SOLVED PAPER 2024 (CDS) (II) (Mathematics)

Total Questions: 100

41. The mean weight of 150 students in a class is 60 kg. The mean weight of boys in the class is 70 kg and that of girls is 55 kg. What is the ratio of number of boys to number of girls?

Correct Answer: (a) 1 : 2
Solution:

42. Two towers A and B of height 23 m and 11 m respectively, stand 9 m apart. A straight rod is joined to the two tops of the towers. A monkey sitting on the top of A, climbs the rod to reach the top of B. If the monkey takes 5 min to reach the other end, what is the average speed of the monkey?

Correct Answer: (d) 5 cm/sec
Solution:

43. A spherical wooden ball of radius r is to be divided into eight identical parts by cutting by planes passing through the same diameter. What is the surface area of each final piece?

Correct Answer: (b) 3πr²/2
Solution:Total surface area of sphere = 4πr²
Sphere is cutting in 8 equal parts by plane.
∴ 8 parts of total surface area
= 4πr² + 4(2πr²) = 12πr²
Each surface area = 12π²/8 = 3πr²/2
∴ (b) is the correct answer.

44. A trolley with two wheels 1m apart is moved clockwise on the circular track around a ground with radius 50 m (described by right wheel). If the size of each wheel is of 1 foot radius and the right wheel turns 1000 times, how many times will the other wheel turn?

Correct Answer: (c) 1020
Solution:

45. What is the remainder when 70 × 71 × 72 × 73 × 74 × 75 × 76 × 77 × 78 × 79 is divided by 1000?

Correct Answer: (d) 0
Solution:

46. A vertical pole of length 80 m is situated on the horizontal plane. The base of the pole is at P. There are two points A and B such that P, A, B are on the same straight line. Let the angles of elevation of top of the pole from A and B be α and β (α > β) respectively. If PA = 64 m and AB = 36 m, then what is (α + β) equal to

Correct Answer: (b) 90°
Solution:

47. Let k be a positive integer. What is the quotient when x⁸ᵏ⁺³ + x⁸ᵏ⁺⁶+ x⁸ᵏ⁺⁹+ x⁸ᵏ⁺¹² is divided by (1 + x³)(1 + x⁶) ?

Correct Answer: (d) x⁸ᵏ⁺³
Solution:

48. A square is drawn inside a square of side 14 cm in such a way that the corners of the inner square coincide with the mid points of the sides of the outer square. What is the area lying between the two squares?

Correct Answer: (a) 98cm²
Solution:

49. The base of a right-angled triangle is 4/3 times the height of triangle. If the area of the triangle is 54cm², then what is the perimeter of the triangle?

Correct Answer: (c) 36 cm
Solution:Given that, ABC is a right angle triangle.
The base of right angle triangle is
times the height of triangle. 4/3

50. What is the area of a triangle having sides 4, 4 and 6 units?

Correct Answer: (a) 3√7 square unit
Solution: