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
A bag contains 11 balls, of which 4 are red. What is the probability of drawing a red ball?
Answer:
0.364
Step-by-step solution: 1. Probability = favourable outcomes / total outcomes. 2. Probability = 4 / 11 = 0.364. 3. Simplify the fraction to decimal form.
22
A bag contains 15 balls, of which 5 are red. What is the probability of drawing a red ball?
Answer:
0.333
Step-by-step solution: 1. Probability = favourable outcomes / total outcomes. 2. Probability = 5 / 15 = 0.333. 3. Simplify the fraction to decimal form.
23
A bag contains 13 balls, of which 3 are red. What is the probability of drawing a red ball?
Answer:
0.231
Step-by-step solution: 1. Probability = favourable outcomes / total outcomes. 2. Probability = 3 / 13 = 0.231. 3. Simplify the fraction to decimal form.
24
A box contains 3 defective and 7 good light bulbs. If one bulb is drawn, what is the probability it is good?
Answer:
7/10
Step 1: Total bulbs = 3 + 7 = 10. Step 2: Favorable outcomes (good bulbs) = 7. Step 3: Probability = Favorable / Total = 7/10.
25
A student guesses on 4 multiple-choice questions, each with 4 options. What is the probability of getting all correct by guessing?
Answer:
1/256
Step 1: Probability of getting one specific question right by guessing = 1/4. Step 2: The questions are independent. Step 3: Combined probability = (1/4)⁴ = 1/256.
26
A student guesses on 3 true/false questions. What is the probability of getting all of them correct?
Answer:
1/8
Step 1: The probability of guessing one correct T/F answer is 1/2. Step 2: Guessing on each question is an independent event. Step 3: Probability = (1/2) × (1/2) × (1/2) = 1/8.
27
Two coins and one die are tossed. Find the probability of getting exactly two Heads and an Even number.
Answer:
1/8
Step 1: The events (coins and die) are independent. P(Exactly 2 Heads with 2 coins) = 1/4. Step 2: P(Even number on a die) = 3/6 = 1/2. Step 3: Combined probability = (1/4) × (1/2) = 1/8.
28
A coin and a die are tossed simultaneously. What is the probability of getting a Head and a 6?
Answer:
1/12
Step 1: The events are independent. P(Head) = 1/2. Step 2: P(Rolling a 6) = 1/6. Step 3: Combined probability = P(Head) × P(6) = (1/2) × (1/6) = 1/12.
29
What is the probability of a sure (certain) event?
Answer:
1
Step 1: A sure event is one that will definitely happen. Step 2: Every possible outcome is a favorable outcome. Favorable outcomes = Total outcomes. Step 3: Hence, Probability = Total / Total = 1.
30
If events A and B are independent with P(A) = 0.3 and P(B) = 0.6, find P(A or B).
Answer:
0.72
Step 1: Since they are independent, P(A and B) = P(A) × P(B) = 0.3 × 0.6 = 0.18. Step 2: Apply the addition rule: P(A or B) = P(A) + P(B) - P(A and B). Step 3: 0.3 + 0.6 - 0.18 = 0.90 - 0.18 = 0.72.