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
51
If the radius of a circle is doubled and the central angle of a sector is halved, how does the area of the sector change?
Answer:
It is doubled
Original area A = 0.5 * r² * θ. New radius = 2r, new angle = θ/2. New area A' = 0.5 * (2r)² * (θ/2) = 0.5 * 4r² * 0.5θ = 1.0 * r² * θ. This new area is exactly twice the original area.
52
What is the area of the region bounded by an arc of 20 m and two radii of 10 m each?
Answer:
100 m²
The region bounded by an arc and two radii is a sector. We can use the formula Area = 0.5 * l * r, where l is the arc length and r is the radius. Area = 0.5 * 20 * 10 = 100 m².
53
A central angle of a circle of radius 15 cm intercepts an arc of 10π cm. Find the angle in degrees.
Answer:
120°
First, find the angle in radians: θ = l/r = 10π / 15 = 2π/3 radians. To convert to degrees, substitute 180° for π: 2(180°) / 3 = 360° / 3 = 120°.
54
If two arcs of the same length in two circles subtend central angles of 60° and 75°, what is the ratio of their radii?
Answer:
5:4
Since the arc lengths are equal, r1*θ1 = r2*θ2. Therefore, r1/r2 = θ2/θ1. Using the angles in degrees: r1/r2 = 75° / 60° = 5/4. The ratio of the radii is 5:4.
55
A fan rotates at 120 RPM. What is its angular velocity in radians per second?
Answer:
4π
120 revolutions per minute equals 120 / 60 = 2 revolutions per second. Since one revolution is 2π radians, the angular velocity is 2 * 2π = 4π radians per second.
56
Which angle is larger: 1 radian or 50 degrees?
Answer:
1 radian
One radian is officially equivalent to 180/π degrees, which is approximately 57.3 degrees. Since 57.3° is strictly greater than 50°, 1 radian is definitively the larger angle.
57
Calculate the difference in radians between an angle of 75° and 60°.
Answer:
π/12
The difference in degrees is 75° - 60° = 15°. To convert 15° to radians, multiply by π/180. 15 * (π/180) = π/12 radians.
58
A pendulum is 50 cm long and swings through an arc of 15 cm. Find the angle of the swing in radians.
Answer:
0.3 rad
Using the formula θ = l/r. Given arc length l = 15 cm and radius r = 50 cm, the angle θ = 15 / 50 = 0.3 radians.
59
If an angle is 120 grades, what is its value in radians?
Answer:
3π/5
A straight angle is exactly 200 grades, which equals π radians. Therefore, the conversion is 120g * (π / 200g) = 120π/200. Dividing both by 40 simplifies this to 3π/5 radians.
60
How many degrees are in one grade?
Answer:
0.9°
A right angle is exactly 90 degrees and also exactly 100 grades. Therefore, 100g = 90°, which simplifies directly to 1 grade (1g) = 90/100 = 0.9°.