Polytechnic Math Set 13

241. The sum of two numbers is 161. If one number is 30% more than the other, the numbers are

71 and 90 70 and 91 54 and 107 60 and 101

Answer: 70 and 91

242. The common factor of \( p^2 + 9p + 14 \) and \( p^2 + 13p + 42 \) is

\( p + 2 \) \( p + 6 \) \( p + 3 \) \( p + 7 \)

Answer: p + 7

243. Pramod and Praveen are the sons of Prajwal. Prajwal’s current age is 4 times the age of Pramod and 6 times the age of Praveen. If the sum of their ages is 51 years, the sons’ current ages are

9 years and 6 years 8 years and 9 years 9 years and 4 years 5 years and 9 years

Answer: 9 years and 6 years

244. In \( ΔMNO \), an inscribed circle touches sides \( MN = 12 \) cm, \( MO = 14 \) cm, and \( NO = 18 \) cm at points \( P \), \( Q \), and \( R \) respectively. Then, \( MP + NQ + RO \) is

18 cm 20 cm 22 cm 44 cm

Answer: 22 cm

245. The angle between the hands of a clock at 4 o’clock is

60° 90° 150° 120°

Answer: 120°

246. If sinθ + cosecθ = 2, then sin²θ + cosec²θ =

4 3 2 1

Answer: 2

247. Two vertices of a triangle are (1, 3) and (4, 5). If its centroid is (7, 2), the third vertex is

(16, 8) (8, 12) (12, 8) (8, 16)

Answer: (16, 8)

248. Which of the following statements about parallel lines is always correct?

The sum of their slopes is zero The difference of their slopes is zero The product of their slopes is zero The ratio of their slopes is 1

Answer: The difference of their slopes is zero

249. Solving 2 sin 60° cos 30° cosec 45° / tan 45° cos 60° sin 45° gives

6 3√2 3/√2 3√2/2

Answer: 6

250. The sum of the first 20 odd natural numbers is

210 250 200 400

Answer: 400

251. Mr. A and Miss B are friends. The probability that their birthdates are different is (ignoring leap years)

1/365 2/365 364/365 1

Answer: 364/365

252. There is an empirical relationship between the three measures of central tendency

2 Mean + Mode = 3 Median Median + Mode = 2 Mean Mean + 2 Mode = 3 Median Mode + Mean = 2 Median

Answer: Mode + Mean = 2 Median

253. A cone made of modeling clay has a height of 24 cm and a base radius of 6 cm. A child reshapes it into a sphere. What will be the radius of the sphere?

6 cm 8 cm 9 cm 3 cm

Answer: 6 cm

254. If two cubes, each with a volume of 64 cm³, are joined at their faces, the surface area of the resulting cuboid is

128 cm² 160 cm² 162 cm² 64 cm²

Answer: 160 cm²

255. The area of a quarter circle with a circumference of 22 cm (in cm²) is

77/8 70 100 11

Answer: 77/8

256. In the figure, if TP and TQ are two tangent lines from center O to a circle, and ∠POQ = 110°, then what is ∠PTQ?

60° 70° 80° 90°

Answer: 70°

257. From a point on the ground, which is 30 meters away from the base of a tower, the elevation angle to the top of the tower is 30°. What is the height of the tower in meters?

√3 30√3 10√3 10

Answer: 10√3

258. (sec A + tan A) (1 – sin A) =

sec A sin A cosec A cos A

Answer: cos A

259. The value of sin² 63° + sin² 27° is

0 1 1/2 3/2

Answer: 1

260. If sin 2A = 2sin A, then what is A?

0° 30° 45° 60°

Answer: 0°