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Permutation and Combination - JEE Main Previous Year Questions with Solutions and Weightage

Sahaj Anand's profile photo

Sahaj Anand

Content Writer | Journalism Graduate | Updated 3+ months ago

Permutation and Combination carries 3.3% weightage in the JEE Main Mathematics Question Paper, generally 1-2 questions are asked from this topic.

Permutation and Combination is an Important topic in JEE Main 2025 Mathematics as it forms the basis of Probability and many counting problems.

Permutation and Combination is considered to be of a moderate difficulty level with major focus on subtopics such as Circular Permutations, Derangements.

Must Read Articles:

The Permutation and Combination related questions with detailed solutions asked in JEE Main are listed below:

Question 1

  1. PRNAKU
  2. PRKANU
  3. PRKAUN
  4. PRNAUK

View Solution

Question 2

View Solution

Question 3

  1. 8925
  2. 8750
  3. 9100
  4. 8575

View Solution

Question 4

  1. 5719
  2. 4608
  3. 5720
  4. 4607

View Solution

Question 5

  1. 3
  2. 1
  3. 2
  4. 4

View Solution

Question 6

View Solution

Question 7

  1. 8925
  2. 8750
  3. 9100
  4. 8575

View Solution

Question 8

View Solution

Question 9

View Solution

Question 10

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JEE Main 2025 Mathematics Question Paper Pattern

The JEE Main 2025 Mathematics question paper consists of 25 mandatory questions worth a total of 100 marks. Each correct answer will be awarded +4 marks and 1 mark will be deducted for every incorrect answer.

Features Highlights
Mode of Exam Computer Based Test (Online)
Marking Scheme +4 for the correct answers and -1 for incorrect answer
Duration of Exam 3 Hours
Language of Exam Hindi, English and Gujarati (Only for centers in Gujarat, Daman and Diu, and Dadra and Nagar Haveli)
Types of Questions Multiple Choice Questions (MCQs) and Numerical Value Based
Total Number of Questions 25 questions
Total Marks 100

JEE Main Mathematics Chapter Wise Weightage

The JEE Main Mathematics chapters are divided into three categories: High weightage, Medium Weightage and Low Weightage.

High Weightage Chapters: Coordinate Geometry (15.33%), Calculus (12%) and Algebra (27%) are the highest weightage chapters in Mathematics. Candidates should have a strong hold on the concept and formulas in order to maximize their score.

Medium Weightage Chapters: Vector Algebra (6.33%), 3D Geometry (6.6%), Probability and Statistics (6.5%) and Differential Equations (5.6%) are categorized in the medium weightage chapters as they are responsible for approximately 2-4 questions in the Mathematics question paper.

Low Weightage Chapters: Trigonometry (4.5%), Permutation and Combination (3.5%) and Binomial Theorem (3.1%) are categorized in the low weightage chapters. Questions from these chapters are not frequently asked in the mathematics paper.

Chapters Weightage (%) Approximate Marks
Coordinate Geometry 15.33% 16
Limits, Continuity, and Differentiability 12.00% 12
Integral Calculus 11.17% 12
Complex Numbers and Quadratic Equations 7.17% 8
Sets, Relations, and Functions 7.17% 8
Matrices and Determinants 6.50% 8
Sequences and Series 6.50% 8
Statistics and Probability 6.50% 8
Vector Algebra 6.33% 8
Differential Equations 5.67% 8
Three-Dimensional Geometry 4.50% 4
Trigonometry 4.50% 4
Permutations and Combinations 3.50% 4
Binomial Theorem and Its Applications 3.17% 4

JEE Main Mathematics Previous Year Question Papers with Solutions

The JEE Main Mathematics question paper PDFs along with the detailed solution PDFs for the last 5 years is tabulated below:

JEE Main 2024 Mathematics Question Paper Session 1

Exam Date Question Paper Solution PDF
JEE Main 2024 Feb 1 Shift 2 Mathematics Question Paper Download Check Solution
JEE Main 2024 Feb 1 Shift 1 Mathematics Question Paper Download Check Solution
JEE Main 2024 Jan 31 Shift 2 Mathematics Question Paper Download Check Solution
JEE Main 2024 Jan 31 Shift 1 Mathematics Question Paper Download Check Solution
JEE Main 2024 Jan 30 Shift 2 Mathematics Question Paper Download Check Solution
JEE Main 2024 Jan 30 Shift 1 Mathematics Question Paper Download Check Solution
JEE Main 2024 Jan 29 Shift 2 Mathematics Question Paper Download Check Solution
JEE Main 2024 Jan 29 Shift 1 Mathematics Question Paper Download Check Solution
JEE Main 2024 Jan 27 Shift 2 Mathematics Question Paper Download Check Solution
JEE Main 2024 Jan 27 Shift 1 Mathematics Question Paper Download Check Solution

