All Categories MCQs
Topic Notes: All Categories
General Description
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
2761
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.
2762
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.
2763
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.
2764
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.
2765
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.
2766
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.
2767
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.
2768
If two unbiased coins are tossed simultaneously, what is the probability of getting exactly two heads?
Answer:
1/4
Step 1: The sample space is {HH, HT, TH, TT}. Total outcomes = 4. Step 2: The favorable outcome for exactly two heads is {HH}. Favorable outcomes = 1. Step 3: Probability = 1/4.
2769
What is the probability of getting a head when a single unbiased coin is tossed?
Answer:
1/2
Step 1: The sample space for a single coin toss is {Head, Tail}. Total possible outcomes = 2. Step 2: The favorable outcome is {Head}. Number of favorable outcomes = 1. Step 3: Probability = Favorable outcomes / Total outcomes = 1/2.
2770
The area of the base of a right circular cone is 154 cm² and its height is 14 cm. Its curved surface area is:
Answer:
154√5 cm²
Base area = πr² = 154 => (22/7)r² = 154 => r² = 49 => r = 7 cm. Height h = 14 cm. Slant height l = √(7² + 14²) = √(49 + 196) = √245 = √(49 × 5) = 7√5 cm. Curved surface area = πrl = (22/7) × 7 × 7√5 = 154√5 cm².