SOLVED PAPER 2022 (CDS) (II) (Elementary Mathematics)

Total Questions: 100

21. (Questions 21-23) Consider the following information for the next three questions that follow.

A conical vessel of radius 12 cm and height 16 cm is filled with water. A sphere is lowered into water and its size is such that it touches the sides of the vessel and it is just immersed.

What is the radius of the sphere?

Correct Answer: (b) 6 cm
Solution:Here, diameter of the sphere is
equal to the radius of the cone
= 12cm
∴ Radius of sphere = 6 cm

22. How much water will remain in the vessel after the overflow?

Correct Answer: (c) 480π mL
Solution:

23. What is the ratio of lateral surface area of the conical vessel to the surface area of the sphere?

Correct Answer: (c) ⁵⁄₃
Solution:

24. (Questions 24 and 25) Consider the following for the next two questions that follow.

A chord of length I of a circle makes an angle 90° at the centre of the circle.

What is the area of the minor segment ?

Correct Answer: (c)
Solution:

25. What is the area of the major segment?

Correct Answer: (a)
Solution:

26. Triangle ABC is right-angled at A and AD is perpendicular to BC. If BD = 7.5cm and DC = 10cm then what is AD equal to ?

Correct Answer: (c) 5√3 cm
Solution:

27. The perpendicular AD on the base BC of a triangle ABC intersects BC at D so that DB = 3CD Which one of the following is correct?

Correct Answer: (a) 2(AB + AC) (AB - AC) = BC²
Solution:

28. Triangle ABC is right-angled at C and AC = √3 BC. What is ∠ABC equal to

Correct Answer: (c) 60°
Solution:

29. In a triangle ABC, ∠A = 60°. What is AB° + AC° - BC² equal to?

Correct Answer: (a) AB ⋅ AC
Solution:

30. The diameter of a sphere made of copper is 3 cm. The sphere is melted and recast into a wire. If the length of the wire is half metre, then what is the diameter of the wire?

Correct Answer: (c) 0.6 cm
Solution: