode - Median =........ × 102. (Median - Mean). A. 1 B. 2  C. 3 D. 4 103. The HCF of the smallest prime number and the smallest composite number is......... (2, 1, 4) 2 The graph of 𝑝(𝑥) = 𝑥 + 4𝑥 + 3 104. is a......... (line, parabola opening upwards, parabola opening downwards) The probability of the month of January having 5 Sundays is......... ( 1 7 , 2 7 , 3 7 ) 1 If 𝑠𝑖𝑛⁡α = 2 and 𝑐𝑜𝑡⁡β = 1 , then α + β = 105.......... (75°, 90°, 105°) 106. Quadrilateral XYZW circumscribes a circle. If XY = 13.8 cm, YZ = 10.7 cm and ZW = 7.5 cm, then XW =........ cm. (17, 4.4, 10.6) The mean of first 𝑛 ( ) 2 𝑛+1 𝑛(𝑛+1) 𝑛 natural numbers is......... 2 , 2 , 2 (9 + 5 )(9 - 5 107. ) is an irrational number. A polynomial of degree 𝑛 has at the most 𝑛 + 1 108. zeroes. The graph of the equation 3𝑦 − 8 = 7 109. is a line parallel to the x-axis. 110. The sum of probabilities of all elementary events is 1. If 𝑘 − 3 ,𝑘 + 7 , 2𝑘 + 7 are three consecutive terms of an AP, find the value of 𝑘 111.. 112. Find the inradius of a triangle with sides measuring 12 cm, 35 cm and 37 cm. If 𝑃(𝐴) − 𝑃(𝐴) = 0. 2 , find 𝑃(𝐴) 113.. 114. State the mid-value of the class 30 - 40. The number of zeroes of 𝑦 = 𝑝(𝑥) 115. is 2 from the figure given below. If the pair of linear equations in two variables are 2𝑥 + 3𝑦 = 12 and 3𝑥 + 2𝑦 = 18 , then 𝑥 + 𝑦 = 5 116.. 117.The probability of an impossible event is zero (0). 𝑎, 2𝑎, 3𝑎, 4𝑎,... 118. is an Arithmetic Progression or not? 119. How many tangents can be drawn to a circle passing through a point lying inside the circle? 120. A die is thrown once. What is the probability of not getting number 6? 121. Find the mean of the first 11 natural numbers. 122. Base area of a hemisphere A. 2π𝑟ℎ 2 B. π𝑟 2 C. π𝑟 ℎ 125. Volume of a 5 rupee coin A. 2π𝑟ℎ 2 B. π𝑟 2 C. π𝑟 ℎ Length of an arc of a sector of angle θ A. π𝑑 B. π𝑟 π𝑟θ C. 180 127. Circumference of a circle A. π𝑑 B. π𝑟 π𝑟θ C. 180 𝑎1 𝑏1 For a given pair of linear equations in two variables, if 𝑎2 ≠ 𝑏2 128. , then the equation has.......... solution. A. one B. two C. three D. no solution 2 If the two roots of the quadratic equation 𝑎𝑥 + 𝑏𝑥 + 𝑐 = 0 (𝑎 ≠ 0 129. ) are real and equal, then.......... 2 A. 𝑏 − 4𝑎𝑐 < 0 2 B. 𝑏 − 4𝑎𝑐 = 0 2 C. 𝑏 − 4𝑎𝑐 > 0 2 D. 𝑏 − 4𝑎𝑐 ≠ 0 130. For the AP: 4, 10, 16, 22,... the common difference (d) is.......... A. 8 B. 5 C. 6 D. 12 131. The distance between the points (0, 5) and (-5, 0) is.......... A. 5 B. 5 2 C. 2 5 D. 10 2 2 𝑠𝑒𝑐 ⁡θ − 𝑡𝑎𝑛 ⁡θ = 132........... A. 0 B. 1 C. -1 D. 2 For any data 𝑥‾ = 25 and 𝑍 = 25 , then 𝑀 = 133........... A. 25 B. -25 C. 5 D. -5 3+2 5 134. is a/an.......... number. (rational, irrational, negative integer) 2 The sum of zeroes of the quadratic polynomial 4𝑥 − 3𝑥 − 7 135. is.......... 3 A. 4 4 B. 3 7 C. 3 136. When a coin is tossed three times, the total number of possible outcomes is.......... (4, 6, 8) 𝑡𝑎𝑛⁡θ · 𝑐𝑜𝑡⁡θ = 137........... (−1, 0, 1) 138. A circle can have.......... parallel tangents at the most. (1, 2, 3) 139. The median of -2, -3, 0, 1, 3, 2, 7 is.......... (−2, 1, 3) 140. HCF of 17, 23 and 29 is 1.