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
111
When a single die is rolled, what is the probability of getting a prime number?
Answer:
1/2
Step 1: Total outcomes = 6. Step 2: The prime numbers on a die are {2, 3, 5}. Favorable outcomes = 3. (Note: 1 is not a prime number). Step 3: Probability = 3/6 = 1/2.
112
What is the probability of rolling an even number on a standard six-sided die?
Answer:
1/2
Step 1: The sample space is {1, 2, 3, 4, 5, 6}. Total outcomes = 6. Step 2: The even numbers are {2, 4, 6}. Favorable outcomes = 3. Step 3: Probability = 3/6 = 1/2.
113
A biased coin has a 60% chance of landing on heads. If tossed twice, what is the probability of getting two heads?
Answer:
0.36
Step 1: The probability of heads P(H) = 0.6. Step 2: The tosses are independent events. Probability of two heads = P(H) × P(H). Step 3: 0.6 × 0.6 = 0.36.
114
If four coins are tossed together, find the probability of getting at least one tail.
Answer:
15/16
Step 1: Total outcomes = 16. Step 2: The complement of 'at least one tail' is 'no tails' (all heads, {HHHH}), which is 1 outcome. Step 3: Probability = 1 - P(all heads) = 1 - 1/16 = 15/16.
115
When four coins are tossed, what is the probability of getting no heads?
Answer:
1/16
Step 1: Total outcomes = 16. Step 2: 'No heads' means all tails {TTTT}, which is exactly 1 outcome. Step 3: Probability = 1/16.
116
Four coins are tossed. What is the probability of getting exactly two heads?
Answer:
3/8
Step 1: Total outcomes = 2⁴ = 16. Step 2: The number of ways to choose 2 heads from 4 coins is given by combination 4C2 = (4×3)/(2×1) = 6. Step 3: Probability = 6/16 = 3/8.
117
If three coins are tossed, what is the probability of getting at most two heads?
Answer:
7/8
Step 1: Total outcomes = 8. 'At most two heads' means 0, 1, or 2 heads. Step 2: It is easier to find the complement: getting 3 heads, which is {HHH} (1 outcome). Step 3: Favorable outcomes = Total - Complement = 8 - 1 = 7. Probability = 7/8.
118
Three coins are tossed simultaneously. Find the probability of getting all tails.
Answer:
1/8
Step 1: Total possible outcomes for 3 coins is 8. Step 2: The only outcome with all tails is {TTT}. Favorable outcomes = 1. Step 3: Probability = 1/8.
119
Three unbiased coins are tossed. What is the probability of getting exactly two heads?
Answer:
3/8
Step 1: The total number of outcomes for 3 coins is 2³ = 8. Step 2: Outcomes with exactly two heads are {HHT, HTH, THH}. Total favorable = 3. Step 3: Probability = 3/8.
120
When two coins are tossed, what is the probability of getting at least one head?
Answer:
3/4
Step 1: The sample space is {HH, HT, TH, TT}, totaling 4 outcomes. Step 2: 'At least one head' includes {HH, HT, TH}. Favorable outcomes = 3. Step 3: Probability = 3/4.