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
3481
In an 800 m race, A beats B by 80 m or 16 seconds. What is A's time?
Answer:
144 seconds
Step 1: B covers the final 80 m in 16 seconds. Step 2: B's speed = 80 / 16 = 5 m/s. Step 3: B's total time = 800 / 5 = 160 seconds. A's time = 160 - 16 = 144 seconds.
3482
In a 400 m race, A beats B by 40 m or 5 seconds. Find A's time.
Answer:
45 seconds
Step 1: B covers the final 40 m in 5 seconds. Step 2: B's speed = 40 / 5 = 8 m/s. Step 3: B's total time = 400 / 8 = 50 seconds. A's time = 50 - 5 = 45 seconds.
3483
In a 500 m race, A beats B by 50 m or 10 seconds. What is A's time?
Answer:
90 seconds
Step 1: B covers the final 50 m in 10 seconds. Step 2: B's speed = 50 / 10 = 5 m/s. Step 3: B's total time = 500 / 5 = 100 seconds. A's time = 100 - 10 = 90 seconds.
3484
In a 1000 m race, A beats B by 200 m or 25 seconds. Find A's time.
Answer:
100 seconds
Step 1: B covers the final 200 m in 25 seconds. Step 2: B's speed = 200 / 25 = 8 m/s. Step 3: B's total time = 1000 / 8 = 125 seconds. A's time = 125 - 25 = 100 seconds.
3485
In a 1000 m race, A beats B by 50 m or 5 seconds. What is A's time over the course?
Answer:
95 seconds
Step 1: B covers the final 50 m in 5 seconds. Step 2: B's speed = 50 / 5 = 10 m/s. Step 3: B's total time = 1000 / 10 = 100 seconds. A's time = 100 - 5 = 95 seconds.
3486
In a 1000 m race, A beats B by 100 m or 10 seconds. What is A's time over the course?
Answer:
90 seconds
Step 1: Understand that A beats B by 100 m or 10 seconds. This means B covers the last 100 m in 10 seconds. Step 2: B's speed = 100 m / 10 s = 10 m/s. Step 3: B's total time for 1000 m = 1000 / 10 = 100 seconds. Since A beats B by 10 seconds, A's time = 100 - 10 = 90 seconds.
3487
What is the ratio of the area of a circular sector with angle θ (in radians) to the area of the entire circle?
Answer:
θ / 2π
The area of the entire circle represents a full revolution of 2π radians. The area of a sector with angle θ represents a proportional fraction of that full circle, which mathematically reduces identically to θ / 2π.
3488
How many degrees does the earth rotate about its axis in exactly 2 hours?
Answer:
30°
The Earth completes a full 360° rotation in 24 hours. Therefore, its rotational speed is 360° / 24 hours = 15° per hour. In 2 hours, it rigorously rotates 2 * 15° = 30°.
3489
Find the area of a circle if an arc length of 4π cm subtends a central angle of π/2 radians.
Answer:
64π cm²
First, find the radius using l = rθ. 4π = r * (π/2). Dividing by π yields 4 = r / 2, so r = 8 cm. The full area of the circle is mathematically defined as πr², which is π(8²) = 64π cm².
3490
If the angular speed of a particle is constant at π rad/s, what angle does it cover in 1 minute?
Answer:
60π
The total angle covered is the product of angular speed and time. The time is 1 minute, which is 60 seconds. The angle covered is π rad/s * 60 s = exactly 60π radians.