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
151
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. r² = (616 * 7) / 88 = 7 * 7 = 49, so r = 7 cm. Volume = (4/3)πr³ = (4/3) * (22/7) * 7³ = (4/3) * 22 * 49 = 4312 / 3 ≈ 1437.33 cm³.
152
A right circular cone has a base radius of 8 cm and a slant height of 10 cm. Find its vertical height.
Answer:
6 cm
In a cone, the radius, height, and slant height form a right triangle. Using Pythagoras: r² + h² = l². So, 8² + h² = 10², which gives 64 + h² = 100. h² = 36, meaning the vertical height h = 6 cm.
153
The diameter of a sphere is 12 cm. What is its surface area in terms of π?
Answer:
144π cm²
If the diameter is 12 cm, the radius r = 6 cm. The surface area of a sphere is 4πr² = 4 * π * 6² = 4 * 36 * π = 144π cm².
154
Find the coordinates of the midpoint of the line segment joining (2, 8) and (6, 12).
Answer:
(4, 10)
The midpoint formula is ((x1 + x2) / 2, (y1 + y2) / 2). Midpoint = ((2 + 6) / 2, (8 + 12) / 2) = (8 / 2, 20 / 2) = (4, 10).
155
What is the distance between the points (3, 4) and (7, 1) on a Cartesian plane?
Answer:
5 units
Using the distance formula d = √((x2 - x1)² + (y2 - y1)²). d = √((7 - 3)² + (1 - 4)²) = √(4² + (-3)²) = √(16 + 9) = √25 = 5 units.
156
Two parallel lines are intersected by a transversal. If one interior angle is 110 degrees, what is the measure of the consecutive interior angle on the same side of the transversal?
Answer:
70 degrees
Consecutive interior angles (also known as allied angles) on the same side of a transversal intersecting parallel lines are supplementary. Therefore, the angle is 180 - 110 = 70 degrees.
157
The areas of two similar triangles are 25 cm² and 64 cm² respectively. What is the ratio of their corresponding sides?
Answer:
5:8
The ratio of the areas of two similar triangles equals the square of the ratio of their corresponding sides. So, (Side1 / Side2)² = 25 / 64. Taking the square root gives Side1 / Side2 = 5 / 8, or a ratio of 5:8.
158
A hollow cylinder has an external radius of 10 cm, an internal radius of 8 cm, and a height of 14 cm. Find the volume of the material used. (Use π ≈ 22/7)
Answer:
1584 cm³
Volume of material = External Volume - Internal Volume = π * h * (R² - r²). V = (22/7) * 14 * (10² - 8²) = 44 * (100 - 64) = 44 * 36 = 1584 cm³.
159
If the diagonals of a quadrilateral bisect each other at right angles, the quadrilateral must be a:
Answer:
Rhombus
A fundamental property of a rhombus is that its diagonals bisect each other exactly at 90 degrees (right angles). While squares also share this property, a rhombus is the broader category that fits this precise definition.
160
The total surface area of a cube is 24 cm². What is the volume of the cube?
Answer:
8 cm³
Total Surface Area = 6 * side² = 24. Therefore, side² = 4, and the side length is 2 cm. Volume = side³ = 2³ = 8 cm³.