Permutations and Combinations

JEE Advanced · Mathematics · 28 past questions

1. Q1 2026 Paper 1

   Let $S = \{1, 2, 3, \ldots, 10\}$. Consider the set…

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2. Q2 2026 Paper 1

   The number of ways to distribute 10 identical red pens and 14 identical blue pens among four persons such…

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3. Q3 2025 Paper 1

   Let $S$ be the set of all seven-digit numbers that can be formed using the digits 0, 1 and 2. For example…

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4. Q4 2024 Paper 1

   A group of $9$ students, $s_1, s_2, \ldots, s_9$, is to be divided to form three teams $X, Y$, and $Z$ of…

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5. Q5 2024 Paper 2

   PARAGRAPH “I”…

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6. Q6 2022 Paper 1

   The number of 4-digit integers in the closed interval $[2022,\ 4482]$ formed by using the digits…

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7. Q7 2022 Paper 2

   Consider 4 boxes, where each box contains 3 red balls and 2 blue balls. Assume that all 20 balls are…

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8. Q8 2021 Paper 2

   Let…

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9. Q9 2020 Paper 2

   An engineer is required to visit a factory for exactly four days during the first 15 days of every month and…

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10. Q10 2020 Paper 2

    In a hotel, four rooms are available. Six persons are to be accommodated in these four rooms in such a way…

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11. Q11 2019 Paper 2

    Five persons $A, B, C, D$ and $E$ are seated in a circular arrangement. If each of them is given a hat of one…

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12. Q12 2018 Paper 1

    The number of 5 digit numbers which are divisible by 4, with digits from the set $\{1,2,3,4,5\}$ and the…

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13. Q13 2018 Paper 2

    In a high school, a committee has to be formed from a group of 6 boys $M_1, M_2, M_3, M_4, M_5, M_6$ and 5…

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14. Q14 2017 Paper 1

    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…

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15. Q15 2017 Paper 2

    Let $S=\{1,2,3,\ldots,9\}$. For $k=1,2,\ldots,5$, let $N_k$ be the number of subsets of $S$, each containing…

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16. Q16 2016 Paper 1

    A debate club consists of 6 girls and 4 boys. A team of 4 members is to be selected from this club including…

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17. Q17 2015 Paper 1

    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…

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18. Q18 2015 Paper 2

    The coefficient of $x^9$ in the expansion of $(1+x)(1+x^2)(1+x^3)\ldots(1+x^{100})$ is

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19. Q19 2014 Paper 1

    Let $n \ge 2$ be an integer. Take $n$ distinct points on a circle and join each pair of points by a line…

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20. Q20 2014 Paper 1

    Let $n_1 < n_2 < n_3 < n_4 < n_5$ be positive integers such that $n_1+n_2+n_3+n_4+n_5=20$. Then the number of…

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21. Q21 2013 Paper 1

    Consider the set of eight vectors $V=\{a\hat i+b\hat j+c\hat k : a,b,c\in\{-1,1\}\}$. Three non-coplanar…

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22. Q22 2012 Paper 1

    The total number of ways in which 5 balls of different colours can be distributed among 3 persons so that…

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23. Q23 2012 Paper 2

    Paragraph for Questions 49 and 50…

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24. Q24 2012 Paper 2

    Paragraph for Questions 49 and 50…

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25. Q25 2010 Paper 2

    Let $S = \{1, 2, 3, 4\}$. The total number of unordered pairs of disjoint subsets of $S$ is equal to

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26. Q26 2009 Paper 1

    The number of seven digit integers, with sum of the digits equal to 10 and formed by using the digits 1, 2…

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27. Q27 2008 Paper 2

    Consider all possible permutations of the letters of the word ENDEANOEL.…

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28. Q28 2007 Paper 2

    The letters of the word COCHIN are permuted and all the permutations are arranged in an alphabetical order as…

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