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
31
Calculate the central angle in radians if an arc of length 4π m is cut from a circle of radius 6 m.
Answer:
2π/3
Using the radian formula θ = l / r, we substitute the arc length l = 4π and the radius r = 6. This gives θ = 4π / 6, which simplifies exactly to 2π/3 radians.
32
What is the equivalent of 400 grades in the sexagesimal (degree) system?
Answer:
360°
In the centesimal grade system, one right angle equals exactly 100 grades. Therefore, four right angles, representing a full circle, correspond to 400 grades. In degrees, a full circle is exactly 360°.
33
Convert the angle 22° 30' into radians.
Answer:
π/8
First, convert to a decimal: 22° + (30/60)° = 22.5° = 45/2 degrees. Now, multiply by π/180: (45/2) * (π/180) = 45π / 360. Dividing by 45 yields exactly π/8 radians.
34
A chord of a circle of radius 10 cm subtends a right angle at the center. Find the area of the corresponding minor sector.
Answer:
25π cm²
A right angle is exactly π/2 radians. The area of the sector is defined as A = 0.5 * r² * θ. Substituting the given values: A = 0.5 * (10²) * (π/2) = 0.5 * 100 * (π/2) = 25π cm².
35
If a circle's circumference is 40π cm, what is the length of an arc subtending an angle of π/4 radians?
Answer:
5π cm
The full circumference of 40π corresponds to a total angle of 2π radians. An angle of π/4 radians represents exactly 1/8 of the full circle (since (π/4) / 2π = 1/8). The arc length is (1/8) * 40π = 5π cm.
36
What is the total angle covered by the hour hand of a clock from 12:00 PM to 4:00 PM in radians?
Answer:
2π/3
In 12 hours, the hour hand covers a full circle (2π radians). In 4 hours, the fraction of the circle covered is 4/12 = 1/3. The angle covered is (1/3) * 2π = 2π/3 radians.
37
In a right triangle, one acute angle is π/6 radians. What is the other acute angle in radians?
Answer:
π/3
The two acute angles in a right-angled triangle must sum perfectly to 90 degrees, which is π/2 radians. If one angle is π/6, the other is π/2 - π/6 = 3π/6 - π/6 = 2π/6 = π/3 radians.
38
An angle of 1 degree is roughly equal to how many radians? (Use π ≈ 3.1416)
Answer:
0.0175 rad
We know that 1 degree equals π/180 radians. Calculating this numerical value gives approximately 3.14159 / 180 ≈ 0.01745 radians, which rounds appropriately to 0.0175 rad.
39
If an arc of a circle is equal in length to its diameter, what is the central angle subtended by this arc in radians?
Answer:
2 rad
The formula for the central angle in radians is θ = l / r. We are given that the arc length l equals the diameter, which is 2r. Substituting this in gives θ = 2r / r = 2 radians.
40
What is the degree measure of an angle whose radian measure is exactly 1?
Answer:
180/π degrees
Since π radians is identically equal to 180 degrees, dividing both sides of the equation by π demonstrates that 1 radian is mathematically equivalent to 180/π degrees.