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
181
If the circumference of the base of a cylinder is 44 cm and its height is 10 cm, find its lateral surface area.
Answer:
440 cm²
Step 1: Circumference = 2πr = 44. Step 2: Lateral surface area (CSA) = 2πrh. Step 3: CSA = 44 × 10 = 440 cm².
182
A cone and a hemisphere have the same base and same volume. Find the ratio of their heights.
Answer:
2:1
Step 1: Vol of cone = (1/3)πr²h. Vol of hemisphere = (2/3)πr³. Step 2: Since volumes are equal, (1/3)πr²h = (2/3)πr³. Step 3: This simplifies to h = 2r. The height of the hemisphere is r. So ratio is 2r : r = 2:1.
183
The base radius of a cylinder is 14 cm and its height is 30 cm. Find its volume.
Answer:
18480 cm³
Step 1: V = πr²h. Step 2: V = (22/7) × (14)² × 30 = (22/7) × 196 × 30. Step 3: V = 22 × 28 × 30 = 18480 cm³.
184
A solid cube is melted to form five solid cubes whose volumes are in the ratio 1:1:8:27:27. Find the percentage by which the sum of the surface areas of these five cubes exceeds the surface area of the original cube.
Answer:
50%
Step 1: Let volumes be x, x, 8x, 27x, 27x. Total V = 64x. So original cube side = 4(x^(1/3)). Original SA = 6(16x^(2/3)) = 96x^(2/3). Step 2: Sides of the 5 cubes are 1, 1, 2, 3, 3 times x^(1/3). Their SA sum = 6(1² + 1² + 2² + 3² + 3²)x^(2/3) = 6(1+1+4+9+9)x^(2/3) = 6(24)x^(2/3) = 144x^(2/3). Step 3: Increase = 144 - 96 = 48. % increase = (48/96) × 100 = 50%.
185
The total surface area of a solid hemisphere is 108π cm². The volume of the hemisphere is:
Answer:
144π cm³
Step 1: TSA of hemisphere = 3πr² = 108π -> r² = 36 -> r = 6 cm. Step 2: Volume = (2/3)πr³ = (2/3)π(6)³. Step 3: V = (2/3)π(216) = 144π cm³.
186
A cylindrical pillar is 50 cm in diameter and 3.5 m in height. Find the cost of painting the curved surface of the pillar at the rate of Rs. 12.50 per sq. m.
Answer:
Rs. 68.75
Step 1: r = 25 cm = 0.25 m, h = 3.5 m. CSA = 2πrh = 2 × (22/7) × 0.25 × 3.5 = 5.5 m². Step 2: Cost = Area × Rate. Step 3: Cost = 5.5 × 12.50 = Rs. 68.75.
187
How many solid cylinders of radius 2 cm and height 3 cm can be made by melting a solid cylinder of radius 6 cm and height 12 cm?
Answer:
36
Step 1: Volume of large cylinder = π(6)²(12) = 432π. Step 2: Volume of small cylinder = π(2)²(3) = 12π. Step 3: Number of cylinders = 432π / 12π = 36.
188
Find the length of the longest stick that can be put in a cubical room of side 10 m.
Answer:
10√3 m
Step 1: The longest stick corresponds to the body diagonal of the cube. Step 2: The formula for the body diagonal of a cube is a√3. Step 3: Substitute a = 10 to get 10√3 m.
189
If a right circular cylinder and a right circular cone have the same radius and same volume, what is the ratio of the height of the cylinder to the height of the cone?
Answer:
1:3
Step 1: Volume of cylinder = πr²h1. Volume of cone = (1/3)πr²h2. Step 2: πr²h1 = (1/3)πr²h2. Step 3: h1 = (1/3)h2, so h1/h2 = 1/3, meaning the ratio is 1:3.
190
The surface area of a sphere is 616 cm². Find its volume. (Take π = 22/7)
Answer:
1437.33 cm³
Step 1: 4πr² = 616 -> 4 × (22/7) × r² = 616 -> r² = 49 -> r = 7 cm. Step 2: Volume = (4/3)πr³ = (4/3) × (22/7) × 343. Step 3: V = 4312 / 3 = 1437.33 cm³.