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
61
A number is selected at random from the integers 1 to 20. Find the probability that it is a prime number.
Answer:
2/5
Step 1: Total numbers = 20. Step 2: Primes from 1 to 20 are 2, 3, 5, 7, 11, 13, 17, 19. (Total 8). Step 3: Probability = 8/20 = 2/5.
62
A number is chosen at random from 1 to 10. What is the probability that it is an even number?
Answer:
1/2
Step 1: Total numbers = 10. Step 2: Even numbers from 1 to 10 are 2, 4, 6, 8, 10 (Total 5). Step 3: Probability = 5/10 = 1/2.
63
A box has 7 red and 3 blue chips. What is the probability of drawing a blue chip?
Answer:
3/10
Step 1: Total chips = 7 + 3 = 10. Step 2: Favorable chips (blue) = 3. Step 3: Probability = Favorable / Total = 3/10.
64
A bag contains 5 yellow and 4 pink balls. Two balls are drawn at random. What is the probability they are of different colors?
Answer:
5/9
Step 1: 'Different colors' is the complement of 'same color'. Step 2: The probability of same color is 4/9. Step 3: Probability = 1 - 4/9 = 5/9.
65
A bag contains 5 yellow and 4 pink balls. Two balls are drawn at random. What is the probability they are of the same color?
Answer:
4/9
Step 1: Total balls = 9. We need P(Both Yellow) OR P(Both Pink). Step 2: P(YY) = (5/9) × (4/8) = 20/72. P(PP) = (4/9) × (3/8) = 12/72. Step 3: Add probabilities: 20/72 + 12/72 = 32/72 = 4/9.
66
An urn contains 6 white and 4 black balls. If 3 balls are drawn at random without replacement, what is the probability they are all white?
Answer:
1/6
Step 1: Total balls = 10. Draw 1: P(W) = 6/10. Draw 2: P(W) = 5/9. Draw 3: P(W) = 4/8. Step 2: Multiply probabilities: (6/10) × (5/9) × (4/8). Step 3: (3/5) × (5/9) × (1/2) = (3/9) × (1/2) = (1/3) × (1/2) = 1/6.
67
Bag A has 3 red and 2 blue balls. Bag B has 2 red and 4 blue balls. A bag is chosen at random, and a ball is drawn. What is the probability it is red?
Answer:
Both A and B
Step 1: Probability of picking Bag A = 1/2, Bag B = 1/2. Step 2: P(Red) = P(Bag A)×P(Red|A) + P(Bag B)×P(Red|B) = (1/2)×(3/5) + (1/2)×(2/6). Step 3: = 3/10 + 1/6 = 9/30 + 5/30 = 14/30, which simplifies to 7/15. Both A and B represent the same value.
68
From a bag of 3 red, 4 blue, and 5 green marbles, two are drawn without replacement. What is the probability both are blue?
Answer:
1/11
Step 1: Total marbles = 12. P(First Blue) = 4/12 = 1/3. Step 2: Remaining total = 11, remaining blue = 3. P(Second Blue) = 3/11. Step 3: Probability = (1/3) × (3/11) = 1/11.
69
A bag contains 3 red, 4 blue, and 5 green marbles. What is the probability of drawing a red or a blue marble in one draw?
Answer:
7/12
Step 1: Total marbles = 3 + 4 + 5 = 12. Step 2: The events are mutually exclusive. Favorable outcomes = (3 red) + (4 blue) = 7. Step 3: Probability = 7/12.
70
A box contains 4 white and 5 black balls. Two balls are drawn with replacement. Probability of getting first white and second black is:
Answer:
20/81
Step 1: Events are independent due to replacement. Step 2: P(First White) = 4/9. P(Second Black) = 5/9. Step 3: Combined probability = (4/9) × (5/9) = 20/81.