All Categories MCQs
Topic Notes: All Categories
General Description
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
3561
How many grades are there in a complete circle?
Answer:
400g
A complete circle consists of 4 right angles. Since one right angle is exactly 100 grades (100g), a full circle contains 4 * 100g = 400 grades.
3562
Convert 100 grades into radians.
Answer:
π/2
100 grades represents exactly one right angle. In radian measure, a right angle (90°) is defined precisely as π/2 radians.
3563
Convert the angle 54° into grades (gradians).
Answer:
60g
In the centesimal system, a right angle is 100 grades (g), whereas it is 90° in the sexagesimal system. Thus, 90° = 100g, or 1° = 10/9g. To convert 54°, multiply by 10/9: 54 * (10/9) = 6 * 10 = 60g.
3564
A train is moving on a circular curve of radius 1500 m at the rate of 66 km/hr. Through what angle has it turned in 10 seconds?
Answer:
11/90 rad
Convert speed to m/s: 66 * (5/18) = 55/3 m/s. Distance traveled in 10s is arc length l = (55/3) * 10 = 550/3 m. The radius r = 1500 m. Angle θ = l/r = (550/3) / 1500 = 550 / 4500 = 11/90 radians.
3565
What is the angle in radians between the hands of a clock at exactly 6:00?
Answer:
π
At exactly 6:00, the hour hand points to 6 and the minute hand points to 12. They form a perfectly straight line, making a 180° angle, which is exactly π radians.
3566
Find the angle between the hour hand and the minute hand of a clock at exactly 3:00.
Answer:
π/2 rad
At 3:00, the minute hand is perfectly at 12 and the hour hand is exactly at 3. The angle between them is 90 degrees, which corresponds to π/2 radians.
3567
A flywheel rotates at 300 RPM (revolutions per minute). What is its angular velocity in radians per second?
Answer:
10π
Revolutions per second = 300 / 60 = 5 rev/sec. To convert to radians, multiply by 2π. Angular velocity = 5 * 2π = 10π radians per second.
3568
A wheel makes 180 revolutions per minute. Through how many radians does it turn in one second?
Answer:
6π
First, find the revolutions per second: 180 rev / 60 sec = 3 rev/sec. Since each revolution is 2π radians, the wheel turns 3 * 2π = 6π radians per second.
3569
Through what angle in degrees does the hour hand of a clock turn in 20 minutes?
Answer:
10°
The hour hand moves 360° in 12 hours, which is 720 minutes. Its speed is 360/720 = 0.5 degrees per minute. In 20 minutes, it turns 20 * 0.5 = 10°.
3570
Through what angle in radians does the minute hand of a clock turn in 45 minutes?
Answer:
3π/2
The minute hand turns exactly 2π radians in 60 minutes. In 45 minutes, it turns (45/60) * 2π = (3/4) * 2π = 3π/2 radians.