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
101
In how many ways can 5 students be arranged in a straight line?
Answer:
120
Step 1: Arranging n distinct objects in a line is calculated by n!. Step 2: Here, n = 5. Step 3: Total arrangements = 5! = 5 × 4 × 3 × 2 × 1 = 120.
102
If nP2 = 30, what is the value of n?
Answer:
6
Step 1: Expand nP2 using the formula: n(n - 1) = 30. Step 2: Look for two consecutive integers whose product is 30. Step 3: 6 × 5 = 30, so n = 6.
103
Calculate the value of 7P7.
Answer:
5040
Step 1: The formula for nPn is n!. Step 2: Substitute n = 7 to get 7!. Step 3: 7! = 7 × 6 × 5 × 4 × 3 × 2 × 1 = 5040.
104
What is the value of 5P3 (Permutations of 5 objects taken 3 at a time)?
Answer:
60
Step 1: The formula for nPr is n! / (n - r)!. Step 2: Substitute n = 5 and r = 3: 5! / (5 - 3)! = 5! / 2!. Step 3: Calculate: (5 × 4 × 3 × 2!) / 2! = 5 × 4 × 3 = 60.
105
There are 5 routes from City A to City B, and 4 routes from City B to City C. How many different routes are there from City A to City C via City B?
Answer:
20
Step 1: Use the Multiplication Principle of Counting. Step 2: Number of ways from A to B is 5. Number of ways from B to C is 4. Step 3: Total ways from A to C = 5 × 4 = 20.
106
If a person has 4 different shirts and 3 different pairs of pants, in how many ways can they choose an outfit?
Answer:
12
Step 1: Use the Fundamental Counting Principle. Step 2: The number of ways to choose a shirt is 4, and the number of ways to choose a pair of pants is 3. Step 3: Total outfits = 4 × 3 = 12.
107
Evaluate 8! / 6!.
Answer:
56
Step 1: Expand the numerator to match the denominator: 8! = 8 × 7 × 6!. Step 2: The expression becomes (8 × 7 × 6!) / 6!. Step 3: Cancel out 6! from the numerator and denominator to get 8 × 7 = 56.
108
What is the value of 0!?
Answer:
1
Step 1: By mathematical convention and the definition of the gamma function, the factorial of zero is defined. Step 2: There is exactly one way to arrange zero objects (doing nothing). Step 3: Therefore, 0! = 1.
109
What is the value of 6! (6 factorial)?
Answer:
720
Step 1: The factorial of a number n, denoted by n!, is the product of all positive integers less than or equal to n. Step 2: 6! = 6 × 5 × 4 × 3 × 2 × 1. Step 3: 6! = 30 × 24 = 720.