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Permutations and Combinations

JEE Mains Maths. Try each one first, then open its answer.

Top 10 JEE Mains PYQs to practise first

The questions and kinds of question asked most often come first. Each one says how often and in which papers.

  1. Question 1

    This type asked 12 times: 2021 Paper 3, 14 Jun 2022, 28 Jun 2022, 26 Jul 2022, 29 Jul 2022, 30 Jan 2023, 1 Feb 2023, 12 Apr 2023, 13 Apr 2023, 15 Apr 2023, 8 Apr 2024, 24 Jan 2026 S1. This one: 24 Jan 2026 S1 See all 12 of this type

    73
    The number of numbers greater than 5000 , less than 9000 and divisible by 3 , that can be formed using the digits 0,1,2,5,90,1,2,5,9, if the repetition of the digits is allowed, is ____\_\_\_\_

  2. Question 2

    This type asked 8 times: 2021 Paper 24, 25 Jul 2022, 29 Jan 2023, 6 Apr 2023, 11 Apr 2023, 13 Apr 2023, 29 Jan 2024, 24 Jan 2026 S2. This one: 24 Jan 2026 S2 See all 8 of this type

    59
    The letters of the word "UDAYPUR" are written in all possible ways with or without meaning and these words are arranged as in a dictionary. The rank of the word "UDAYPUR" is :

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  3. Question 3

    This type asked 7 times: 2021 Paper 1, 26 Jun 2022, 24 Jan 2023, 25 Jan 2023, 30 Jan 2024, 7 Apr 2025, 5 Apr 2026 S2. This one: 5 Apr 2026 S2 See all 7 of this type

    59
    A box contains 5 blue, 6 yellow and 4 red balls. The number of ways, of drawing 8 balls containing at least two balls of each colour, is:

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  4. Question 4

    This type asked 7 times: 2021 Paper 1, 2021 Paper 5, 25 Jun 2022, 27 Jun 2022, 29 Jul 2022, 31 Jan 2023, 24 Jan 2026 S1. This one: 24 Jan 2026 S1 See all 7 of this type

    75
    The number of 3×23 \times 2 matrices A , which can be formed using the elements of the set {−2,−1,0,1,2}\{ - 2, - 1,0,1,2\} such that the sum of all the diagonal elements of ATAA^{T}A is 5, is ____\_\_\_\_

  5. Question 5

    This type asked 6 times: 28 Jun 2022, 1 Feb 2023, 11 Apr 2023, 31 Jan 2024, 5 Apr 2024, 23 Jan 2026 S2. This one: 23 Jan 2026 S2 See all 6 of this type

    65
    The number of ways, in which 16 oranges can be distributed to four children such that each child gets at least one orange, is

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  6. Question 6

    This type asked 6 times: 2021 Paper 25, 25 Jun 2022, 13 Apr 2023, 9 Apr 2024, 28 Jan 2025, 29 Jan 2025. This one: 29 Jan 2025 See all 6 of this type

    56
    Let PP be the set of seven -digit numbers with sum of their digits equal to 11 . If the numbers in P are formed by using the digits 1,2 and 3 only, then the number of elements in the set PP is :

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  7. Question 7

    This type asked 5 times: 2021 Paper 6, 2021 Paper 8, 4 Apr 2024, 3 Apr 2025, 22 Jan 2026 S1. This one: 22 Jan 2026 S1 See all 5 of this type

    75
    Let ABC be a triangle. Consider four points p1,p2p_{1},p_{2}, p3,p4p_{3},p_{4} on the side AB , five points p5,p6,p7,p8,p9p_{5},p_{6},p_{7},p_{8},p_{9} on the side BC and four points p10,p11,p12,p13p_{10},p_{11},p_{12},p_{13} on the side AC . None of these points is a vertex of the triangle ABC . Then the total number of pentagons, that can be formed by taking all the vertices from the points p1,p2,….p13p_{1},p_{2},\ldots.p_{13}, is ____\_\_\_\_ .

  8. Question 8

    This type asked 5 times: 2021 Paper 23, 29 Jan 2023, 31 Jan 2023, 1 Feb 2023, 24 Jan 2025. This one: 24 Jan 2025 See all 5 of this type

    73
    The number of 3-digit numbers, that are divisible by 2 and 3 , but not divisible by 4 and 9 , is

  9. Question 9

    This type asked 4 times: 2021 Paper 2, 10 Apr 2023, 2 Apr 2026 S1, 8 Apr 2026 S2. This one: 8 Apr 2026 S2 See all 4 of this type

    59
    A person has three different bags and four different books. The number of ways, in which he can put these books in the bags so that no bag is empty, is

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  10. Question 10

    This type asked 4 times: 8 Apr 2023, 22 Jan 2025, 23 Jan 2025, 4 Apr 2026 S1. This one: 4 Apr 2026 S1 See all 4 of this type

    58
    The number of ways, of forming a queue of 4 boys and 3 girls such that all the girls are not together, is:

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