Mensuration (Railway Maths) (Part – III)

Total Questions: 50

1. The area of a rectangle is 225 cm². The length (x) of the rectangle is 4 more than 4 times the breadth (y). The area in terms of a quartic form (in x) is: [Group D 15/09/2022 (Evening)]

Correct Answer: (a) x² − 4x − 900 = 0
Solution:

2. The total surface area (in m²) of a cube, each of whose edges measures 4 m, is: [Group D 16/09/2022 (Morning)]

Correct Answer: (d) 96
Solution:

Given, side of the cube = 4 m
T.S.A of the cube = 6 × 𝑠𝑖𝑑e²
= 6 × 4 × 4 = 96 m²

3. The ratio of the lengths of two corresponding sides of two similar triangles is 2 : 1. The ratio of the areas of these two triangles, in the order mentioned, is: [Group D 16/09/2022 (Afternoon)]

Correct Answer: (c) 4 : 1
Solution:

From the properties of similar triangle, The ratio of the area of two similar triangles is equal to the squares of the ratio of its corresponding sides. So, ratio of area of the triangles
= 2² : 1² ⇒ 4 : 1

4. The volumes of two spheres are in the ratio of 27 : 8. The ratio of the surface areas of these spheres, in the order in which they are mentioned here, is________: [Group D 16/09/2022 (Afternoon)]

Correct Answer: (b) 9 : 4
Solution:

5. If the radius of a sphere is halved, then the new volume will become ______ the original volume. [Group D 16/09/2022 (Evening)]

Correct Answer: (a) 1/8 times
Solution:

6. If the area of a triangle whose base measures 3 cm is 4 cm², then its corresponding height is: [Group D 16/09/2022 (Evening)]

Correct Answer: (c)
Solution:

7. If a square has a side of (5x − 8) cm, then the area of the square (in cm²) is: [Group D 16/09/2022 (Evening)]

Correct Answer: (d) 25x² − 80x + 64
Solution:

8. If the curved surface area of a right circular cylinder is 880 cm² and the diameter of its base is 7 cm, then the height (in cm) of the cylinder is ________. Take π = 22/7 [Group D 17/09/2022 (Morning)]

Correct Answer: (a) 40
Solution:

9. 1000 identical small spheres are cast from a sphere of radius 10 cm, with the total volume of the small spheres being equal to the volume of the larger sphere. The diameter (in cm) of each of the small spheres is: [Group D 17/09/2022 (Evening)]

Correct Answer: (b) 2
Solution:

10. The length of a rectangular park is 22 m more than its breadth. Its area is 1400 m². Its breadth (in m) is: [Group D 17/09/2022 (Evening)]

Correct Answer: (c) 28
Solution: