NUMBER SYSTEMS AND PROGRESSION

 NUMBER SYSTEMS AND PROGRESSION

41. Find the sum of 17 terms of the A.P. 5, 9, 13, 17, …

a) 623 

b) 580 

c) 629 

d) 650 

ANS. c 

42. Find the sum of the series 2+5+8+ … +182 

a) 5520 

b) 5612 

c) 5623 

d) 5418 

ANS. b 

43. Insert A.M.’s (Arithmetic Mean) between 7 and 71 in such a way that the 5th A.M. is 27. The 

number of A.M.s are 

a) 12 

b) 17 

c) 15 

d) 51 

ANS. b 

44. Find the 5th term from the end of the G.P. 3, 6, 12, 24, …, 12,288 

a) 384 

b) 192 

c) 1536 

d) 768 

ANS. d 

45. Find the Harmonic Mean between 2/3 and -4/3. 

a) 8/3 

b) 16/3 

c) -8/3 

d) -16/3 

ANS. a 

46. If z = (2-3i) and z²-4z+13 = 0 and hence find the value of (4z³-3z²+169) 

a) 0 

b) -1 

c) 10 

d) 9 

ANS. a 

47. Write the modulus of 2+ √-3. 

a) √ 7 

b) √ 5 

c) √ 13 

d) √8 

ANS. a 

48. A car travels 432 km on 48 litres of petrol. How far will it travel on 20 litres of petrol? 

a) 18 

b) 9 

c) 34 

d) 180 

ANS. d 

49. If x and y vary inversely as each other, x = 10 when y = 6. Find y when x=15. 

a) 25 

b) 4 

c) 90 

d) 60 

ANS. b 

50. 55 cows can graze a field in 16 days. How many cows will graze the same field in 10 days? 

a) 84 cows 

b) 34 cows 

c) 88 cows 

d) 44 cows 

ANS. b 

51. Solve log √8/log 8 is the same as 

a) 1/√8 

b) 1/8 

c) ¼ 

d) ½ 

ANS. d 

52. If log 27 = 1.431, then the value of log 9 is:

a) 0.934 

b) 0.958 

c) 0.945 

d) 0.954 

ANS. d 

53. If log10 2 = 0.3010, then log2 10 is equal to:

a) 0.6990 

b) 1000/301 

c) 699/301 

d) 0.3010 

ANS. b 

54. A private taxi charges a fare of Rs. 260 for a journey of 200 km. How much would it travel 

for Rs 279.50? 

a) 215 

b) 363.35 

c) 186 

d) 240 

ANS. a 

55. Log 36 / log 6 

a) 5 

b) 8 

11

c) 3 

d) 2 

ANS. d 

56. Evaluate Log 243 / Log 9 

a) 3/2 

b) 5/2 

c) 7/2 

d) 9/2 

ANS. b 

57. The value of (1+ i)(1 +i²)(1+i³)(1+ ) 

a) 2 

b) 0 

c) 1 

d) i 

ANS. b 

58. The polar form of ( )³ is 

a) Cos π/2 + i Sin π/2 

b) Cos π + i Sin π

c) Cos π – i Sin π

d) Cos π/2 - i Sin π/2 

ANS. d 

59. If a = 1 + i , then a² equals 

a) 1 – i 

b) 2i 

c) (1 + i)(1 - i) 

d) i – 1 

ANS. b 

60. If θ is the amplitude of (a + ib) / (a – ib), then tan θ = 

a) 2a / a² + b² 

b) (a² - b²) / (a² + b²) 

c) 2ab / ( a² - b²) 

d) None of these 

ANS. c 

61. The argument of (1 – i) / (1 + i) is 

a) – π / 2 

b) π / 2 

c) 3 π / 2 

d) 5 π / 2 

ANS. a 

62. The conjugate of a complex number z = (a + ib) is 

a) – a – ib 

b) b – ai 

c) b + ai 

d) a – ib 

ANS. d 

63. If a = cos θ + I sin θ, then (1 + a) / (1 – a) = 

a) cot θ / 2 

b) cot θ

c) i cot θ / 2 

d) i tan θ / 2 

ANS. c 

64. The sum of three numbers in G.P. is 35 and their product is 1000. The numbers are 

a) 5, 10, 20 

b) 20, 10, 15 

c) 10, 5, 0 

d) 20, 10, 10 

ANS. a 

65. How many terms of the A.P. 1, 4, 7, 10, … are needed to give the sum 715. 

a) 21 

b) 11 

c) 22 

d) 19 

ANS. c 

66. How many terms of A.P. 21, 18, 15, 12, … must be taken to give the sum zero. 

a) 10 

b) 15 

c) 22 

d) 11 

ANS. b 

67. The sum of all odd numbers between 100 and 200 is 

a) 7,000 

b) 8,000 

c) 8,500 

d) 7,500 

ANS. d 

68. (-3/5) x (-10/9) x (21/-4) x (-6) 