JEE Main 2024 Mathematics Question Paper Session 2

Exam Date and Shift Question Paper Solution PDF
JEE Main 2024 April 4 Shift 1 Mathematics Question Paper Download Check Solution
JEE Main 2024 April 4 Shift 2 Mathematics Question Paper Download Check Solution
JEE Main 2024 April 5 Shift 1 Mathematics Question Paper Download Check Solution
JEE Main 2024 April 5 Shift 2 Mathematics Question Paper Download Check Solution
JEE Main 2024 April 6 Shift 1 Mathematics Question Paper Download Check Solution
JEE Main 2024 April 6 Shift 2 Mathematics Question Paper Download Check Solution
JEE Main 2024 April 8 Shift 1 Mathematics Question Paper Download Check Solution
JEE Main 2024 April 8 Shift 2 Mathematics Question Paper Download Check Solution
JEE Main 2024 April 9 Shift 1 Mathematics Question Paper Download Check Solution
JEE Main 2024 April 9 Shift 2 Mathematics Question Paper Download Check Solution

JEE Main 2023 Mathematics Question Paper

Exam Date Mathematics Question Paper PDF
Mathematics 6 April Shift 1 Question Paper Check Here
Mathematics 6 April Shift 2 Question Paper Check Here
Mathematics 8 April Shift 1 Question Paper Check Here
Mathematics 8 April Shift 2 Question Paper Check Here
Mathematics 10 April Shift 1 Question Paper Check Here
Mathematics 10 April Shift 2 Question Paper Check Here
Mathematics 11 April Shift 1 Question Paper Check Here
Mathematics 11 April Shift 2 Question Paper Check Here
Mathematics 12 April Shift 1 Question Paper Check Here
Mathematics 13 April Shift 1 Question Paper Check Here
Mathematics 13 April Shift 2 Question Paper Check Here
Mathematics 15 April Shift 1 Question Paper Check Here

JEE Main 2023 Mathematics Question Paper Session 1

Exam Date and Shift Mathematics Question Paper PDF
Mathematics 24 January Shift 1 Question Paper Check Here
Mathematics 24 January Shift 2 Question Paper Check Here
Mathematics 25 January Shift 1 Question Paper Check Here
Mathematics 25 January Shift 2 Question Paper Check Here
Mathematics 29 January Shift 1 Question Paper Check Here
Mathematics 29 January Shift 2 Question Paper Check Here
Mathematics 30 January Shift 1 Question Paper Check Here
Mathematics 30 January Shift 2 Question Paper Check Here
Mathematics 31 January Shift 1 Question Paper Check Here
Mathematics 31 January Shift 2 Question Paper Check Here
Mathematics 1 February Shift 1 Question Paper Check Here
Mathematics 1 February Shift 2 Question Paper Check Here

JEE Main 2022 Mathematics Question Paper with Solution PDF

Exam Date Shift/ Slot Question Paper PDF
July 25 Shift 1 Check Here
July 25 Shift 2 Check Here
July 26 Shift 1 Check Here
July 26 Shift 2 Check Here
July 27 Shift 1 Check Here
July 27 Shift 2 Check Here
July 28 Shift 1 Check Here
July 28 Shift 2 Check Here
July 29 Shift 1 Check Here
July 29 Shift 2 Check Here

JEE Main 2022 Mathematics Question Paper with Solution PDF- Phase 1

Exam Date Shift/ Slot Question Paper PDF
June 29 Shift 1 Check Here
June 29 Shift 2 Check Here
June 28 Shift 1 Check Here
June 28 Shift 2 Check Here
June 27 Shift 1 Check Here
June 27 Shift 2 Check Here
June 26 Shift 1 Check Here
June 26 Shift 2 Check Here
June 25 Shift 1 Check Here
June 25 Shift 2 Check Here
June 24 Shift 1 Check Here
June 24 Shift 2 Check Here

JEE Main 2021 Mathematics Question Paper- Download PDF

Exam Date Shift/ Slot Question Paper PDF
August 26 Shift 1 Check Here
August 26 Shift 2 Check Here
August 27 Shift 1 Check Here
August 27 Shift 2 Check Here
August 31 Shift 1 Check Here
August 31 Shift 2 Check Here
September 1 Shift 2 Check Here

JEE Main 2021 Mathematics Question Paper with Solution (Session3- July)- Download PDF

Exam Date Shift/ Slot JEE Main Question Paper PDF
July 22 Shift 2 Check Here
July 25 Shift 1 Check Here
July 25 Shift 2 Check Here
July 27 Shift 1 Check Here
August 3 Shift 1 Check Here
August 3 Shift 2 Check Here
August 4 Shift 1 Check Here
August 4 Shift 2 Check Here

JEE Main 2021 Mathematics Question Paper with Solution (Session 2- March)- Download PDF

Exam Date Shift/ Slot Question Paper PDF
March 16 Shift 1 Check Here
March 16 Shift 2 Check Here
March 17 Shift 1 Check Here
March 17 Shift 2 Check Here
March 18 Shift 1 Check Here
March 18 Shift 2 Check Here

JEE Main 2021 Mathematics Question Paper with Solution (Session 1- February) - Download PDF

