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Permutations and Combinations Practice Questions

JEE · Mathematics · 1645 free MCQs with instant results and detailed explanations.

1645
Total
442
Easy
741
Medium
462
Hard

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Topics in Permutations and Combinations

Fundamental Principle 243
Permutations 207
Combinations 228
Binomial Theorem 177
Fundamental Counting 200
Binomial Coefficients 220
Derangements 199
Grouping and Distribution 171

Sample Questions from Permutations and Combinations

Here are 10 sample questions. Start a quiz to get randomized questions with scoring.

Q1
Easy
In how many ways can 5 different books be arranged on a shelf?
A. 120
B. 60
C. 5
D. 24
Show Answer & Explanation
Correct Answer: A
The number of arrangements of n distinct objects is given by n!. Here, n = 5, so the arrangements are 5! = 120.
Q2
Easy
A committee of 3 members is to be formed from a group of 5 people. How many different committees can be formed?
A. 10
B. 15
C. 5
D. 20
Show Answer & Explanation
Correct Answer: A
The number of ways to form a committee of 3 from 5 people is given by the combination formula C(n, r) = n! / [r!(n-r)!]. Here, C(5, 3) = 5!/(3!2!) = 10.
Q3
Easy
In how many ways can 4 different colored balls be placed in 3 distinct boxes if each box can hold any number of balls?
A. 81
B. 64
C. 48
D. 12
Show Answer & Explanation
Correct Answer: A
Each ball can go into any of the 3 boxes. Therefore, for 4 balls, the number of arrangements is 3^4 = 81.
Q4
Medium
In how many ways can the letters of the word 'MATH' be arranged?
A. 24
B. 12
C. 16
D. 8
Show Answer & Explanation
Correct Answer: A
The word 'MATH' has 4 distinct letters. The number of arrangements is 4! = 24.
Q5
Medium
How many ways can you choose 4 subjects from a total of 10 subjects?
A. 210
B. 120
C. 300
D. 40
Show Answer & Explanation
Correct Answer: A
Using the combination formula C(10, 4) = 10! / (4! * (10 - 4)!) = 210, we find the number of ways to choose 4 subjects.
Q6
Medium
If there are 6 different books, how many ways can you arrange them on a shelf?
A. 720
B. 120
C. 360
D. 480
Show Answer & Explanation
Correct Answer: A
The number of arrangements of 6 distinct books is given by 6! = 720.
Q7
Medium
From a group of 8 people, how many ways can a committee of 3 be formed?
A. 56
B. 24
C. 48
D. 36
Show Answer & Explanation
Correct Answer: A
Using the combination formula C(8, 3) = 8! / (3! * 5!) = 56, we find the number of ways to form the committee.
Q8
Hard
In how many ways can you arrange 5 different books on a shelf if 2 specific books must be together?
A. 48
B. 120
C. 60
D. 24
Show Answer & Explanation
Correct Answer: A
When two specific books must be together, treat them as a single unit. This gives us 4 units to arrange: (AB), Book 3, Book 4, Book 5. The number of arrangements is 4! = 24. Within the unit (AB), the two books can be arranged among themselves in 2! = 2 ways. Thus, total arrangements = 4! * 2! = 24 * 2 = 48.
Q9
Hard
If there are 8 different flags and you want to arrange 3 of them on a pole, how many different arrangements are possible?
A. 336
B. 128
C. 56
D. 64
Show Answer & Explanation
Correct Answer: A
To arrange 3 flags out of 8, we use permutations since the order matters. The formula for permutations is P(n, r) = n! / (n - r)!. For this case, P(8, 3) = 8! / (8 - 3)! = 8 × 7 × 6 = 336.
Q10
Hard
A password consists of 4 letters followed by 2 digits. If letters can be repeated but digits cannot, how many different passwords can be formed?
A. 676000
B. 676100
C. 676200
D. 676300
Show Answer & Explanation
Correct Answer: A
For the letters, since they can be repeated, there are 26 choices for each of the 4 letters: 26^4. For the digits, since they cannot be repeated, there are 10 choices for the first digit and 9 for the second: 10 × 9. Thus, total passwords = 26^4 * (10 * 9) = 456976 * 90 = 676000.

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Permutations and Combinations — JEE Mathematics Practice Questions Online

This page contains 1645 practice MCQs for the chapter Permutations and Combinations in JEE Mathematics. The questions are organized by difficulty — 442 easy, 741 medium, 462 hard — so you can choose the right level for your preparation.

Every question includes a detailed explanation to help you understand the concept, not just memorize answers. Take a timed quiz to simulate exam conditions, or practice at your own pace with no time limit. This chapter covers 8 topics, giving you comprehensive coverage of the entire chapter.