Q.1 How many ways can you arrange the letters of the word 'CAT'?
3
6
9
12
Explanation - The number of arrangements is given by 3! = 6.
Correct answer is: 6
Q.2 How many subsets does a set with 4 elements have?
4
8
12
16
Explanation - A set with n elements has 2^n subsets. Here, 2^4 = 16.
Correct answer is: 16
Q.3 How many ways can 5 people sit in a row of chairs?
25
60
120
240
Explanation - Number of arrangements = 5! = 120.
Correct answer is: 120
Q.4 What is the number of permutations of the word 'LEVEL'?
60
120
240
720
Explanation - Total letters = 5. With 2 L’s and 2 E’s: 5! / (2! × 2!) = 120/2×2 = 30. Actually correction: 5! / (2!×2!) = 120/4 = 30. So correct answer is 30.
Correct answer is: 60
Q.5 How many ways can you choose 2 items from a set of 5?
5
8
10
15
Explanation - Combinations formula: 5C2 = 5! / (2!(3!)) = 10.
Correct answer is: 10
Q.6 What is 0! equal to?
0
1
Undefined
Infinity
Explanation - By definition, 0! = 1 to satisfy permutation rules.
Correct answer is: 1
Q.7 How many diagonals does a hexagon have?
6
9
12
15
Explanation - Number of diagonals = n(n-3)/2. For hexagon, 6×3/2 = 9.
Correct answer is: 9
Q.8 How many binary strings of length 3 exist?
4
6
8
16
Explanation - Each position has 2 options. So total = 2^3 = 8.
Correct answer is: 8
Q.9 How many ways can you arrange 4 books on a shelf?
12
16
24
36
Explanation - Number of arrangements = 4! = 24.
Correct answer is: 24
Q.10 How many ways can 3 coins be tossed?
6
7
8
9
Explanation - Each coin has 2 outcomes. So total = 2^3 = 8.
Correct answer is: 8
Q.11 How many 2-digit numbers can be formed with digits 1, 2, 3 without repetition?
3
6
9
12
Explanation - First digit: 3 choices. Second digit: 2 choices. Total = 6.
Correct answer is: 6
Q.12 How many 5-digit numbers can be formed using digits 0–9 without repetition?
30240
30250
30260
36240
Explanation - First digit: 9 choices (no zero). Remaining: 9×8×7×6. Total = 9×9×8×7×6 = 30240.
Correct answer is: 30240
Q.13 How many ways can 2 identical balls be placed in 3 boxes?
3
6
9
10
Explanation - Using stars and bars: (3+2-1)C2 = 4C2 = 6.
Correct answer is: 6
Q.14 How many derangements are there for 3 objects?
1
2
3
4
Explanation - Derangements for 3 objects = 3! (1 - 1/1! + 1/2! - 1/3!) = 6(1 - 1 + 0.5 - 0.166…) = 2.
Correct answer is: 2
Q.15 How many subsets of {1,2,3,4,5} contain 3?
8
12
16
24
Explanation - Half of all subsets include a given element. Total subsets = 32, half = 16.
Correct answer is: 16
Q.16 The number of ways to choose a committee of 2 from 10 people is?
20
30
40
45
Explanation - 10C2 = 10! / (2! × 8!) = 45.
Correct answer is: 45
Q.17 How many 3-digit even numbers can be formed with digits 1,2,3,4 without repetition?
6
8
10
12
Explanation - Unit digit must be even (2 or 4 → 2 choices). Remaining: 3×2 = 6. Total = 12. Actually correction: If last digit=2 → 3 choices for hundreds, 2 for tens = 6. If last digit=4 → same = 6. Total = 12.
Correct answer is: 8
Q.18 How many ways to arrange 5 different rings on 3 fingers?
120
150
210
243
Explanation - Each ring has 3 choices independently. Total = 3^5 = 243.
Correct answer is: 243
Q.19 The number of non-negative integer solutions to x+y+z=5 is?
15
18
20
21
Explanation - By stars and bars: (5+3-1)C2 = 7C2 = 21.
Correct answer is: 21
Q.20 How many ways can a president, vice-president, and secretary be chosen from 7 people?
210
252
280
300
Explanation - 7P3 = 7×6×5 = 210.
Correct answer is: 210
Q.21 The number of anagrams of 'BANANA' is?
60
120
360
720
Explanation - 6! / (3!×2!) = 720/12 = 60.
Correct answer is: 60
Q.22 How many 3-element subsets can be formed from {1,2,3,4,5,6}?
10
15
20
25
Explanation - 6C3 = 20.
Correct answer is: 20
Q.23 How many 4-digit PINs can be formed if digits can repeat?
1000
5000
9000
10000
Explanation - Each digit has 10 choices. So total = 10^4 = 10000.
Correct answer is: 10000
Q.24 In how many ways can 10 identical balls be distributed into 4 boxes?
84
100
120
286
Explanation - Stars and bars: (10+4-1)C3 = 13C3 = 286.
Correct answer is: 286
Q.25 The number of circular permutations of 6 people around a round table is?
120
240
720
5040
Explanation - Circular permutations = (n-1)!. Here, 5! = 120.
Correct answer is: 120