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
81
What is the probability of drawing a card with a prime number (2, 3, 5, or 7) from a standard deck?
Answer:
Both A and B
Step 1: Prime numbers on cards are 2, 3, 5, and 7. That's 4 cards per suit. Step 2: Total prime number cards = 4 × 4 = 16. Step 3: Probability = 16/52 = 4/13. Both A and B are correct.
82
A card is drawn from a standard deck. What is the probability it is a number card from 2 to 10?
Answer:
Both A and B
Step 1: Cards numbered 2 through 10 total 9 cards per suit. Step 2: Across 4 suits, there are 9 × 4 = 36 such cards. Step 3: Probability = 36/52, which simplifies to 9/13. Both A and B are correct representations.
83
If three cards are drawn sequentially without replacement, what is the probability that they are all Aces?
Answer:
1/5525
Step 1: P(First Ace) = 4/52. P(Second Ace) = 3/51. P(Third Ace) = 2/50. Step 2: Multiply them: (1/13) × (1/17) × (1/25). Step 3: (1 × 1 × 1) / (13 × 17 × 25) = 1 / (221 × 25) = 1/5525.
84
Two cards are drawn from a deck without replacement. What is the probability that both are black?
Answer:
25/102
Step 1: Probability of first black card = 26/52 = 1/2. Step 2: Probability of second black card = 25/51. Step 3: Total probability = (1/2) × (25/51) = 25/102.
85
Two cards are drawn sequentially WITH replacement. What is the probability that both are Aces?
Answer:
1/169
Step 1: With replacement, the events are independent. Probability of first Ace = 4/52 = 1/13. Step 2: Probability of second Ace = 4/52 = 1/13. Step 3: Combined probability = (1/13) × (1/13) = 1/169.
86
What is the probability of drawing two Spades sequentially without replacement from a deck of 52 cards?
Answer:
1/17
Step 1: Probability of first Spade = 13/52 = 1/4. Step 2: Probability of second Spade = 12/51 = 4/17. Step 3: Combined probability = (1/4) × (4/17) = 1/17.
87
Two cards are drawn without replacement. What is the probability of drawing one King and one Queen in that exact order?
Answer:
4/663
Step 1: Probability of the first card being a King = 4/52. Step 2: Probability of the second card being a Queen = 4/51. Step 3: Combined probability = (4/52) × (4/51) = (1/13) × (4/51) = 4/663.
88
If two cards are drawn from a pack without replacement, what is the probability that both are red?
Answer:
25/102
Step 1: Probability of drawing the first red card = 26/52 = 1/2. Step 2: Probability of drawing the second red card = 25/51. Step 3: Combined probability = (1/2) × (25/51) = 25/102.
89
Two cards are drawn sequentially without replacement from a standard deck. What is the probability that both are Kings?
Answer:
1/221
Step 1: Probability of first card being a King = 4/52 = 1/13. Step 2: Probability of second card being a King (without replacement) = 3/51 = 1/17. Step 3: Combined probability = (1/13) × (1/17) = 1/221.
90
A card is drawn from a 52-card deck. What is the probability that it is neither a heart nor a king?
Answer:
9/13
Step 1: Total hearts = 13. Total kings = 4. Heart king is 1. P(Heart or King) = (13 + 4 - 1)/52 = 16/52 = 4/13. Step 2: 'Neither' is the complement of 'either'. Step 3: Probability = 1 - 4/13 = 9/13.