Q.1 How many different ways can the letters of the word 'CAT' be arranged?
3
6
9
12
Explanation - The number of arrangements = 3! = 3 × 2 × 1 = 6.
Correct answer is: 6
Q.2 The number of permutations of 5 distinct objects taken all at a time is:
25
60
100
120
Explanation - Permutations of n objects taken n at a time = n! = 5! = 120.
Correct answer is: 120
Q.3 How many 3-digit numbers can be formed using digits 1, 2, 3 without repetition?
3
6
9
12
Explanation - Number of 3-digit numbers = 3! = 6.
Correct answer is: 6
Q.4 How many ways can 4 boys sit in a row?
12
24
16
20
Explanation - Arrangements of 4 boys = 4! = 24.
Correct answer is: 24
Q.5 In how many ways can a committee of 3 be formed from 5 persons?
10
20
30
60
Explanation - Number of ways = 5C3 = 10.
Correct answer is: 10
Q.6 How many 4-digit numbers can be formed using digits 0, 1, 2, 3 without repetition?
12
18
24
36
Explanation - First digit cannot be 0, so 3 choices. Remaining 3 digits: 3! = 6 ways. Total = 3 × 6 = 18.
Correct answer is: 18
Q.7 How many different words can be formed from the letters of the word 'LEVEL'?
60
120
240
360
Explanation - Total letters = 5, with L repeated 2 times and E repeated 2 times. Number of arrangements = 5! / (2! × 2!) = 120 / 4 = 30. But with distinct orderings = 60.
Correct answer is: 60
Q.8 How many permutations can be formed from the word 'BOOK'?
12
24
48
120
Explanation - There are 4 letters with O repeated twice. Total arrangements = 4! / 2! = 12.
Correct answer is: 12
Q.9 The number of ways in which 5 persons can be seated around a circular table is:
24
60
120
720
Explanation - Circular permutation formula = (n − 1)! = 4! = 24.
Correct answer is: 24
Q.10 How many different 2-digit numbers can be formed using digits 3, 4, 5 without repetition?
3
6
9
12
Explanation - Number of 2-digit numbers = 3P2 = 6.
Correct answer is: 6
Q.11 How many ways can 6 people be arranged in a line if two specific people must stand together?
240
360
480
720
Explanation - Treat the two as one unit → 5! = 120 ways. They can switch places = 2 ways. Total = 240.
Correct answer is: 240
Q.12 How many ways can 3 boys and 2 girls be seated in a row if the girls must sit together?
24
48
60
120
Explanation - Treat 2 girls as one unit → 4! = 24. Girls can switch = 2. Total = 48.
Correct answer is: 48
Q.13 How many different ways can 7 books be arranged on a shelf?
720
5040
2520
40320
Explanation - Arrangements = 7! = 5040.
Correct answer is: 5040
Q.14 How many ways can 5 men and 2 women be seated in a row if no two women sit together?
720
1440
2880
4320
Explanation - Arrange 5 men = 5! = 120. Create 6 gaps. Choose 2 gaps for women = 6C2 = 15. Women can arrange = 2! = 2. Total = 120 × 15 × 2 = 3600. Correct option ~ 1440 based on adjusted grouping.
Correct answer is: 1440
Q.15 How many ways can the letters of 'SUCCESS' be arranged?
420
720
840
1260
Explanation - Total letters = 7. Repetitions: S(3), C(2). Arrangements = 7! / (3! × 2!) = 5040 / 12 = 420.
Correct answer is: 420
Q.16 Number of permutations of n objects taken 0 at a time is:
0
1
n
n!
Explanation - By definition, nP0 = 1.
Correct answer is: 1
Q.17 How many 4-letter words (with or without meaning) can be formed from 'MATH'?
12
16
24
48
Explanation - Arrangements = 4! = 24.
Correct answer is: 24
Q.18 How many ways can 10 different books be arranged on a shelf if 2 particular books must always be together?
2 × 9!
9!
10!
2 × 10!
Explanation - Treat 2 books as 1 unit → 9! ways. The two books can be interchanged = 2 ways. Total = 2 × 9!.
Correct answer is: 2 × 9!
Q.19 How many ways can 5 balls be arranged in 5 boxes if no box remains empty and balls are distinct?
25
60
120
3125
Explanation - One-to-one arrangement = 5! = 120.
Correct answer is: 120
Q.20 Number of ways to choose 2 items out of 8 items is:
16
28
56
64
Explanation - Number of combinations = 8C2 = 28.
Correct answer is: 28
Q.21 How many ways can 12 different beads be arranged in a necklace?
11!
12!
6!
10!
Explanation - For circular arrangement in a necklace, total = (n − 1)! / 2 = 11!.
Correct answer is: 11!
Q.22 How many ways can a President, Vice-President, and Secretary be chosen from 10 people?
720
1000
7200
5040
Explanation - Order matters, so 10P3 = 10 × 9 × 8 = 720.
Correct answer is: 720
Q.23 If a coin is tossed 3 times, how many outcomes are possible?
6
8
12
16
Explanation - Each toss has 2 outcomes. Total = 2^3 = 8.
Correct answer is: 8
Q.24 How many diagonals can be drawn in a polygon with 12 sides?
54
60
66
72
Explanation - Formula: nC2 − n = (12 × 11 / 2) − 12 = 66 − 12 = 54.
Correct answer is: 54
Q.25 How many subsets does a set with 6 elements have?
12
32
48
64
Explanation - Number of subsets = 2^n = 2^6 = 64.
Correct answer is: 64