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
101
Two trains are traveling in opposite directions at 126 km/hr and 90 km/hr. A passenger in the slower train observes the faster train passing him in 5 seconds. The length of the faster train is:
Answer:
300 meters
Step 1: Relative speed = 126 + 90 = 216 km/hr = 60 m/s. Step 2: Length of faster train = Relative speed * Time = 60 * 5 = 300 meters.
102
A train moving at 108 km/hr completely crosses a man sitting in a train running in the opposite direction at 72 km/hr in 5 seconds. What is its length?
Answer:
250 meters
Step 1: Relative speed = 108 + 72 = 180 km/hr = 50 m/s. Step 2: Length of the crossing train = Relative speed * Time = 50 * 5 = 250 meters.
103
Two trains run in opposite directions at 90 km/hr and 54 km/hr. A man in the slower train finds that the faster train passes him in 6 seconds. Find the length of the faster train.
Answer:
240 meters
Step 1: Relative speed = 90 + 54 = 144 km/hr = 40 m/s. Step 2: Length of faster train = Relative speed * Time = 40 * 6 = 240 meters.
104
A train running at 72 km/hr crosses a man sitting in another train moving at 36 km/hr in the opposite direction in 7 seconds. The length of the first train is:
Answer:
210 meters
Step 1: Relative speed = 72 + 36 = 108 km/hr = 30 m/s. Step 2: Length of the first train = 30 * 7 = 210 meters.
105
Two trains are moving in opposite directions at 54 km/hr and 36 km/hr. The first train completely crosses a passenger sitting in the second train in 6 seconds. What is the length of the first train?
Answer:
150 meters
Step 1: Relative speed in opposite directions = 54 + 36 = 90 km/hr = 25 m/s. Step 2: The distance covered is the length of the crossing train. Length = Speed * Time = 25 * 6 = 150 meters.
106
Two trains travel in the same direction at 99 km/hr and 63 km/hr. A man in the slower train observes that the faster train passes him in 24 seconds. The length of the faster train is:
Answer:
240 meters
Step 1: Relative speed = 99 - 63 = 36 km/hr = 10 m/s. Step 2: Length of faster train = Relative speed * Time = 10 * 24 = 240 meters.
107
A train running at 81 km/hr overtakes a man sitting in another train running at 45 km/hr in the same direction. If it takes 18 seconds to cross him, what is the length of the faster train?
Answer:
180 meters
Step 1: Relative speed = 81 - 45 = 36 km/hr = 10 m/s. Step 2: Length of faster train = 10 * 18 = 180 meters.
108
Two trains run in the same direction at 108 km/hr and 72 km/hr. The faster train completely passes a man in the slower train in 25 seconds. Find the length of the faster train.
Answer:
250 meters
Step 1: Relative speed = 108 - 72 = 36 km/hr = 10 m/s. Step 2: Length of faster train = Relative speed * Time = 10 * 25 = 250 meters.
109
A faster train running at 90 km/hr passes a man sitting in a slower train running at 54 km/hr in the same direction in 20 seconds. The length of the faster train is:
Answer:
200 meters
Step 1: Relative speed = 90 - 54 = 36 km/hr = 10 m/s. Step 2: Length of faster train = Relative speed * Time = 10 * 20 = 200 meters.
110
Two trains are moving in the same direction at 72 km/hr and 36 km/hr. The faster train crosses a man sitting in the slower train in 15 seconds. What is the length of the faster train?
Answer:
150 meters
Step 1: Relative speed in same direction = 72 - 36 = 36 km/hr = 10 m/s. Step 2: To cross a man, the faster train only needs to cover its own length. Distance (Length) = Speed * Time = 10 * 15 = 150 meters.