Mathematics/General Ability MCQs
Topic Notes: Mathematics/General Ability
MCQs and preparation resources for competitive exams, covering important concepts, past papers, and detailed explanations.
Plato
- Biography: Ancient Greek philosopher (427–347 BCE), student of Socrates and teacher of Aristotle, founder of the Academy in Athens.
- Important Ideas:
- Theory of Forms
- Philosopher-King
- Ideal State
101
Two cylinders have equal volumes. The ratio of their heights is 1:9. What is the ratio of their radii?
Answer:
3:1
Since volumes are equal, πr₁²h₁ = πr₂²h₂. We know h₁/h₂ = 1/9. Therefore, r₁²/r₂² = h₂/h₁ = 9/1. Taking the square root, r₁/r₂ = 3/1.
102
The curved surface area of a right circular cylinder is 4400 cm² and its base circumference is 110 cm. Find its height.
Answer:
40 cm
Curved surface area = base circumference × height. So, 4400 = 110 × h. Height (h) = 4400 / 110 = 40 cm.
103
A cylindrical tank has a capacity of 6160 cubic meters. If the radius of its base is 14 m, find its depth. (Use π = 22/7)
Answer:
10 m
Volume V = πr²h. So, 6160 = (22/7) × 14 × 14 × h. 6160 = 616 × h. Depth (h) = 6160 / 616 = 10 m.
104
If the ratio of the volumes of two cubes is 27:64, what is the ratio of their total surface areas?
Answer:
9:16
Let the sides be a and b. V1/V2 = a³/b³ = 27/64, so a/b = 3/4. The ratio of their surface areas is a²/b² = (3/4)² = 9:16.
105
How many bricks, each measuring 20 cm × 10 cm × 5 cm, will be needed to build a wall 10 m long, 5 m high, and 20 cm thick?
Answer:
10000
First convert all dimensions to cm. Wall dimensions: 1000 cm × 500 cm × 20 cm. Volume of wall = 10000000 cm³. Volume of one brick = 20 × 10 × 5 = 1000 cm³. Number of bricks = 10000000 / 1000 = 10000.
106
Three solid metallic cubes of sides 3 cm, 4 cm, and 5 cm are melted and recast into a single solid cube. Find the side of the new cube.
Answer:
6 cm
The volume of the new cube equals the sum of the volumes of the three cubes. Total V = 3³ + 4³ + 5³ = 27 + 64 + 125 = 216 cm³. Side of new cube = ³√216 = 6 cm.
107
If the side of a cube is doubled, its volume becomes how many times the original volume?
Answer:
8 times
The volume of a cube is V = s³. If the side is doubled, the new side is 2s. The new volume is (2s)³ = 8s³, which is 8 times the original volume.
108
Find the total surface area of a solid hemisphere of radius 7 cm. (Use π = 22/7)
Answer:
462 cm²
The total surface area of a solid hemisphere is 3πr² (curved surface + circular base). TSA = 3 × (22/7) × 7 × 7 = 3 × 22 × 7 = 462 cm².
109
Calculate the volume of a sphere of radius 21 cm. (Use π = 22/7)
Answer:
38808 cm³
The volume of a sphere is (4/3)πr³. V = (4/3) × (22/7) × 21 × 21 × 21 = 4 × 22 × 21 × 21 = 38808 cm³.
110
What is the surface area of a sphere with a radius of 14 cm? (Use π = 22/7)
Answer:
2464 cm²
The surface area of a sphere is 4πr². Area = 4 × (22/7) × 14 × 14 = 4 × 22 × 2 × 14 = 2464 cm².