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
121
What is the volume of a cube whose side length is 8 cm?
Answer:
512 cm³
The formula for the volume of a cube is V = side³. Given the side length is 8 cm, the volume is 8 × 8 × 8 = 512 cm³.
122
Find the total surface area of a cone whose radius is r/2 and slant height is 2l.
Answer:
πr(l + r/4)
Step 1: TSA of a cone = πR(R + L). Step 2: Here, R = r/2 and L = 2l. Step 3: TSA = π(r/2)(r/2 + 2l) = πr/2(r/2 + 2l) = πr(r/4 + l) = πr(l + r/4).
123
A sphere of radius 6 cm is dropped into a cylindrical vessel partly filled with water. The radius of the vessel is 8 cm. If the sphere is submerged completely, by how much will the surface of water be raised?
Answer:
4.5 cm
Step 1: Volume of sphere = (4/3)π(6)³ = 288π cm³. Step 2: Volume of raised water = π(8)²h = 64πh. Step 3: 64πh = 288π -> h = 288 / 64 = 4.5 cm.
124
What is the volume of a hemisphere if its radius is 21 cm?
Answer:
19404 cm³
Step 1: V = (2/3)πr³. Step 2: V = (2/3) × (22/7) × (21)³ = 44 × 21 × 21. Step 3: 44 × 441 = 19404 cm³.
125
A room is 15 m long, 10 m broad, and 5 m high. Find the cost of painting its four walls at Rs. 10 per m².
Answer:
Rs. 2500
Step 1: Area of 4 walls (LSA) = 2h(l + b). Step 2: LSA = 2 × 5 × (15 + 10) = 10 × 25 = 250 m². Step 3: Cost = 250 × 10 = Rs. 2500.
126
If the surface area of a cube is 384 cm², find its volume.
Answer:
512 cm³
Step 1: 6a² = 384 -> a² = 64 -> a = 8 cm. Step 2: Volume = a³ = 8³. Step 3: V = 512 cm³.
127
A cone and a cylinder have equal bases and equal heights. The ratio of their volumes is:
Answer:
1:3
Step 1: Volume of cone = (1/3)πr²h. Volume of cylinder = πr²h. Step 2: Ratio = (1/3)πr²h : πr²h. Step 3: 1/3 : 1 = 1:3.
128
What is the ratio of the volume of a cylinder to the volume of a cone with the same base radius and height?
Answer:
3:1
Step 1: Volume of cylinder = πr²h. Volume of cone = (1/3)πr²h. Step 2: Ratio = πr²h / ((1/3)πr²h) = 1 / (1/3). Step 3: Ratio is 3:1.
129
The dimensions of a cuboid are 5 cm, 4 cm, and 2 cm. It is melted to form a cube. What is the side of the cube?
Answer:
³√40 cm
Step 1: Volume of cuboid = 5 × 4 × 2 = 40 cm³. Step 2: Volume of cube = a³ = 40. Step 3: a = ³√40 cm.
130
The total surface area of a cube is 216 cm². Find its diagonal.
Answer:
6√3 cm
Step 1: 6a² = 216 -> a² = 36 -> a = 6 cm. Step 2: Diagonal = a√3. Step 3: Diagonal = 6√3 cm.