Polytechnic Math Set 6

101. In a batch of 20 bulbs, 4 are defective. If a bulb is randomly selected from this batch, what is the probability that the bulb is defective?

1/5 1/20 4/5 None of these

Answer: 1/20

102. If tan(A + B) = √3, tan(A – B) = 1/√3, and 0 < A + B ≤ 90°, then A and B are:

30°, 15° 30°, 30° 60°, 45° 45°, 15°

Answer: 30°, 15°

103. 2 women and 5 men can finish a task in 4 days, while 3 women and 6 men can finish the task in 3 days. How many days will it take for one woman to complete the task alone?

20 days 18 days 15 days 28 days

Answer: 20 days

104. In ΔABC, ∠C = 3∠B = 2(∠A + ∠B), then ∠C =

100° 120° 110° 80°

Answer: 120°

105. If the HCF and LCM of ‘a’ and 96 are 4 and 9696 respectively, then a =

44 4040 4004 404

Answer: 4040

106. If cotθ = 7/8, what is the value of (1 + sinθ)(1 – sinθ) / (1 + cosθ)(1 – cosθ)?

49/64 9/64 49/8 None of these

Answer: 49/64

107. Which of the following is not true?

sin30° = 1/2 cos30° = √3/2 sin90° = 0 cos0° = 1

Answer: sin90° = 0

108. If the circumference of a circle is 22 cm, what will be the area of its semicircle?

77/8 cm² 77 cm² 77/2 cm² 77/4 cm²

Answer: 77/4 cm²

109. The length of the tangent from point Q to a circle is 8 cm, and the distance from Q to the center is 10 cm. What is the radius of the circle?

2 cm 7 cm 6 cm 18 cm

Answer: 6 cm

110. If α and β are the roots of the equation 2x² – 4x – 3 = 0, what is the value of α² + β²?

5 7 3 -4

Answer: 7

111. If sinA = 5/13, 0 < A < 90°, find tan A.

4/5 12/5 5/12 None of these

Answer: 4/5

112. If the endpoints of a diameter are (-1, 5) and (5, -1), what are the coordinates of the center of the circle?

(2, 2) (-2, -2) (4, 4) None of these

Answer: (2, 2)

113. What is the 30th term of the sequence 10, 7, 4, …?

97 77 -77 -87

Answer: -77

114. The roots of the equation 3x² – 2x + 1/3 are

Real and equal Imaginary Real and distinct None of these

Answer: Imaginary

115. If x(x + 1) + 8 = (x + 2)(x – 2), what is the value of x?

12 -12 10 None of these

Answer: -12

116. The average of 40 numbers is 35. If two numbers, 84 and 62, are excluded, what is the average of the remaining numbers?

34 33 30 37

Answer: 34

117. The average weight of 5 men is 63 kg, and the average weight of 4 women is 38 kg. What is the average weight of 15 members?

54 kg 57 kg 60 kg Cannot be determined

Answer: Cannot be determined

118. A sum of money triples in 18 years at simple interest. What is the annual rate of interest?

9.09% 11.11% 9% 18%

Answer: 11.11%

119. If 3a + b = 9 × 81 × 27, what is the value of (a + b)²?

9 81 196 576

Answer: 196

120. The difference between the current ages of a father and son is 20 years. After 5 years, their ages will be in the ratio 2:1. What is the current age of the son?

5 years 15 years 10 years 20 years

Answer: 10 years