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
101
The minute hand of a clock is 14 cm long. How far does the tip of the hand move in 15 minutes?
Answer:
7π cm
In 60 minutes, the minute hand completes a full 2π radians. In 15 minutes, it covers (15/60) * 2π = π/2 radians. The distance covered is the arc length l = rθ = 14 * (π/2) = 7π cm.
102
A pendulum of length 20 cm swings through an angle of 18°. Find the length of the arc described by its tip.
Answer:
2π cm
Convert 18° to radians: 18 * π/180 = π/10 radians. Using l = rθ, where r is the pendulum length. Arc length l = 20 * (π/10) = 2π cm.
103
Find the area of a sector if the circle's radius is 6 cm and the central angle is 60°.
Answer:
6π cm²
First convert 60° to radians: 60° = π/3 rad. Using the area formula A = 0.5 * r² * θ: A = 0.5 * 36 * (π/3) = 18 * (π/3) = 6π cm².
104
If a circle has a radius of 10 cm, what is the length of an arc that subtends an angle of 30°?
Answer:
5π/3 cm
First, convert the angle to radians: 30° = π/6 radians. Then, use the formula l = rθ. Arc length l = 10 * (π/6) = 10π/6 = 5π/3 cm.
105
What is the degree measure for π/12 radians?
Answer:
15°
To convert from radians to degrees, substitute 180° for π. Thus, 180° / 12 = 15°.
106
Convert 105° into radians.
Answer:
7π/12
Multiply 105 by π/180. 105π / 180 simplifies by dividing both by 15, giving 7π/12 radians.
107
What is the radian measure of 75°?
Answer:
5π/12
Multiply 75 by π/180. 75π / 180 simplifies by dividing both the numerator and the denominator by 15, resulting in 5π/12 radians.
108
Convert 15° into radians.
Answer:
π/12
Multiply 15 by π/180. 15π / 180 simplifies by dividing both the numerator and the denominator by 15, yielding π/12 radians.
109
Convert 11π/6 radians to degrees.
Answer:
330°
Substitute 180° for π in the expression: (11 * 180°) / 6. This simplifies to 11 * 30° = 330°.
110
What is the radius of a circle if an arc of length 20 m subtends a central angle of 5 radians?
Answer:
4 m
By rearranging the arc length formula l = rθ to solve for r, we get r = l / θ. Substitute l = 20 m and θ = 5 radians. The radius r = 20 / 5 = 4 m.