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
111
If the arc length is 12 cm and the radius is 3 cm, what is the central angle in radians?
Answer:
4 radians
Using the fundamental relation θ = l / r, where l is arc length and r is radius. Here l = 12 cm and r = 3 cm. Therefore, θ = 12 / 3 = 4 radians.
112
Calculate the area of a sector if the radius is 4 m and the central angle is 1.5 radians.
Answer:
12 m²
Using the sector area formula A = 0.5 * r² * θ. Substitute r = 4 and θ = 1.5. A = 0.5 * (4²) * 1.5 = 0.5 * 16 * 1.5 = 8 * 1.5 = 12 m².
113
Find the arc length of a circle with a radius of 5 cm and a central angle of 2 radians.
Answer:
10 cm
Using the arc length formula l = rθ, where the angle is already in radians. Here r = 5 cm and θ = 2 rad. The arc length l = 5 * 2 = 10 cm.
114
What is the formula for the area of a circular sector if the central angle θ is in radians?
Answer:
A = 0.5 * r² * θ
The area of a full circle is πr². A sector with angle θ in radians represents a fraction θ/(2π) of the circle. Therefore, the sector area is (θ/2π) * πr² = (1/2)r²θ.
115
How many radians are in a straight angle?
Answer:
π
A straight angle is 180 degrees. Since 360° corresponds to 2π radians, a straight angle corresponds to exactly half of that, which is π radians.
116
Convert 7π/6 radians to degrees.
Answer:
210°
Substitute 180° for π in the expression. (7 * 180°) / 6 = 7 * 30° = 210°.
117
What is the radian measure for 315°?
Answer:
7π/4
Convert using the factor π/180. 315 * (π/180) = 315π/180. Dividing numerator and denominator by 45 gives 7π/4.
118
Convert 270° into radians.
Answer:
3π/2
Multiply 270 by π/180. 270π / 180 simplifies by dividing by 90, which yields exactly 3π/2 radians.
119
What is the degree equivalent of 5π/3 radians?
Answer:
300°
Replace π with 180° to easily convert to degrees. Thus, 5 * 180° / 3 = 5 * 60° = 300°.
120
Which of the following represents 150° in radians?
Answer:
5π/6
Multiply 150 by π/180 to convert it. 150π / 180 simplifies by dividing both numbers by 30, resulting in 5π/6 radians.