Q.1 How many ways can 3 books be arranged on a shelf?
3
6
9
12
Explanation - The number of ways to arrange n objects is n! = 3! = 6.
Correct answer is: 6
Q.2 How many subsets does a set with 5 elements have?
10
16
32
64
Explanation - The total number of subsets of a set with n elements is 2^n. For n=5, 2^5=32.
Correct answer is: 32
Q.3 How many different 3-letter codes can be formed from the letters A, B, C, D without repetition?
24
12
6
36
Explanation - Number of permutations of 4 objects taken 3 at a time: P(4,3)=4×3×2=24.
Correct answer is: 24
Q.4 How many ways can you choose 2 balls from a bag of 6?
12
15
18
30
Explanation - This is a combination: C(6,2)=6×5/2=15.
Correct answer is: 15
Q.5 How many 4-digit numbers can be formed using digits 1–9 without repetition?
3024
4096
5040
6561
Explanation - P(9,4)=9×8×7×6=3024.
Correct answer is: 3024
Q.6 In how many ways can the letters of the word 'LEVEL' be arranged?
60
120
240
360
Explanation - 5 letters with repetition: 5! / (2!2!) = 120/2=60.
Correct answer is: 60
Q.7 How many binary strings of length 4 are possible?
8
12
16
32
Explanation - Each digit has 2 choices, so total is 2^4=16.
Correct answer is: 16
Q.8 The number of ways to arrange 10 people in a line is:
10
100
1000
3628800
Explanation - Arranging 10 people = 10! = 3628800.
Correct answer is: 3628800
Q.9 How many ways to select a committee of 3 from 8 people?
56
64
72
80
Explanation - C(8,3)=8×7×6/6=56.
Correct answer is: 56
Q.10 How many diagonals does a polygon with 12 sides have?
54
60
66
72
Explanation - Formula: n(n−3)/2. For n=12: 12×9/2=54.
Correct answer is: 54
Q.11 How many ways can the letters of the word 'BANANA' be arranged?
60
120
360
720
Explanation - 6 letters with 3 A’s and 2 N’s: 6!/(3!2!)=720/12=60.
Correct answer is: 60
Q.12 How many ways can a president and a secretary be chosen from 10 members?
90
100
110
120
Explanation - This is permutation: 10×9=90.
Correct answer is: 90
Q.13 How many handshakes occur in a party of 15 people if each pair shakes hands?
90
100
105
120
Explanation - Number of handshakes = C(15,2)=15×14/2=105.
Correct answer is: 105
Q.14 How many ways can you arrange the word 'MISSISSIPPI'?
34650
34680
34620
34640
Explanation - 11 letters with repetitions: 11! / (4!4!2!) = 34650.
Correct answer is: 34650
Q.15 How many ways can you choose 4 cards from a deck of 52?
270725
270400
2707250
27000
Explanation - C(52,4)=270725.
Correct answer is: 270725
Q.16 How many strings of length 5 can be formed from 3 letters if repetition is allowed?
81
125
243
3125
Explanation - Total = 3^5=243.
Correct answer is: 243
Q.17 The number of permutations of n objects taken 0 at a time is:
0
1
n
n!
Explanation - By definition, P(n,0)=1.
Correct answer is: 1
Q.18 How many ways can 6 identical balls be placed in 3 distinct boxes?
28
30
32
36
Explanation - This is stars and bars: C(6+3−1,3−1)=C(8,2)=28.
Correct answer is: 28
Q.19 How many 3-digit numbers can be formed with digits 1–9 without repetition?
504
648
720
729
Explanation - P(9,3)=9×8×7=504.
Correct answer is: 504
Q.20 How many non-empty subsets does a set with 7 elements have?
63
64
128
127
Explanation - Total subsets = 2^7=128. Non-empty = 128−1=127.
Correct answer is: 127
Q.21 How many ways can a coin be tossed 6 times?
32
48
64
128
Explanation - Each toss has 2 outcomes: total=2^6=64.
Correct answer is: 64
Q.22 The binomial coefficient C(10,3) is:
60
100
120
150
Explanation - C(10,3)=10×9×8/3!=120.
Correct answer is: 120
Q.23 How many arrangements of the word 'APPLE' are possible?
60
120
240
360
Explanation - 5 letters with 2 P’s: 5!/2!=60.
Correct answer is: 60
Q.24 How many different 5-digit numbers can be formed using digits 0–9 without repetition?
30240
27216
30000
40000
Explanation - First digit 9 choices (1–9), then remaining 9×8×7×6 = total 9×9×8×7×6=30240.
Correct answer is: 30240
Q.25 How many derangements are there for 4 objects?
6
8
9
10
Explanation - Derangement formula: !n = n!(1−1/1!+1/2!−1/3!+...+(−1)^n/n!). For n=4, !4=9.
Correct answer is: 9