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

Total Questions: 100

11. The height of a cone is 30 cm. A small cone is cut off at the top by a plane parallel to its base. If its volume is ⅐ of the volume of the given cone, then what is the height of the frustum of the cone?

Correct Answer: (a) 10 cm
Solution:

12. A rectangular metal sheet is of length 24 cm and breadth 18 cm. From each of its corners a square of side x cm is cut off and an open box is made of the remaining sheet. If the volume of the box is 640 cubic cm, then what is the value of x?

Correct Answer: (c) 4

13. Let x, y, z be the length, breadth, height of a cuboid. If its volume is 400 cubic cm and total surface area is 340 square cm, then what is x⁻¹ + y⁻¹ + z⁻¹ equal to?

Correct Answer: (b) ¹⁷⁄₄₀
Solution:

14. Two parallel sides of a trapezium are 29 cm and 21 cm. Non-parallel sides are equal and each is of length 8.5 cm. What is the area of the trapezium?

Correct Answer: (a) 187.5 square cm
Solution:

15. A square copper plate of side 16 cm weighs 128 gm. A circular disc of diameter 14 cm is cut off from the plate. What is the weight of the remaining part? (Take π = ²²⁄₇)

Correct Answer: (d) 51 gm
Solution:

16. The area of a rhombus is 96 square cm and one of its diagonals is of length 12 cm. What is the perimeter of the rhombus?

Correct Answer: (b) 40 cm
Solution:

17. A right-angled triangle ABC is inscribed in a circle of radius 10 cm. The altitude drawn to the hypotenuse AC is of length 8 cm. If AB = x cm and BC = y cm then what is the value of xy?

Correct Answer: (a) 60
Solution:

18. Two circles touch externally. The sum of their areas is 89π square cm and the distance between their centres is 13 cm. What is the difference in their radii?

Correct Answer: (c) 3 cm
Solution:

19. A square and a rectangle have same perimeter. They differ in areas by 1 square cm. The length of the rectangle exceeds its breadth by

Correct Answer: (a) 1 cm
Solution:Here, a square and a rectangle
have same perimeter.
Let side of square be x cm and
dimension of rectangle be length y,
and breadth z.

4(y + z) = 4x
y + z = x,  .....(i)
According to the question,
(Area of a square)2
- (Area of rectangle)² = 1

x² - (yz)² = 1
⇒ (y + z)² - (yz)² = 1
⇒ (y + z - yz) (y + z + yz) = 1
If yz = 0 and y + z = 1

So, the length of the rectangle
exceeds its breadth by 1 cm.

20. Two rectangles are of same area equal to 480 square cm. They differ in lengths by 6 cm and breadths by 4 cm. What is the difference in their perimeters?

Correct Answer: (b) 4 cm
Solution:Let R₁ be the first rectangle
having length l₁ and breadth b₁ and
R₂ be the second rectangle having
length (l₁ + 6) and breadth (b₁ - 4)
respectively.
Perimeter of first rectangle (R₁)
= 2(I₁ + b₁)
Perimeter of second rectangle (R₂)
= 2(l₁ + 6 + b₁ - 4)
Difference between the perimeter of
both rectangle
= 2(l₁ + b₁ + 2) - 2(l₁ + b₁)
= 2(l₁ + b₁) + 4 - 2(l₁ + b₁)
= 4