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
91
What is the length of the body diagonal of a cube whose volume is 343 cm³?
Answer:
7√3 cm
First, find the side length. V = s³ = 343, so s = 7 cm. The length of the body diagonal of a cube is given by the formula s√3. Therefore, the diagonal is 7√3 cm.
92
If the radius of a cylinder is doubled and its height is halved, the volume will be:
Answer:
Doubled
Original volume V = πr²h. New volume V' = π(2r)²(h/2) = π(4r²)(h/2) = 2πr²h. The new volume is twice the original volume, so it is doubled.
93
A solid cube of edge 14 cm is melted and cast into a cuboid whose base measures 28 cm by 14 cm. Find the height of the cuboid.
Answer:
7 cm
Volume of the cuboid must equal the volume of the cube. Volume of cube = 14 × 14 × 14 = 2744 cm³. Volume of cuboid = L × W × H = 28 × 14 × H. So, 392 × H = 2744, which gives H = 2744 / 392 = 7 cm.
94
A cone, a hemisphere, and a cylinder stand on equal bases and have the same height. The ratio of their volumes is:
Answer:
1:2:3
Let the base radius be r. Since the height is the same as the base radius of the hemisphere, h = r. Volume of cone = (1/3)πr³; Hemisphere = (2/3)πr³; Cylinder = πr³. The ratio is (1/3) : (2/3) : 1, which simplifies to 1:2:3.
95
If the volume of a hemisphere is 19404 cm³, find its radius. (Use π = 22/7)
Answer:
21 cm
Volume of hemisphere = (2/3)πr³. So, (2/3) × (22/7) × r³ = 19404. r³ = (19404 × 21) / 44 = 441 × 21 = 9261. Therefore, r = ³√9261 = 21 cm.
96
What is the capacity in liters of a conical vessel with base radius 7 cm and height 24 cm? (Use π = 22/7)
Answer:
1.232 liters
Volume = (1/3)πr²h = (1/3) × (22/7) × 7 × 7 × 24 = 22 × 7 × 8 = 1232 cm³. Since 1000 cm³ = 1 liter, the capacity is 1232 / 1000 = 1.232 liters.
97
A rectangular sheet of paper 44 cm × 20 cm is rolled along its length to form a cylinder. Find the volume of the cylinder formed. (Use π = 22/7)
Answer:
3080 cm³
When rolled along its length, the circumference of the base becomes 44 cm and the height becomes 20 cm. 2πr = 44, so 2 × (22/7) × r = 44, yielding r = 7 cm. Volume = πr²h = (22/7) × 7 × 7 × 20 = 3080 cm³.
98
If the radius of a sphere is increased by 10%, its surface area increases by:
Answer:
21%
Surface area is proportional to the square of the radius. If radius becomes 1.1 times, the new area becomes (1.1)² = 1.21 times the original area. This represents a 21% increase.
99
What is the volume of a sphere whose surface area is 616 cm²? (Use π = 22/7)
Answer:
1437.33 cm³
Surface Area = 4πr² = 616. 4 × (22/7) × r² = 616, so r² = (616 × 7) / 88 = 49. Radius r = 7 cm. Volume = (4/3)πr³ = (4/3) × (22/7) × 7³ = (4/3) × 22 × 49 = 4312 / 3 ≈ 1437.33 cm³.
100
A solid metallic cylinder of base radius 3 cm and height 5 cm is melted to form cones, each of height 1 cm and base radius 1 mm. How many such cones are formed?
Answer:
13500
Volume of cylinder = π × 3² × 5 = 45π cm³. Volume of one cone = (1/3)πr²h. r = 1 mm = 0.1 cm. Volume of cone = (1/3)π(0.1)²(1) = 0.01π/3 cm³. Number of cones = 45π / (0.01π/3) = 45 × 3 / 0.01 = 13500.