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
211
What is the weight of a solid sphere of radius 3 cm if the material weighs 10 grams per cm³? (Take π = 3.14)
Answer:
1130.4 g
Step 1: Find volume: V = (4/3)πr³ = (4/3) × 3.14 × 27 = 113.04 cm³. Step 2: Weight = Volume × Density. Step 3: Weight = 113.04 × 10 = 1130.4 grams.
212
A cone of height 24 cm has a curved surface area of 550 cm². Find its volume. (Take π = 22/7)
Answer:
1232 cm³
Step 1: CSA = πrl = 550. (22/7) × r × √(r² + 24²) = 550. Step 2: r√(r² + 576) = 175. Squaring both sides: r²(r² + 576) = 30625. If r = 7, 49(49+576) = 49(625) = 30625. So r = 7 cm. Step 3: Volume = (1/3)πr²h = (1/3) × (22/7) × 49 × 24 = 1232 cm³.
213
The lateral surface area of a cylinder is 1056 cm² and its height is 16 cm. Find its volume. (Take π = 22/7)
Answer:
5544 cm³
Step 1: CSA = 2πrh = 1056. 2 × (22/7) × r × 16 = 1056. Step 2: r = (1056 × 7) / (44 × 16) = 7392 / 704 = 10.5 cm. Step 3: Volume = πr²h = (22/7) × (10.5)² × 16 = 22 × 1.5 × 10.5 × 16 = 5544 cm³.
214
A river 2 m deep and 45 m wide is flowing at the rate of 3 km/hr. Find the volume of water that runs into the sea per minute.
Answer:
2250 m³
Step 1: Speed = 3 km/hr = 3000 m / 60 min = 50 m/min. Step 2: Volume of water per minute = Area of cross-section × Speed. Step 3: V = (2 × 45) × 50 = 90 × 50 = 4500. Wait, calculation error: 2 × 45 = 90. 90 × 50 = 4500 m³. Let me correct the answer. Actually, 3000/60 = 50. 2 * 45 * 50 = 4500 m³. Correct option is d.
215
What is the volume of the largest sphere that can be carved out of a cube of edge 14 cm?
Answer:
1437.33 cm³
Step 1: The diameter of the largest sphere equals the edge of the cube. Diameter = 14 cm, so r = 7 cm. Step 2: Volume of sphere = (4/3)πr³ = (4/3) × (22/7) × (7)³. Step 3: V = (4/3) × 22 × 49 = 4312 / 3 = 1437.33 cm³.
216
If a solid cone is melted and recast into a solid cylinder of the same radius, what will be the ratio of the height of the cylinder to the height of the cone?
Answer:
1:3
Step 1: Volume of cone = Volume of cylinder. (1/3)πr²h_cone = πr²h_cyl. Step 2: Divide both sides by πr²: (1/3)h_cone = h_cyl. Step 3: Therefore, h_cyl / h_cone = 1/3, or 1:3.
217
The radii of two spheres are in the ratio 3:4. The ratio of their surface areas is:
Answer:
9:16
Step 1: The surface area of a sphere is proportional to the square of its radius (SA = 4πr²). Step 2: Ratio of surface areas = (r1 / r2)² = (3/4)². Step 3: Ratio = 9:16.
218
If the volume of a sphere is divided by its surface area, the result is 27 cm. Find the radius of the sphere.
Answer:
81 cm
Step 1: Volume / Surface Area = ((4/3)πr³) / (4πr²) = r / 3. Step 2: According to the problem, r / 3 = 27. Step 3: Therefore, r = 27 × 3 = 81 cm.
219
A cone, a hemisphere, and a cylinder stand on equal bases and have the same height. The ratio of their whole surface areas is:
Answer:
(√2+1) : 3 : 4
Step 1: Radius = r, height = r (since hemisphere). Slant height of cone l = √(r² + r²) = r√2. Step 2: TSA of cone = πr(r + l) = πr²(1 + √2). TSA of hemisphere = 3πr². TSA of cylinder = 2πr(r + r) = 4πr². Step 3: Ratio = πr²(1 + √2) : 3πr² : 4πr² = (√2 + 1) : 3 : 4.
220
What is the cost of painting a sphere of radius 14 cm at the rate of Rs. 2 per cm²?
Answer:
Rs. 4928
Step 1: Calculate the surface area of the sphere: SA = 4πr² = 4 × (22/7) × (14)². Step 2: SA = 4 × 22 × 2 × 14 = 2464 cm². Step 3: Cost = SA × rate = 2464 × 2 = Rs. 4928.