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
11
In a race of 1300 m, A runs at 10 m/s and B at 9 m/s. What head start should A give B to finish together?
Answer:
130.0
Step-by-step solution: 1. For a dead heat, both runners must take equal time. 2. Use time = distance / speed for each runner. 3. A covers 1300 m while B must cover 1430.0 m at the slower speed. 4. Head start = distance * (1 - speed_B/speed_A) = 130.0 m.
12
In a race of 1600 m, A runs at 10 m/s and B at 9 m/s. What head start should A give B to finish together?
Answer:
160.0
Step-by-step solution: 1. For a dead heat, both runners must take equal time. 2. Use time = distance / speed for each runner. 3. A covers 1600 m while B must cover 1760.0 m at the slower speed. 4. Head start = distance * (1 - speed_B/speed_A) = 160.0 m.
13
In a race of 1150 m, A runs at 10 m/s and B at 9 m/s. What head start should A give B to finish together?
Answer:
115.0
Step-by-step solution: 1. For a dead heat, both runners must take equal time. 2. Use time = distance / speed for each runner. 3. A covers 1150 m while B must cover 1265.0 m at the slower speed. 4. Head start = distance * (1 - speed_B/speed_A) = 115.0 m.
14
In a race of 1250 m, A runs at 11 m/s and B at 10 m/s. What head start should A give B to finish together?
Answer:
113.64
Step-by-step solution: 1. For a dead heat, both runners must take equal time. 2. Use time = distance / speed for each runner. 3. A covers 1250 m while B must cover 1363.64 m at the slower speed. 4. Head start = distance * (1 - speed_B/speed_A) = 113.64 m.
15
In a race of 550 m, A runs at 8 m/s and B at 7 m/s. What head start should A give B to finish together?
Answer:
68.75
Step-by-step solution: 1. For a dead heat, both runners must take equal time. 2. Use time = distance / speed for each runner. 3. A covers 550 m while B must cover 618.75 m at the slower speed. 4. Head start = distance * (1 - speed_B/speed_A) = 68.75 m.
16
In a race of 650 m, A runs at 8 m/s and B at 7 m/s. What head start should A give B to finish together?
Answer:
81.25
Step-by-step solution: 1. For a dead heat, both runners must take equal time. 2. Use time = distance / speed for each runner. 3. A covers 650 m while B must cover 731.25 m at the slower speed. 4. Head start = distance * (1 - speed_B/speed_A) = 81.25 m.
17
In a race of 1300 m, A runs at 8 m/s and B at 7 m/s. What head start should A give B to finish together?
Answer:
162.5
Step-by-step solution: 1. For a dead heat, both runners must take equal time. 2. Use time = distance / speed for each runner. 3. A covers 1300 m while B must cover 1462.5 m at the slower speed. 4. Head start = distance * (1 - speed_B/speed_A) = 162.5 m.
18
In a race of 1100 m, A runs at 11 m/s and B at 10 m/s. What head start should A give B to finish together?
Answer:
100.0
Step-by-step solution: 1. For a dead heat, both runners must take equal time. 2. Use time = distance / speed for each runner. 3. A covers 1100 m while B must cover 1200.0 m at the slower speed. 4. Head start = distance * (1 - speed_B/speed_A) = 100.0 m.
19
In a race of 1200 m, A runs at 10 m/s and B at 9 m/s. What head start should A give B to finish together?
Answer:
120.0
Step-by-step solution: 1. For a dead heat, both runners must take equal time. 2. Use time = distance / speed for each runner. 3. A covers 1200 m while B must cover 1320.0 m at the slower speed. 4. Head start = distance * (1 - speed_B/speed_A) = 120.0 m.
20
In a race of 1150 m, A runs at 9 m/s and B at 8 m/s. What head start should A give B to finish together?
Answer:
127.78
Step-by-step solution: 1. For a dead heat, both runners must take equal time. 2. Use time = distance / speed for each runner. 3. A covers 1150 m while B must cover 1277.78 m at the slower speed. 4. Head start = distance * (1 - speed_B/speed_A) = 127.78 m.