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
21
In a race of 1000 m, A runs at 9 m/s and B at 8 m/s. What head start should A give B to finish together?
Answer:
111.11
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 1000 m while B must cover 1111.11 m at the slower speed. 4. Head start = distance * (1 - speed_B/speed_A) = 111.11 m.
22
In a race of 850 m, A runs at 11 m/s and B at 10 m/s. What head start should A give B to finish together?
Answer:
77.27
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 850 m while B must cover 927.27 m at the slower speed. 4. Head start = distance * (1 - speed_B/speed_A) = 77.27 m.
23
In a race of 1600 m, A runs at 9 m/s and B at 8 m/s. What head start should A give B to finish together?
Answer:
177.78
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 1600 m while B must cover 1777.78 m at the slower speed. 4. Head start = distance * (1 - speed_B/speed_A) = 177.78 m.
24
In a race of 800 m, A runs at 8 m/s and B at 7 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 800 m while B must cover 900.0 m at the slower speed. 4. Head start = distance * (1 - speed_B/speed_A) = 100.0 m.
25
In a race of 500 m, A runs at 9 m/s and B at 8 m/s. What head start should A give B to finish together?
Answer:
55.56
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 500 m while B must cover 555.56 m at the slower speed. 4. Head start = distance * (1 - speed_B/speed_A) = 55.56 m.
26
In a race of 750 m, A runs at 8 m/s and B at 7 m/s. What head start should A give B to finish together?
Answer:
93.75
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 750 m while B must cover 843.75 m at the slower speed. 4. Head start = distance * (1 - speed_B/speed_A) = 93.75 m.
27
In a race of 500 m, A runs at 11 m/s and B at 10 m/s. What head start should A give B to finish together?
Answer:
45.45
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 500 m while B must cover 545.45 m at the slower speed. 4. Head start = distance * (1 - speed_B/speed_A) = 45.45 m.
28
In a race of 1000 m, A runs at 12 m/s and B at 11 m/s. What head start should A give B to finish together?
Answer:
83.33
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 1000 m while B must cover 1083.33 m at the slower speed. 4. Head start = distance * (1 - speed_B/speed_A) = 83.33 m.
29
In a race of 700 m, A runs at 12 m/s and B at 11 m/s. What head start should A give B to finish together?
Answer:
58.33
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 700 m while B must cover 758.33 m at the slower speed. 4. Head start = distance * (1 - speed_B/speed_A) = 58.33 m.
30
In a race of 800 m, A runs at 10 m/s and B at 9 m/s. What head start should A give B to finish together?
Answer:
80.0
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 800 m while B must cover 880.0 m at the slower speed. 4. Head start = distance * (1 - speed_B/speed_A) = 80.0 m.