Must-Know Permutations and Combinations Questions for Competitive Exams 2025
Permutations and Combinations is a fundamental chapter in JEE Maths, essential for mastering advanced problem-solving and probability. This test covers nPr, nCr, circular arrangements, selection, and real-world applications, empowering you to crack even the trickiest questions. Challenge yourself with this test to strengthen your exam approach and boost your confidence for JEE Main 2025!
Mock Test Instructions for the Permutations And Combinations Mock Test 1:
- 20 questions from Permutations And Combinations Mock Test 1
- Time limit: 20 minutes
- Single correct answer per question
- Correct answers appear in bold green after submission
How Can JEE Mock Tests Help You Master Permutations and Combinations?
- Identify your strengths and weaknesses in arrangement and selection problems.
- Practice time management for complex permutation and combination questions.
- Enhance application of nPr, nCr, and the Fundamental Counting Principle.
- Develop strategies for circular arrangements and selection-based MCQs.
- Receive instant feedback to target revision for high-weightage JEE topics.
Excel in JEE Permutations and Combinations with Expert-Designed Mock Tests
- Test your understanding with real JEE exam pattern MCQs on arrangement and selection.
- Refine your approach for questions based on circular permutations and restrictions.
- Strengthen basics and special cases through immediate error analysis.
- Get familiar with advanced scenarios such as repetition and non-repetition cases.
- Track your progress topic-wise and revisit weak areas with targeted practice.
Subject-Wise Excellence: JEE Main Mock Test Links
| S.No. | Subject-Specific JEE Main Online Mock Tests |
|---|---|
| 1 | Online FREE Mock Test for JEE Main Chemistry |
| 2 | Online FREE Mock Test for JEE Main Maths |
| 3 | Online FREE Mock Test for JEE Main Physics |
Important Study Materials Links for JEE Exams
FAQs on Permutations and Combinations Mock Test 2025 with Answers
1. What are permutations and combinations?
Permutations refer to the different ways of arranging a set of objects in a specific order, while combinations are the ways of selecting objects without considering the order. Both are key concepts in combinatorics, commonly used in mathematics and competitive exams.
2. How do you calculate the number of permutations of n objects taken r at a time?
The number of permutations of n distinct objects taken r at a time is given by the formula: P(n, r) = n! / (n - r)!. Here, ‘!’ denotes the factorial operation.
3. What is the formula for combinations?
The number of combinations of n objects taken r at a time is: C(n, r) = n! / [r! (n - r)!], where ‘!’ stands for the factorial of a number.
4. Where are permutations and combinations used in real life?
Applications of permutations and combinations are seen in seating arrangements, lottery systems, password generation, event planning, card games, and probability calculations in science and engineering.
5. What is the difference between permutation and combination with an example?
Permutation cares about the order: Arranging 3 students (A, B, C) in a row (ABC, BCA, CAB etc.). Combination does not care about order: Selecting any 2 students from A, B, C (AB, AC, BC).
6. How do you master permutations and combinations for exams like JEE or NDA?
To master permutations and combinations, practice a variety of problems, identify patterns, revise key formulas, solve previous year and mock tests, and clarify concepts using summary notes and example-based learning.
7. What is a circular permutation?
A circular permutation is the arrangement of objects in a circle, where only relative positions matter. The number of circular permutations of n distinct objects is (n – 1)!.
8. How do restrictions (like fixing a seat or excluding an option) change permutation problems?
When restrictions are applied in permutation problems, first arrange the restricted element(s), then solve for the remaining positions. This usually reduces the total number of outcomes and requires careful stepwise calculation respecting each condition.
9. Can you provide a JEE-level permutation and combination example with solution?
Example: Find the number of ways to arrange the word ‘EXAM’ so that vowels never come together.
Solution: Arrange consonants (X, M): 2! ways. Place vowels (E, A) in gaps: 3 gaps, select 2 gaps: 3C2 = 3 ways. So, total = 2! × 3 = 6 ways.
10. What is a mock test in permutations and combinations and how do I use it for exam preparation?
A mock test is a practice exam with questions on permutations and combinations, designed to simulate real exam conditions. Take these regularly, analyze your mistakes, and time your attempts for maximum benefit.
11. Are there downloadable permutation and combination question bank PDFs with solutions?
Yes, many educational portals offer free and paid downloadable PDFs of permutation and combination questions with detailed solutions, curated for exams like JEE, NDA, and Class 11 practice (search for ‘permutations and combinations mock test PDF’).
12. What are the most common mistakes students make in permutation and combination problems?
Common mistakes include confusing order with selection, misusing formulas, overlooking restrictions, missing cases, and not considering all possible arrangements or combinations. Always clarify if the problem needs an arrangement (permutation) or selection (combination).