Exam Date Shift/ Slot Question Paper PDF
February 24 Shift 1 Check Here
February 24 Shift 2 Check Here
February 25 Shift 1 Check Here
February 25 Shift 2 Check Here
February 26 Shift 1 Check Here
February 26 Shift 2 Check Here

JEE Main 2020 Mathematics Question Paper with Solutions- Download PDF

Exam Date Shift/ Slot Question Paper PDF
September 2 Shift 1 Check Here
September 2 Shift 2 Check Here
September 3 Shift 1 Check Here
September 3 Shift 2 Check Here
September 4 Shift 1 Check Here
September 4 Shift 2 Check Here
September 5 Shift 1 Check Here
September 5 Shift 2 Check Here
September 6 Shift 1 Check Here
September 6 Shift 2 Check Here

JEE Main 2020 Mathematics Question Paper with Solutions (Session 1- January) - Download PDF

Exam Date Shift/ Slot JEE Main Question Paper PDF
January 8 Shift 1 Check Here
January 8 Shift 2 Check Here
January 9 Shift 1 Check Here
January 9 Shift 2 Check Here

Also Check:

Frequently Asked Questions

What are the 4 types of permutations?

The four main types of permutations are-

Permutations with Repetition: In this type of permutation, elements can be repeated in the arrangement.

Permutation without Repetition: In this each element can appear only once in the arrangement. For example, permutations of the letters ‘ABC’ are ‘ABC’, ‘ACB’, ‘BAC’, ‘BCA’, ‘CAB’ AND ‘CBA’ without repetition.

Permutation with Multi Sets: It involves arranging elements in a way where some elements are repeated but the order of the repetitions matters.For example, the permutations of the letters ‘AAB’ are ‘AAB’, ‘ABA’ and ‘BAA’.

Circular Permutations: In this type, the arrangement is circular, meaning that the starting point is not fixed. For example, arranging 3 people around a circular table.

What is Permutation and Combination?

Permutations are used when order of arrangement is needed. Combinations are used when only the number of possible groups are to be found and the order of arrangements is not needed. Permutations are used for things of a similar kind.

What is 7 permutation?

Here is an example to explain what is 7 permutation:

7! = 7*6*5*4*3*2*1 = 5,040. To calculate permutations, use the equation nPr where n is the total number of choices and r is the amount of items being selected. The formula used to slove this equation is nPr = n! / (n - r)!.

What is the nPr and nCr formula?

The formulas for permutations (nPr) and combinations (nCr) are as follows: nPr = n! / (n - r)!

and nCr = n! / (r! * (n - r)!). In these formulas, where ‘n’ is the total number of items and ‘r’ is the number of items being chosen.

nPr (Permutations)

This formula calculates the number of ways to arrange ‘r’ items out of the ‘n’ items where the order of arrangement matters.

Formula: nPr = n! / (n-r)!

nCr (Combinations)

This formula calculated the number of ways to choose ‘r’ items out of ‘n’ items where the order of selection does not matter.

Formula: nCr = n! / (r! * (n-r)!)

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JEE Main Questions

  • 1.
    Let A and B be the two points of intersection of the line \( y + 5 = 0 \) and the mirror image of the parabola \( y^2 = 4x \) with respect to the line \( x + y + 4 = 0 \). If \( d \) denotes the distance between A and B, and \( a \) denotes the area of \( \Delta SAB \), where \( S \) is the focus of the parabola \( y^2 = 4x \), then the value of \( (a + d) \) is:

        View Solution

      • 2.
        Two iron solid discs of negligible thickness have radii \( R_1 \) and \( R_2 \) and moment of inertia \( I_1 \) and \( I_2 \), respectively. For \( R_2 = 2R_1 \), the ratio of \( I_1 \) and \( I_2 \) would be \( \frac{1}{x} \), where \( x \) is:

            View Solution

          • 3.
            Total number of non-bonded electrons present in \( \text{NO}_2 \); ion based on Lewis theory is:

                View Solution

              • 4.
                Let $ x_1, x_2, x_3, x_4 $ be in a geometric progression. If 2, 7, 9, 5 are subtracted respectively from $ x_1, x_2, x_3, x_4 $, then the resulting numbers are in an arithmetic progression. Then the value of $ \frac{1}{24} (x_1 x_2 x_3 x_4) $ is:

                  • 72
                  • 18
                  • 36
                  • 216
                  View Solution

                • 5.

                  If the equation \( a(b - c)x^2 + b(c - a)x + c(a - b) = 0 \) has equal roots, where \( a + c = 15 \) and \( b = \frac{36}{5} \), then \( a^2 + c^2 \) is equal to               .

                      View Solution

                    • 6.
                      Let the distance between two parallel lines be 5 units and a point \( P \) lies between the lines at a unit distance from one of them. An equilateral triangle \( POR \) is formed such that \( Q \) lies on one of the parallel lines, while \( R \) lies on the other. Then \( (QR)^2 \) is equal to _____________.

                          View Solution
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