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
91
What is the probability of drawing a card that is both red and a face card?
Answer:
3/26
Step 1: Total cards = 52. Step 2: The red suits are Hearts and Diamonds. Each has 3 face cards, making 6 red face cards. Step 3: Probability = 6/52 = 3/26.
92
One card is drawn from a well-shuffled deck. Find the probability that the card is either black or a King.
Answer:
7/13
Step 1: Total black cards = 26. Total Kings = 4. Step 2: Black Kings (2) are counted twice, so favorable outcomes = 26 + 4 - 2 = 28. Step 3: Probability = 28/52 = 7/13.
93
A card is drawn from a deck of 52 cards. What is the probability that it is NOT an Ace?
Answer:
12/13
Step 1: Probability of drawing an Ace is 4/52 = 1/13. Step 2: The probability of NOT drawing an Ace is the complement. Step 3: Probability = 1 - 1/13 = 12/13.
94
If a card is drawn from a standard 52-card deck, what is the probability that it is a face card?
Answer:
3/13
Step 1: Total cards = 52. Step 2: Face cards are Jacks, Queens, and Kings. There are 3 per suit, and 4 suits, giving 3 × 4 = 12 face cards. Step 3: Probability = 12/52 = 3/13.
95
One card is drawn randomly from a standard deck. What is the probability of drawing a Red Queen?
Answer:
1/26
Step 1: Total cards = 52. Step 2: There are 2 red Queens (Hearts and Diamonds). Favorable outcomes = 2. Step 3: Probability = 2/52 = 1/26.
96
A card is drawn from a standard deck of 52 cards. What is the probability that the card is a Spade?
Answer:
1/4
Step 1: Total outcomes = 52. Step 2: There are 13 spades in a deck. Favorable outcomes = 13. Step 3: Probability = 13/52 = 1/4.
97
From a well-shuffled deck of 52 cards, one card is drawn. What is the probability that it is a King?
Answer:
1/13
Step 1: Total number of cards = 52. Step 2: There are 4 Kings in a standard deck. Favorable outcomes = 4. Step 3: Probability = 4/52 = 1/13.
98
If three dice are rolled, what is the probability that the sum of the upward faces is 18?
Answer:
1/216
Step 1: Total outcomes = 216. Step 2: The only combination to achieve a sum of 18 is (6, 6, 6). Favorable outcomes = 1. Step 3: Probability = 1/216.
99
Three standard dice are rolled. What is the probability that the sum of the numbers is 3?
Answer:
1/216
Step 1: Total outcomes for 3 dice = 6 × 6 × 6 = 216. Step 2: The only way to get a sum of 3 is (1, 1, 1). Favorable outcomes = 1. Step 3: Probability = 1/216.
100
Two dice are rolled. What is the probability that the product of the numbers is odd?
Answer:
1/4
Step 1: For the product to be odd, both numbers must be odd. Step 2: The probability of getting an odd number on one die is 3/6 = 1/2. Step 3: Since rolls are independent, P(Odd AND Odd) = (1/2) × (1/2) = 1/4.