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
251
Find the curved surface area of a cylinder with radius 14 cm and height 5 cm. (Take π = 22/7)
Answer:
440 cm²
Step 1: The curved surface area (CSA) of a cylinder is 2πrh. Step 2: Substitute the values: CSA = 2 × (22/7) × 14 × 5. Step 3: CSA = 2 × 22 × 2 × 5 = 440 cm².
252
A cylindrical tank has a radius of 7 m and a height of 10 m. What is its volume? (Take π = 22/7)
Answer:
1540 m³
Step 1: The volume of a cylinder is V = πr²h. Step 2: Substitute the values: V = (22/7) × (7)² × 10. Step 3: V = (22/7) × 49 × 10 = 22 × 7 × 10 = 1540 m³.
253
If each edge of a cube is doubled, its surface area becomes how many times the original surface area?
Answer:
4 times
Step 1: Original surface area = 6a². Step 2: New edge = 2a, so new surface area = 6(2a)² = 6(4a²) = 24a². Step 3: 24a² is 4 times 6a².
254
If each edge of a cube is doubled, how many times will its volume become?
Answer:
8 times
Step 1: Let the original edge be 'a', so V1 = a³. Step 2: The new edge is '2a', so the new volume V2 = (2a)³ = 8a³. Step 3: V2 is 8 times the original volume V1.
255
Three solid cubes of sides 3 cm, 4 cm, and 5 cm are melted to form a new cube. What is the side of the new cube?
Answer:
6 cm
Step 1: Find the total volume of the three cubes: V = 3³ + 4³ + 5³. Step 2: V = 27 + 64 + 125 = 216 cm³. Step 3: The volume of the new cube is 216 cm³, so its side is ³√216 = 6 cm.
256
What is the total surface area of a cuboid with dimensions 8 cm × 6 cm × 5 cm?
Answer:
236 cm²
Step 1: The total surface area formula is TSA = 2(lb + bh + hl). Step 2: Substitute the values: TSA = 2(8×6 + 6×5 + 5×8). Step 3: TSA = 2(48 + 30 + 40) = 2(118) = 236 cm².
257
The volume of a cuboid is 320 cm³. If its length and breadth are 10 cm and 8 cm respectively, find its height.
Answer:
4 cm
Step 1: The volume of a cuboid is V = l × b × h. Step 2: Substitute the known values: 320 = 10 × 8 × h. Step 3: Solve for h: 320 = 80h, therefore h = 320 / 80 = 4 cm.
258
Find the length of the longest pole that can be placed in a room 12 m long, 4 m broad, and 3 m high.
Answer:
13 m
Step 1: The longest pole corresponds to the diagonal of the cuboid. Step 2: The formula is d = √(l² + b² + h²). Step 3: d = √(12² + 4² + 3²) = √(144 + 16 + 9) = √169 = 13 m.
259
If the surface area of a cube is 150 cm², what is its volume?
Answer:
125 cm³
Step 1: The surface area of a cube is 6a² = 150. Step 2: Solve for a²: a² = 150 / 6 = 25. So, a = 5 cm. Step 3: Calculate the volume: V = a³ = 5³ = 125 cm³.
260
What is the volume of a cube whose side measures 6 cm?
Answer:
216 cm³
Step 1: The formula for the volume of a cube is V = a³, where 'a' is the side length. Step 2: Substitute a = 6 cm into the formula. Step 3: V = 6 × 6 × 6 = 216 cm³.