Permutations & Combinations JEE Main PYQs PDF, 2020–2026

Permutations & Combinations questions per year

in the free PDF asked, not in the PDFThe PDF only has questions we can print in full with a checked answer, so it holds 162 of the 163 asked.

Topic-wise weightage by year

How many Permutations & Combinations questions each topic had in every JEE Main year (all shifts), counting every question asked, including ones not in the PDF. Darker cells mean more questions.

Swipe the table sideways for older years.

Newest questions (2026)

The 12 newest of the 22 JEE Main 2026 Permutations & Combinations questions in the free PDF, latest shift first.

1. JEE Main 2026 · 8 Apr · Shift 2 · Distribution Problems

   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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2. JEE Main 2026 · 6 Apr · Shift 1 · Combinations

   The number of 4-letter words, with or without meaning, each consisting of two vowels and two consonants that can be formed from the letters of the word INCONSEQUENTIAL, without repeating any letter, is:

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3. JEE Main 2026 · 6 Apr · Shift 2 · Distribution Problems

   A building has ground floor and 10 more floors. Nine persons enter in a lift at the ground floor. The lift goes up to the ${10}^{{\text{th}}}$ floor. The number of ways, in which any 4 persons exit at a floor and the remaining 5 persons exit at a different floor, if the lift does not stop at the first and the second floors, is equal to :

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4. JEE Main 2026 · 5 Apr · Shift 2 · Combinations

   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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5. JEE Main 2026 · 5 Apr · Shift 1 · Combinations

   Two players A and B play a series of games of badminton. The player, who wins 5 games first, wins the series. Assuming that no game ends in a draw, the number of ways, in which player A wins the series is $\_\_\_\_$ .

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6. JEE Main 2026 · 4 Apr · Shift 1 · Permutations

   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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7. JEE Main 2026 · 4 Apr · Shift 2 · Combinations

   Let

   ${\mathrm{A}}=\{(a,b,c):a,b,c$ are non-negative integers and $a+b+2c=22\}$.

   Then $n({\ \mathrm{A}})$ is equal to :

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8. JEE Main 2026 · 2 Apr · Shift 2 · Combinations

   Let $p_{n}$ denote the total number of triangles formed by joining the vertices of an $n$-side regular polygon.
   If $p_{{n+1}}-p_{n}=66$, then the sum of all distinct prime divisors of $n$ is :

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9. JEE Main 2026 · 2 Apr · Shift 1 · Permutations

   The number of seven-digit numbers, that can be formed by using the digits 1, 2, 3, 5 and 7 such that each digit is used at least once, is:

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10. JEE Main 2026 · 2 Apr · Shift 1 · Combinations

    The number of elements in the set $S=\left\{(r,k):k\in {\mathbb{Z}}\text{ and}^{{36}}C_{{r+1}}=\frac{6\left({}^{{35}}C_{{r}}\right)}{(k^{2}-3)}\right\}$ is :

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11. JEE Main 2026 · 28 Jan · Shift 2 · Permutations

    Three persons enter in a lift at the ground floor. The lift will go up to 10^th floor. The number of ways, in which the three persons can exit the lift at three different floors, if the lift does not stop at first, second and third floors, is equal to ________.

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12. JEE Main 2026 · 28 Jan · Shift 1 · Permutations

    Let ${\mathrm{S}}=\{1,2,3,4,5,6,7,8,9\}$. Let $x$ be the number of 9-digit numbers formed using the digits of the set S such that only one digit is repeated and it is repeated exactly twice. Let $y$ be the number of 9 -digit numbers formed using the digits of the set S such that only two digits are repeated and each of these is repeated exactly twice. Then,

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Practise the 2026 Permutations & Combinations questions online

Sample questions from recent papers

JEE Main 2026 · 24 Jan · Shift 2 · Fundamental Principle of Counting

The largest value of $n$, for which ${40}^{n}$ divides $60!$, is

1. (A)

   14

2. (B)

   13

3. (C)

   11

4. (D)

   12

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Answer: (A)

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JEE Main 2026 · 24 Jan · Shift 2 · Rank of a Word

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

1. (A)

   1579

2. (B)

   1578

3. (C)

   1580

4. (D)

   1581

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Answer: (C)

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JEE Main 2025 · 2 Apr · Shift 2 · Distribution Problems

The number of ways, in which the letters A, B, C, D, E can be placed in the 8 boxes of the figure below so that no row remains empty and at most one letter can be placed in a box, is :

1. (A)5880
2. (B) 840
3. (C)960
4. (D)5760

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Answer: (D)

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JEE Main 2023 · 8 Apr · Shift 1 · Circular Permutations

The number of ways, in which 5 girls and 7 boys can be seated at a round table so that no two girls sit together, is :

1. (A)720
2. (B)$7(360)^{2}$
3. (C)$7(720)^{2}$
4. (D)$126(5 !)^{2}$

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Answer: (D)

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The free PDF above has all 162 questions grouped by topic, with an answer key.

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JEE Main PYQs by year: 2026 · 2025 · 2024 · 2023 · 2022 · 2021 · 2020