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
What is the probability that the product of the numbers obtained by rolling two fair dice is 12?
Answer:
1/9
Step 1: Total outcomes = 36. Step 2: Favorable pairs yielding a product of 12 are (2,6), (3,4), (4,3), (6,2). Total = 4. Step 3: Probability = 4/36 = 1/9.
102
Two dice are rolled. What is the probability that the sum of the numbers is less than or equal to 4?
Answer:
1/6
Step 1: Total outcomes = 36. Step 2: Sums <= 4 are 2, 3, or 4. Favorable outcomes: (1,1), (1,2), (2,1), (1,3), (2,2), (3,1). Total = 6. Step 3: Probability = 6/36 = 1/6.
103
If two fair dice are rolled, find the probability that the sum is exactly 12.
Answer:
1/36
Step 1: Total outcomes = 36. Step 2: The only way to get a sum of 12 is (6,6). Favorable outcomes = 1. Step 3: Probability = 1/36.
104
Two dice are rolled. What is the probability that both dice show a multiple of 3?
Answer:
1/9
Step 1: Total outcomes = 36. Multiples of 3 on a die are {3, 6}. Step 2: Favorable pairs are (3,3), (3,6), (6,3), (6,6). Total = 4. Step 3: Probability = 4/36 = 1/9.
105
When two dice are thrown simultaneously, what is the probability that the sum is a prime number?
Answer:
5/12
Step 1: Total outcomes = 36. Prime sums possible are 2, 3, 5, 7, 11. Step 2: Number of ways for each: sum 2 (1), sum 3 (2), sum 5 (4), sum 7 (6), sum 11 (2). Total ways = 1 + 2 + 4 + 6 + 2 = 15. Step 3: Probability = 15/36 = 5/12.
106
Two dice are tossed. What is the probability of getting a doublet (same number on both dice)?
Answer:
1/6
Step 1: Total outcomes = 36. Step 2: The doublets are (1,1), (2,2), (3,3), (4,4), (5,5), (6,6). Favorable outcomes = 6. Step 3: Probability = 6/36 = 1/6.
107
What is the probability of getting a sum greater than 9 when rolling two dice?
Answer:
1/6
Step 1: Total outcomes = 36. Step 2: A sum greater than 9 means sums of 10, 11, or 12. Favorable outcomes: (4,6), (5,5), (6,4), (5,6), (6,5), (6,6). Total = 6. Step 3: Probability = 6/36 = 1/6.
108
If two dice are thrown, find the probability that the sum of the faces equals 8.
Answer:
5/36
Step 1: Total outcomes = 36. Step 2: Favorable outcomes for a sum of 8 are (2,6), (3,5), (4,4), (5,3), (6,2). Total = 5. Step 3: Probability = 5/36.
109
Two fair dice are rolled. What is the probability that the sum of the numbers is 7?
Answer:
1/6
Step 1: Total outcomes when two dice are rolled = 6 × 6 = 36. Step 2: Outcomes yielding a sum of 7 are (1,6), (2,5), (3,4), (4,3), (5,2), (6,1). Favorable outcomes = 6. Step 3: Probability = 6/36 = 1/6.
110
What is the probability of rolling a number greater than 4 on a fair die?
Answer:
1/3
Step 1: Total possible outcomes = 6. Step 2: Numbers greater than 4 are {5, 6}. Favorable outcomes = 2. Step 3: Probability = 2/6 = 1/3.