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
2601
How many 4-digit numbers can be formed from the digits 1, 2, 3, 4, 5, 6 assuming no digit is repeated?
Answer:
360
Step 1: We need to select and arrange 4 digits from 6 options without repetition. Step 2: Use the formula 6P4. Step 3: 6P4 = 6 × 5 × 4 × 3 = 360.
2602
How many 3-digit numbers can be formed using the digits 1, 2, 3, 4, 5 without repetition?
Answer:
60
Step 1: We need to choose and arrange 3 digits out of 5 distinct digits. Step 2: This is a permutation problem: 5P3. Step 3: 5P3 = 5 × 4 × 3 = 60.
2603
How many words can be formed from 'STATISTICS'?
Answer:
50400
Step 1: 'STATISTICS' has 10 letters. Step 2: Repetitions: S (3), T (3), I (2). Step 3: Arrangements = 10! / (3! × 3! × 2!) = 3,628,800 / (6 × 6 × 2) = 3,628,800 / 72 = 50400.
2604
Find the number of permutations of the letters in 'ALLAHABAD'.
Answer:
7560
Step 1: 'ALLAHABAD' has 9 letters. Step 2: Repetitions: A (4), L (2). Step 3: Total arrangements = 9! / (4! × 2!) = 362880 / (24 × 2) = 362880 / 48 = 7560.
2605
How many distinct permutations are there of the letters in 'ENGINEERING'?
Answer:
277200
Step 1: 'ENGINEERING' has 11 letters. Step 2: Repetitions: E (3), N (3), G (2), I (2). Step 3: Arrangements = 11! / (3! × 3! × 2! × 2!) = 39,916,800 / (6 × 6 × 2 × 2) = 39,916,800 / 144 = 277200.
2606
How many arrangements can be made out of the letters of the word 'SUCCESS'?
Answer:
420
Step 1: 'SUCCESS' has 7 letters. Step 2: Repetitions: S (3), C (2). Step 3: Total arrangements = 7! / (3! × 2!) = 5040 / (6 × 2) = 5040 / 12 = 420.
2607
In how many ways can the letters of the word 'MATHEMATICS' be arranged?
Answer:
4989600
Step 1: 'MATHEMATICS' has 11 letters. Step 2: Repetitions: M (2), A (2), T (2). Step 3: Arrangements = 11! / (2! × 2! × 2!) = 39,916,800 / 8 = 4989600.
2608
In how many distinct ways can the letters of the word 'MISSISSIPPI' be arranged?
Answer:
34650
Step 1: 'MISSISSIPPI' has 11 letters. Step 2: Repeated letters: I (4 times), S (4 times), P (2 times). Step 3: Arrangements = 11! / (4! × 4! × 2!) = 39,916,800 / (24 × 24 × 2) = 39,916,800 / 1152 = 34650.
2609
In how many distinct ways can the letters of the word 'BANANA' be arranged?
Answer:
60
Step 1: 'BANANA' has 6 letters. Step 2: Repeated letters: 'A' appears 3 times, 'N' appears 2 times. Step 3: Number of arrangements = 6! / (3! × 2!) = 720 / (6 × 2) = 720 / 12 = 60.
2610
How many different words can be formed using the letters of the word 'BOOK'?
Answer:
12
Step 1: 'BOOK' consists of 4 letters. Step 2: The letter 'O' appears 2 times. Step 3: Total arrangements = 4! / 2! = 24 / 2 = 12.