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
191
The lateral surface area of a cuboid with length 12 cm, width 8 cm, and height 5 cm is:
Answer:
200 cm²
The lateral surface area (LSA) of a cuboid accounts for the 4 walls, excluding the top and bottom. Formula: LSA = 2h(l + w). Substituting values: LSA = 2 * 5 * (12 + 8) = 10 * 20 = 200 cm².
192
What is the length of the longest rod that can be placed in a room measuring 12m by 9m by 8m?
Answer:
17 m
The longest rod that can fit in a cuboidal room spans its main diagonal. Diagonal = √(l² + w² + h²) = √(12² + 9² + 8²) = √(144 + 81 + 64) = √289 = 17 m.
193
Find the total surface area of a cuboid measuring 10 cm by 6 cm by 5 cm.
Answer:
280 cm²
The total surface area of a cuboid is 2(lw + wh + hl). Substituting the values: 2 * (10*6 + 6*5 + 5*10) = 2 * (60 + 30 + 50) = 2 * 140 = 280 cm².
194
What is the volume of a cuboid with dimensions length = 8 cm, width = 5 cm, and height = 4 cm?
Answer:
160 cm³
The volume of a cuboid is calculated as Volume = length * width * height. Substituting the given values: Volume = 8 * 5 * 4 = 160 cm³.
195
If the total surface area of a cube is 150 cm², find its volume.
Answer:
125 cm³
Total Surface Area = 6 * side² = 150. Solving for side: side² = 150 / 6 = 25, which means side = 5 cm. The volume is side³ = 5³ = 125 cm³.
196
If the volume of a cube is 512 cm³, what is the length of its side?
Answer:
8 cm
The volume of a cube is V = side³. We know V = 512 cm³. To find the side, we take the cube root of 512. The cube root of 512 is 8, so the side length is 8 cm.
197
What is the length of the main diagonal of a cube with side length 'a'?
Answer:
a√3
The length of the main space diagonal of a cube that connects two opposite corners through the center is calculated using the 3D Pythagorean theorem: Diagonal = √(a² + a² + a²) = √(3a²) = a√3.
198
Find the total surface area of a cube with an edge of 4 cm.
Answer:
96 cm²
A cube has 6 identical square faces. The total surface area is 6 * side². Substituting the side length of 4 cm: Total Surface Area = 6 * (4²) = 6 * 16 = 96 cm².
199
What is the volume of a cube with a side length of 5 cm?
Answer:
125 cm³
The volume of a cube is calculated using the formula: Volume = side³. Given the side length is 5 cm, the volume = 5 * 5 * 5 = 125 cm³.
200
The angle in a semicircle is a:
Answer:
Right angle
According to Thales's theorem, an inscribed angle subtended by a diameter (which creates a semicircle) is always a right angle (90 degrees).