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
2631
Find the value of nP0.
Answer:
1
Step 1: Use the permutation formula: nPr = n! / (n - r)!. Step 2: Substitute r = 0: n! / (n - 0)! = n! / n!. Step 3: Any non-zero number divided by itself is 1. Thus, nP0 = 1.
2632
How many different words can be formed using all the letters of the word 'CAT'?
Answer:
6
Step 1: The word 'CAT' has 3 distinct letters. Step 2: Number of arrangements of n distinct items is n!. Step 3: 3! = 3 × 2 × 1 = 6 words.
2633
In how many ways can 3 books be selected and arranged on a shelf out of 8 different books?
Answer:
336
Step 1: Since order matters for arranging on a shelf, use permutations. Step 2: Find 8P3 = 8! / (8 - 3)! = 8! / 5!. Step 3: 8 × 7 × 6 = 336 ways.
2634
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.
2635
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.
2636
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.
2637
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.
2638
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.
2639
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.
2640
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.