SOLVED PAPER 2023 (CDS) (II) (Elementary Mathematics)

Total Questions: 100

51. What is the radius of the sphere passing through the corners of the cuboid with edges 8 cm, 12 cm and 24 cm?

Correct Answer: (b) 14 cm
Solution:

52. A lamp shade is in the shape of a part of a cone and its top and bottom ends are circles whose circumferences are respectively 30 cm and 40 cm. The perpendicular distance between the ends is 6 cm.

If the cone were to be completed, then how far would its vertex be from the top end?

Correct Answer: (b) 18 cm
Solution:

53. A sum of money at 20% rate of compound interest per annum becomes more than 100 times in n yrs. What is the least value of n?

(use, log₁₀ 2 = 0.301 log₁₀ 3 = 0.477 )

Correct Answer: (d) 26
Solution:

54. The corners of an equilateral triangular plate were cut in such a manner that it forms a regular hexagonal plate. What is the ratio of the area of the triangular plate to the area of the hexagonal plate?

Correct Answer: (b) 3 : 2
Solution:

55. Two equal arcs of different circles C₁ and C₂ subtend angles of 60° and 75° respectively, at the centres. What is the ratio of the radius of C₁ to the radius of C₂ ?

Correct Answer: (b) 5 : 4
Solution:

56. ABC is a triangle with sides AB = 41cm, BC = 28cm and CA = 15cm If D, E and Fare the mid-points of AB, BC and CA respectively, then what is the area of the triangle DEF?

Correct Answer: (c) 31.5 sq cm
Solution:

57. A triangle has sides 13 cm, 14 cm and 15 cm long. What is the length of the smallest altitude of the triangle ?

Correct Answer: (b) 11.2 cm
Solution:

58. The circumference of a circle exceeds the diameter by 16.8 cm. What is the diameter the circle? (take, π = 22/7 )

Correct Answer: (d) 7.84 cm
Solution:

59. The hypotenuse AC of a right-angled ΔABC is 3√5 cm. If AB is doubled and BC is tripled such that ABC remains a right-angled triangle, the hypotenuse becomes 15 cm. What is AB + BC equal to?

Correct Answer: (b) 9 cm
Solution:

60. What is the area of the region between two concentric circles if the chord of the outer circle of length 14 cm is a tangent of the inner circle ? (take, π = 22/7)

Correct Answer: (d) 154 sq cm
Solution: