All Categories MCQs
Topic Notes: All Categories
General Description
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
2991
The sum of length, breadth and depth of a cuboid is 19 cm and the length of its diagonal is 11 cm. Find the surface area of the cuboid.
Answer:
240 cm²
Step 1: Given l + b + h = 19, and √(l² + b² + h²) = 11, so l² + b² + h² = 121. Step 2: We know (l + b + h)² = l² + b² + h² + 2(lb + bh + hl). Step 3: 19² = 121 + TSA -> 361 = 121 + TSA -> TSA = 361 - 121 = 240 cm².
2992
A cube of edge 15 cm is immersed completely in a rectangular vessel containing water. If the dimensions of the base are 20 cm × 15 cm, find the rise in water level.
Answer:
11.25 cm
Step 1: Volume of the cube = 15 × 15 × 15 = 3375 cm³. Step 2: The volume of the displaced water equals the volume of the cube. Step 3: Base area × rise in level = Volume -> (20 × 15) × h = 3375 -> 300h = 3375 -> h = 11.25 cm.
2993
If the areas of the adjacent faces of a rectangular block are in the ratio 2:3:4 and its volume is 9000 cm³, what is the length of the shortest edge?
Answer:
15 cm
Step 1: Let areas be xy = 2k, yz = 3k, zx = 4k. Step 2: (xyz)² = 24k³ -> V² = 24k³ -> 9000² = 24k³ -> 81000000 = 24k³ -> k³ = 3375000 -> k = 150. Step 3: xy = 300, yz = 450, zx = 600. xyz = 9000. Shortest edge is xyz / (largest area) = 9000 / 600 = 15 cm.
2994
The radii of two cylinders are in the ratio 3:5 and their heights are in the ratio 2:3. Find the ratio of their curved surface areas.
Answer:
2:5
Step 1: CSA formula is 2πrh. Step 2: Ratio of CSA = (2π r1 h1) / (2π r2 h2) = (r1/r2) × (h1/h2). Step 3: Ratio = (3/5) × (2/3) = 2/5. Thus, 2:5.
2995
A hollow cylindrical pipe is 21 dm long. Its outer and inner diameters are 10 cm and 6 cm respectively. Find the volume of the copper used in making the pipe.
Answer:
10560 cm³
Step 1: Length h = 21 dm = 210 cm. Outer radius R = 5 cm, Inner radius r = 3 cm. Step 2: Volume of material = πh(R² - r²) = (22/7) × 210 × (5² - 3²). Step 3: V = 660 × (25 - 9) = 660 × 16 = 10560 cm³.
2996
Find the capacity in liters of a conical vessel with radius 7 cm and slant height 25 cm.
Answer:
1.232 L
Step 1: Find height h = √(l² - r²) = √(25² - 7²) = √(625 - 49) = √576 = 24 cm. Step 2: Vol = (1/3)πr²h = (1/3) × (22/7) × 49 × 24 = 1232 cm³. Step 3: Convert to liters (1 L = 1000 cm³): 1232 / 1000 = 1.232 liters.
2997
What is the ratio of the volumes of a cylinder, a cone, and a hemisphere of the same radius and same height?
Answer:
3:1:2
Step 1: For a hemisphere, height h = radius r. So, assume h = r for all. Step 2: Vol of cylinder = πr²(r) = πr³. Vol of cone = (1/3)πr²(r) = (1/3)πr³. Vol of hemisphere = (2/3)πr³. Step 3: Ratio = πr³ : (1/3)πr³ : (2/3)πr³ = 1 : 1/3 : 2/3 = 3:1:2.
2998
A solid metallic cylinder of base radius 3 cm and height 5 cm is melted to make solid cones of height 1 cm and base radius 1 mm. How many cones can be made?
Answer:
13500
Step 1: Vol of cylinder = π(3²)(5) = 45π cm³. Step 2: Vol of cone = (1/3)π(0.1)²(1) = (1/3)π(0.01) = π/300 cm³. Step 3: Number of cones = (45π) / (π/300) = 45 × 300 = 13500.
2999
If the radius of a sphere is increased by 100%, its volume will increase by:
Answer:
700%
Step 1: Let the original radius be r, so V1 = (4/3)πr³. Step 2: New radius = 2r. New volume V2 = (4/3)π(2r)³ = 8 × (4/3)πr³ = 8 × V1. Step 3: Increase = 8V1 - V1 = 7V1. Percentage increase = (7V1 / V1) × 100 = 700%.
3000
The volume of a sphere is 38808 cm³. Find its radius. (Take π = 22/7)
Answer:
21 cm
Step 1: (4/3)πr³ = 38808. Step 2: (4/3) × (22/7) × r³ = 38808 -> (88/21) × r³ = 38808. Step 3: r³ = (38808 × 21) / 88 = 441 × 21 = 9261. r = ³√9261 = 21 cm.