Polytechnic Math Set 10

181. A car has two wipers that do not overlap. Each wiper has a blade of 42 cm length that moves through an angle of 120°. Find the total area cleaned during each sweep of the blade.

4224 cm² 3696 cm² 1848 cm² 5544 cm²

Answer: 3696 cm²

182. In the given figure, point P is 26 cm away from the center O of a circle, and the length of the tangent PT drawn from P to the circle is 24 cm. Find the radius of the circle.

25 cm 26 cm 24 cm 10 cm

Answer: 25 cm

183. Write the decimal expansion of 76/6250 without actual division.

0.01216 1216 12.16 0.1216

Answer: 0.01216

184. If θ is an acute angle such that tan²θ = 8/7, what is the value of (1+sinθ)(1-sinθ)/(1+cosθ)(1-cosθ)?

7/8 8/7 7/4 64/49

Answer: 7/8

185. In the given figure, what are the values of x and y?

x = 10; y = 14 x = 10; y = 40 x = 21; y = 25 x = 21; y = 84

Answer: x = 10; y = 14

186. In the given figure, O is the center of two concentric circles with radii 5 cm and 3 cm. Tangents PA and PB are drawn from an external point P to these circles. If PA = 12 cm, what is the length of PB?

5√2 cm 3√5 cm 4√10 cm 5√10 cm

Answer: 5√10 cm

187. Find the area of a quarter circle whose circumference is 22 cm.

38.5 cm² 77 cm² 9.625 cm² None of these

Answer: 9.625 cm²

188. In the A.P. 6, 13, 20, 27, ……, which term is 98 more than its 24th term?

34 36 38 None of these

Answer: 34

189. If the n-th term of the A.P. 9, 7, 5, … is equal to the n-th term of the A.P. 15, 12, 9, …, find the value of n.

6 9 8 7

Answer: 9

190. For the quadratic polynomial x² + kx + k, where k > 0, the roots are:

Both positive Both negative Always equal Always unequal

Answer: Both positive

191. If the points A(x, y), B(-5, 7), and C(-4, 5) are collinear, then the value of 2x + y + 3 is:

0 1 2 3

Answer: 2

192. sec⁴θ – sec²θ =

tan⁴θ – tan²θ tan²θ – tan⁴θ tan²θ + tan⁴θ None of these

Answer: tan⁴θ – tan²θ

193. If the mean of the numbers 27 + x, 31 + x, 89 + x, 107 + x, 156 + x is 82, then what is the mean of the numbers 130 + x, 126 + x, 68 + x, 50 + x, 1 + x?

125 75 85 105

Answer: 75

194. Find the decimal expansion of the rational number 27/1250.

2.16 0.0216 0.29 0.0296

Answer: 0.0216

195. Three consecutive vertices of a parallelogram are (-2, -1), (1, 0), and (4, 3). The fourth vertex is:

(-1, -2) (1, -2) (-1, 2) (1, 2)

Answer: (1, -2)

196. If the five observations x, x+2, x+4, x+6, and x+8 have a mean of 11, then find the value of x.

7 4 15 2

Answer: 7

197. Find the value of θ (0° < θ ≤ 90°), if 2 cos²θ = 1

30° 45° 60° 90°

Answer: 45°

198. If the length of the minute hand of a clock is 7 cm, then what is the angle formed by the minute hand at the center of the clock between 9:00 AM and 9:10 AM?

30° 45° 60° 75°

Answer: 60°

199. In the given figure, find the value of x in terms of a, b, and c.

ab/(b+c) ac/(b+c) ac/(a+b) None of these

Answer: ab/(b+c)

200. If 6x = secθ and x = tanθ, then find the value of 9(x² – 1/x²).

1 3/4 1/√2 1/4

Answer: 1