JEE Advanced Permutations and Combinations — previous year questions

21 questions from 2026, 2025, 2024, 2022, 2021, 2020, 2019, 2018, 2017, 2016, 2015, 2014, 2012, 2009, 2007.

• The number of ways to distribute 10 identical red pens and 14 identical blue pens among four persons such…2026JEE Advanced
• Let S be the set of all seven-digit numbers that can be formed using the digits 0, 1 and 2. For example,…2025JEE Advanced
• A group of 9 students, s_1, s_2, ..., s_9 is to be divided to form three teams X, Y, and Z of sizes 2, 3, and…2024JEE Advanced
• The number of 4-digit integers in the closed interval [2022, 4482] formed by using the digits 0, 2, 3, 4, 6,…2022JEE Advanced
• Let S₁ = {(i,j,k) : i, j, k ∈ {1,2,…,10}} S₂ = {(i,j) : 1 ≤ i < j + 2 ≤ 10, i, j ∈ {1,2,…,10}}, S₃ =…2021JEE Advanced
• In a hotel, four rooms are available. Six persons are to be accommodated in these four rooms in such a way…2020JEE Advanced
• An engineer is required to visit a factory for exactly four days during the first 15 days of every month and…2020JEE Advanced
• For non-negative integers s and r, let binomsr = s!/(r! (s-r)!) if r ≤ s, [4pt] 0 if r > s. For positive…2020JEE Advanced
• Five persons A, B, C, D and E are seated in a circular arrangement. If each of them is given a hat of one of…2019JEE Advanced
• The number of 5 digit numbers which are divisible by 4, with digits from the set {1, 2, 3, 4, 5} and the…2018JEE Advanced
• In a high school, a committee has to be formed from a group of 6 boys M₁, M₂, M₃, M₄, M₅, M₆ and 5 girls G₁,…2018JEE Advanced
• Words of length 10 are formed using the letters A, B, C, D, E, F, G, H, I, J. Let x be the number of such…2017JEE Advanced
• Let S = {1, 2, 3, ..., 9}. For k = 1, 2, ..., 5, let Nₖ be the number of subsets of S, each containing five…2017JEE Advanced
• A debate club consists of 6 girls and 4 boys. A team of 4 members is to be selected from this club including…2016JEE Advanced
• Let n be the number of ways in which 5 boys and 5 girls can stand in a queue in such a way that all the girls…2015JEE Advanced
• Six cards and six envelopes are numbered 1, 2, 3, 4, 5, 6 and cards are to be placed in envelopes so that…2014JEE Advanced
• Let n₁ < n₂ < n₃ < n₄ < n₅ be positive integers such that n₁ + n₂ + n₃ + n₄ + n₅ = 20. Then the number of…2014JEE Advanced
• Let n ≥ 2 be an integer. Take n distinct points on a circle and join each pair of points by a line segment.…2014JEE Advanced
• The total number of ways in which 5 balls of different colours can be distributed among 3 persons so that…2012JEE Advanced
• The number of seven digit integers, with sum of the digits equal to 10 and formed by using the digits 1, 2…2009JEE Advanced
• The letters of the word COCHIN are permuted and all the permutations are arranged in an alphabetical order as…2007JEE Advanced

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