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
11
What is the length of an arc defined by an angle of 1 radian on a unit circle?
Answer:
1
A unit circle has a radius exactly equal to 1. The arc length formula is l = rθ. Substituting r = 1 and θ = 1 gives an arc length l = 1 * 1 = exactly 1.
12
A sector has a central angle of π/3 radians and an area of 6π cm². Find its radius.
Answer:
6 cm
Using the area formula A = 0.5 * r² * θ. Substitute A = 6π and θ = π/3: 6π = 0.5 * r² * (π/3). The π cancels out on both sides, leaving 6 = r² / 6. Multiplying by 6 gives r² = 36, so r = 6 cm.
13
What is the equivalent of 120° in the grade system?
Answer:
133.3g
Since 90 degrees equal exactly 100 grades, the conversion factor is 100/90 or 10/9. Multiplying 120° by this factor gives 120 * (10/9) = 1200 / 9 = 133.33... grades.
14
A rotating shaft turns at 600 RPM. Calculate its angular velocity in radians per second.
Answer:
20π
First, convert revolutions per minute (RPM) to revolutions per second: 600 / 60 = 10 rev/sec. Since each revolution corresponds to 2π radians, the angular velocity is 10 * 2π = 20π radians per second.
15
An angle measures 50 grades. What is its measure in radians?
Answer:
π/8
In the centesimal system, 200 grades are identically equal to π radians. To convert 50 grades, multiply by (π / 200). 50 * (π / 200) simplifies precisely to π/4 radians.
16
Convert -3π/2 radians into a positive coterminal angle in radians.
Answer:
π/2
To find a positive coterminal angle within the standard circle, add a full revolution (2π) to the negative angle. Thus, -3π/2 + 2π = -3π/2 + 4π/2 = π/2 radians.
17
If an angle in a circle subtends an arc of 15 cm and the sector area is 45 cm², what is the radius of the circle?
Answer:
6 cm
We use the relationship A = 0.5 * l * r, where A is the sector area and l is the arc length. Substituting A = 45 and l = 15 yields 45 = 0.5 * 15 * r. This simplifies to 45 = 7.5r. Dividing both sides by 7.5 gives r = 6 cm.
18
What is the exterior angle of a regular decagon (10-sided polygon) in radians?
Answer:
π/5
The total sum of exterior angles for any regular convex polygon is precisely 2π radians. For a decagon with 10 sides, each individual exterior angle is 2π / 10 = π/5 radians.
19
Find the radian measure of the angle swept out by the second hand of a clock in 15 seconds.
Answer:
π/2
The second hand completes a full circle (2π radians) in 60 seconds. In 15 seconds, it sweeps a fraction of the circle equal to 15/60 = 1/4. Therefore, the angle is (1/4) * 2π = π/2 radians.
20
A circular wheel has a radius of 1 m. It covers a linear distance of 100π m. How many complete revolutions did it make?
Answer:
50
The circumference of the wheel represents the distance covered in one revolution: C = 2πr = 2π(1) = 2π m. The number of revolutions is the total distance divided by the circumference: 100π / 2π = 50 revolutions.