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
If the sum of two adjacent angles on a straight line is 180 degrees, they are called:
Answer:
Linear pair
A linear pair consists of two adjacent angles created by intersecting lines. Because they form a straight line, their measures always add up to exactly 180 degrees.
92
In a circle, the angle subtended by an arc at the center is double the angle subtended by it at:
Answer:
Any point on the remaining part of the circle
The Inscribed Angle Theorem states that the angle subtended by an arc at the center of a circle is exactly double the angle subtended by the same arc at any point on the remaining circumference.
93
What is the volume of a right triangular prism if the base is an equilateral triangle with side 6 cm, and the length of the prism is 10 cm?
Answer:
90√3 cm³
Volume = Base Area * length. Base Area of equilateral triangle = (√3/4) * side² = (√3/4) * 36 = 9√3 cm². Volume = 9√3 * 10 = 90√3 cm³.
94
If a cone is cut by a plane parallel to its base, the lower part of the solid formed is called a:
Answer:
Frustum
When a cone is sliced by a plane parallel to its circular base, the tip forms a smaller cone, and the remaining bottom portion is geometrically defined as a frustum of a cone.
95
What is the total surface area of a hemisphere with a radius of 10 cm? (Use π ≈ 3.14)
Answer:
942 cm²
The total surface area of a solid hemisphere is 3πr². Substituting the values: TSA = 3 * 3.14 * 10² = 3 * 3.14 * 100 = 3 * 314 = 942 cm².
96
A room is 10 m long, 8 m wide, and 3 m high. What is the area of its four walls?
Answer:
108 m²
The area of four walls (Lateral Surface Area) is calculated as 2h(l + w). Substituting the values: Area = 2 * 3 * (10 + 8) = 6 * 18 = 108 m².
97
What is the relation between the number of edges (E), faces (F), and vertices (V) of a cube?
Answer:
F = 6, V = 8, E = 12
A standard cube has 6 square faces, 8 corner vertices, and 12 edges. This perfectly satisfies Euler's formula: 6 + 8 = 12 + 2.
98
A cylindrical tank has a radius of 5 m and a height of 10 m. What is its capacity in liters? (Use π ≈ 3.14)
Answer:
785,000 liters
Volume = πr²h = 3.14 * 5² * 10 = 3.14 * 25 * 10 = 785 m³. Since 1 m³ is equivalent to 1000 liters, the capacity is 785 * 1000 = 785,000 liters.
99
The volume of a sphere is numerically equal to its surface area. What is its radius?
Answer:
3 units
Set the volume formula equal to the surface area formula: (4/3)πr³ = 4πr². Dividing both sides by 4πr² leaves r/3 = 1, which means r = 3 units.
100
What is the circumcenter of a right-angled triangle located?
Answer:
At the midpoint of the hypotenuse
For any right-angled triangle, the circumcenter (the center of the circle that passes through all three vertices) lies exactly at the midpoint of the hypotenuse.