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
171
The diameter of a base of a cone is 10 cm and its altitude is 12 cm. Find its total surface area. (Take π = 3.14)
Answer:
282.6 cm²
Step 1: r = 5 cm, h = 12 cm. Slant height l = √(5² + 12²) = 13 cm. Step 2: TSA = πr(r + l) = 3.14 × 5 × (5 + 13). Step 3: TSA = 3.14 × 5 × 18 = 3.14 × 90 = 282.6 cm².
172
A metallic sphere of radius 10 cm is melted and recast into a cone of height 10 cm. Find the radius of the base of the cone.
Answer:
20 cm
Step 1: Volume of sphere = (4/3)π(10)³. Volume of cone = (1/3)πr²(10). Step 2: (4/3)π(1000) = (1/3)πr²(10). Step 3: 4000 = 10r² -> r² = 400 -> r = 20 cm.
173
What is the ratio of the total surface area to the curved surface area of a cylinder with radius 5 cm and height 15 cm?
Answer:
4:3
Step 1: TSA = 2πr(r+h) and CSA = 2πrh. Step 2: Ratio = [2πr(r+h)] / [2πrh] = (r+h) / h. Step 3: Substitute values: (5+15) / 15 = 20 / 15 = 4:3.
174
The total surface area of a solid right circular cylinder is 1540 cm². If its height is 4 times its base radius, find the radius.
Answer:
7 cm
Step 1: TSA = 2πr(r+h). Given h = 4r. Step 2: 2πr(r + 4r) = 2πr(5r) = 10πr² = 1540. Step 3: 10 × (22/7) × r² = 1540 -> (220/7)r² = 1540 -> r² = 49 -> r = 7 cm.
175
A cylindrical tank has a capacity of 6160 m³. If the diameter of its base is 28 m, find its depth.
Answer:
10 m
Step 1: Radius = 14 m. Volume = πr²h. Step 2: 6160 = (22/7) × 14² × h = 22 × 28 × h = 616h. Step 3: h = 6160 / 616 = 10 m.
176
Find the ratio of the volume of a cube to that of a sphere which will fit exactly inside the cube.
Answer:
6 : π
Step 1: Let the edge of the cube be a. The diameter of the sphere is 'a', so radius r = a/2. Step 2: Vol of cube = a³. Vol of sphere = (4/3)π(a/2)³ = (4/3)π(a³/8) = πa³/6. Step 3: Ratio = a³ : (πa³/6) = 1 : π/6 = 6 : π.
177
Three identical cubes of edge 4 cm are joined end to end. Find the total surface area of the resulting cuboid.
Answer:
224 cm²
Step 1: The new cuboid has dimensions l = 12, b = 4, h = 4. Step 2: TSA = 2(lb + bh + hl) = 2(12×4 + 4×4 + 4×12). Step 3: TSA = 2(48 + 16 + 48) = 2(112) = 224 cm².
178
A right circular cone of radius 3 cm has a curved surface area of 47.1 cm². Find the volume of the cone. (Take π = 3.14)
Answer:
37.68 cm³
Step 1: CSA = πrl = 47.1. So 3.14 × 3 × l = 47.1 -> 9.42l = 47.1 -> l = 5 cm. Step 2: h = √(l² - r²) = √(25 - 9) = 4 cm. Step 3: Volume = (1/3)πr²h = (1/3) × 3.14 × 9 × 4 = 37.68 cm³.
179
A rectangular water tank is 5 m long, 3 m wide, and 2 m deep. How many liters of water can it hold?
Answer:
30,000 L
Step 1: Volume = 5 × 3 × 2 = 30 m³. Step 2: 1 m³ = 1000 Liters. Step 3: Capacity = 30 × 1000 = 30,000 Liters.
180
If the volume of a cuboid is 144 cm³ and its base area is 24 cm², what is its height?
Answer:
6 cm
Step 1: Volume of a cuboid = Base Area × Height. Step 2: 144 = 24 × Height. Step 3: Height = 144 / 24 = 6 cm.