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
1
Convert 165° to radians.
Answer:
2.88
Step-by-step solution: 1. Use conversion: radians = degrees * pi / 180. 2. Radians = 165 * pi / 180 = 2.88. 3. Therefore express result rounded to three decimals.
2
Convert 195° to radians.
Answer:
3.403
Step-by-step solution: 1. Use conversion: radians = degrees * pi / 180. 2. Radians = 195 * pi / 180 = 3.403. 3. Therefore express result rounded to three decimals.
3
Convert 75° to radians.
Answer:
1.309
Step-by-step solution: 1. Use conversion: radians = degrees * pi / 180. 2. Radians = 75 * pi / 180 = 1.309. 3. Therefore express result rounded to three decimals.
4
Convert 135° to radians.
Answer:
2.356
Step-by-step solution: 1. Use conversion: radians = degrees * pi / 180. 2. Radians = 135 * pi / 180 = 2.356. 3. Therefore express result rounded to three decimals.
5
Convert 105° to radians.
Answer:
1.833
Step-by-step solution: 1. Use conversion: radians = degrees * pi / 180. 2. Radians = 105 * pi / 180 = 1.833. 3. Therefore express result rounded to three decimals.
6
Convert 45° to radians.
Answer:
0.785
Step-by-step solution: 1. Use conversion: radians = degrees * pi / 180. 2. Radians = 45 * pi / 180 = 0.785. 3. Therefore express result rounded to three decimals.
7
What is the ratio of the area of a circular sector with angle θ (in radians) to the area of the entire circle?
Answer:
θ / 2π
The area of the entire circle represents a full revolution of 2π radians. The area of a sector with angle θ represents a proportional fraction of that full circle, which mathematically reduces identically to θ / 2π.
8
How many degrees does the earth rotate about its axis in exactly 2 hours?
Answer:
30°
The Earth completes a full 360° rotation in 24 hours. Therefore, its rotational speed is 360° / 24 hours = 15° per hour. In 2 hours, it rigorously rotates 2 * 15° = 30°.
9
Find the area of a circle if an arc length of 4π cm subtends a central angle of π/2 radians.
Answer:
64π cm²
First, find the radius using l = rθ. 4π = r * (π/2). Dividing by π yields 4 = r / 2, so r = 8 cm. The full area of the circle is mathematically defined as πr², which is π(8²) = 64π cm².
10
If the angular speed of a particle is constant at π rad/s, what angle does it cover in 1 minute?
Answer:
60π
The total angle covered is the product of angular speed and time. The time is 1 minute, which is 60 seconds. The angle covered is π rad/s * 60 s = exactly 60π radians.