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
241
A metallic sphere of radius 10.5 cm is melted and then recast into small cones, each of radius 3.5 cm and height 3 cm. How many cones are obtained?
Answer:
126
Step 1: Number of cones = Volume of sphere / Volume of one cone. Step 2: Vol of sphere = (4/3)π(10.5)³. Vol of cone = (1/3)π(3.5)²(3). Step 3: Number = [ (4/3)π × 10.5 × 10.5 × 10.5 ] / [ (1/3)π × 3.5 × 3.5 × 3 ] = [4 × 3 × 3 × 10.5] / 3 = 126.
242
What is the total surface area of a solid hemisphere of radius 7 cm? (Take π = 22/7)
Answer:
462 cm²
Step 1: The total surface area of a solid hemisphere is 3πr². Step 2: Substitute values: TSA = 3 × (22/7) × 7². Step 3: TSA = 3 × 22 × 7 = 462 cm².
243
Find the curved surface area of a hemisphere with radius 7 cm. (Take π = 22/7)
Answer:
308 cm²
Step 1: The curved surface area of a hemisphere is 2πr². Step 2: Substitute values: CSA = 2 × (22/7) × 7². Step 3: CSA = 2 × 22 × 7 = 308 cm².
244
The volume of a sphere is numerically equal to its surface area. What is the radius of the sphere?
Answer:
3 units
Step 1: Volume = Surface Area, so (4/3)πr³ = 4πr². Step 2: Divide both sides by 4πr². Step 3: (1/3)r = 1, which gives r = 3 units.
245
Find the surface area of a sphere of radius 10.5 cm. (Take π = 22/7)
Answer:
1386 cm²
Step 1: The surface area of a sphere is SA = 4πr². Step 2: Substitute values: SA = 4 × (22/7) × (10.5)². Step 3: SA = 4 × (22/7) × 110.25 = 88 × 15.75 = 1386 cm².
246
What is the volume of a sphere of radius 3 cm? (Take π = 3.14)
Answer:
113.04 cm³
Step 1: The volume of a sphere is V = (4/3)πr³. Step 2: Substitute the values: V = (4/3) × 3.14 × 3³. Step 3: V = 4 × 3.14 × 9 = 113.04 cm³.
247
The radius and height of a right circular cone are in the ratio 3:4. If its volume is 301.44 cm³, what is its radius? (Take π = 3.14)
Answer:
6 cm
Step 1: Let radius = 3x and height = 4x. Step 2: V = (1/3)πr²h = (1/3) × 3.14 × (3x)² × (4x) = 301.44. Step 3: (1/3) × 3.14 × 9x² × 4x = 301.44 -> 37.68x³ = 301.44 -> x³ = 8. So x = 2. Radius = 3(2) = 6 cm.
248
Find the curved surface area of a cone if its radius is 5 cm and its slant height is 10 cm. (Take π = 3.14)
Answer:
157 cm²
Step 1: The curved surface area of a cone is CSA = πrl. Step 2: Substitute the values: CSA = 3.14 × 5 × 10. Step 3: CSA = 3.14 × 50 = 157 cm².
249
What is the volume of a right circular cone with radius 6 cm and height 7 cm? (Take π = 22/7)
Answer:
264 cm³
Step 1: The volume of a cone is V = (1/3)πr²h. Step 2: Substitute values: V = (1/3) × (22/7) × (6)² × 7. Step 3: V = (1/3) × 22 × 36 = 22 × 12 = 264 cm³.
250
The total surface area of a solid cylinder is 462 cm². If its curved surface area is one-third of its total surface area, find the radius. (Take π = 22/7)
Answer:
7 cm
Step 1: TSA = 462. CSA = 1/3 × 462 = 154 cm². Step 2: TSA = CSA + 2πr². Therefore, 2πr² = TSA - CSA = 462 - 154 = 308. Step 3: 2 × (22/7) × r² = 308. r² = (308 × 7) / 44 = 49. So, r = 7 cm.