a) 21 

b) 42 

c) 35 

d) 15 

ANS. a 

69. The reciprocal of a negative rational number is 

a) Positive 

b) 0 

c) 1 

d) Negative 

ANS. d 

70. The multiplicative inverse of (-5 / 8) x (16 / 15) 

a) – 2 / 3 

b) 2 / 3 

c) -3 / 2 

d) 3 / 2 

ANS. b 

71. The additive inverse of (-11 / -14) is 

a) 11 / 14 

b) – 14 / 11 

c) 14 / 11 

d) – 11 / 14 

ANS. d 

72. ( - 3 / 2) + (5 / 4) – (- 7 / 4) 

a) -2 

b) 2 

c) 7/4 

d) 3 / 2 

ANS. a 

73. -6 ÷ (-8 / 17) 

a) 48 / 17 

b) – 51 / 4 

c) 51 / 4 

14

d) – 48 / 17 

ANS. c 

74. The twentieth term of √2, 3√2, 5√2, 7√2, … is 

a) 28√2 

b) 19√2 

c) 30√2 

d) 39√2 

 ANS. d 

75. If n arithmetic means are inserted between 1 and 31, such that the ratio of the first mean and 

the nth mean is 3 : 29, then the value of n is 

a) 10 

b) 12 

c) 13 

d) 14 

ANS. d 

76. If in an A.P. = n²p and = m²p, where denotes the sum of r terms of the A.P., then 

 is equal to 

a) 1/2 p³ 

b) mn p 

c) p³ 

d) (m + n) p² 

ANS. c 

77. The sum of all two digit numbers when divided by 4, yield unity as remainder is 

a) 1200 

b) 1210 

c) 1250 

d) None of these 

ANS. b 

78. If the sum of p terms of an A.P. is q and the sum of q terms is p, then the sum of p + q terms 

will be 

a) 0 

b) p – q 

c) p + q 

d) –(p + q) 

ANS. d 

15

79. If in an infinite G.P., the first term is equal to the sum of all successive terms then its 

common ratio is 

a) 1 / 10 

b) 1 / 11 

c) 1 / 9 

d) 1 / 20 

ANS. b 

80. The two geometric means between the numbers 1 and 64 are 

a) 1 and 64 

b) 2 and 16 

c) 4 and 16 

d) 3 and 16 

ANS. c 

81. If the second term of G.P. is 2 and the sum of its infinite terms is 8, then its first term is 

a) 1 / 4 

b) 1 / 2 

c) 2 

d) 4 

ANS. d 

82. In 15 days the earth picks up 1.2 x kgs of dust from the atmosphere. It will pick 4.8 x 

kgs of dust in 

a) 40 days 

b) 60 days 

c) 50 days 

d) 30 days 

ANS. b 

83. Thickness of a pile of 12 cardboards is 35 mm. Hence the thickness of a pile of 294 

cardboards is 

a) 80.50 cm 

b) 83.75 cm 

c) 85.75 cms 

d) 81.50 cms 

ANS. c 

84. 52 men can do a piece of work in 12 days. 28 men will do it in 

a) 65 days 

b) 60 days 

c) 56 days 

d) 67 days 

16

ANS. a 

85.

√14 is called 

a) Cubic surd 

b) Compound surd 

c) Biquadratic surd 

d) Quadratic surd 

ANS. d 

86. Cube root of 5 x cube root of 7 is 

a) Cube root of 35 

b) Cube root of 12 

c) Cube root of 7 / 5 

d) Cube root of 2 

ANS. a 

87. 4 

√5 + 6

√5 + ½

√5 = 

a) 23 / 2

√5 

b) 12

√5 

c) 21/2

√5 

d) 2 / 3 

√5 

ANS. c 

88. = 243 is same as 

a) Log3 243 = 5 

b) Log5 243 = 3 

c) Log243 5 = 3 

d) Log243 3 = 5 

ANS. a 

89. The set of irrational numbers is 

a) Finite 

b) Countable 

c) Uncountable 

d) Infinite 

ANS. c 

90. The union of infinite number of open sets is 

a) An open set 

b) A closed set 

c) Need not be an open set 

d) Not a set 

ANS. a