Mathematics - Permutation Combination
Practise 30 JEE Advanced previous year questions on Permutation Combination, compiled from papers spanning 2006 to 2026. Each question is pulled directly from the actual exam paper it appeared in, so you're practising in the exact style and difficulty JEE Advanced tests.
Permutation Combination has been asked in 18 of the 27 years of JEE Advanced papers analysed (2000–2026), with 30 questions in all. 27% of them were easy, 37% moderate and 37% tough. Most of its questions came from 2014, with 5 questions that year. In the last three years (2024–2026) it had 4 questions across 6 papers, about 0.7 per paper.
The chapter's 8 topics are not weighted equally: Arrangement under Constraint (15 questions, 50%), Combination (4 questions, 13%), and Selection of one or more item (3 questions, 10%) have been asked the most. Arrangement under Constraint has also led over the last five years, with 3 questions. Arrangement under Constraint has produced the most tough questions (5).
- 1The number of ways to distribute identical red pens and identical blue pens among four persons such that each person gets pens, is _________2026 (Paper 1)Division of Identical items
- 2A bookshelf contains distinct books of Mathematics and distinct books of Physics. From these books, books are chosen at random. Let be the a2026 (Paper 2)Combination
- 3Let be the set of all seven-digit numbers that can be formed using the digits 0,1 and 2 . For example, 2210222 is in , but 0210222 is NOT in2025 (Paper 1)Permutation
- 4A group of 9 students, , is to be divided to from three teams , and of sizes 2,3 , and 4 , respectively. Suppose that cannot be selected for2024 (Paper 1)Arrangement under Constraint
- 5Let X be the set of all five digit numbers formed using 1 , 2 , 2 , 2 , 4 , 4 , 0 . For example, 22240 is in X while 02244 and 44422 are not2023 (Paper 2)Arrangement under Constraint
- 6Consider the 6 6 square in the figure. Let A 1 , A 2 , , A 49 be the points of intersections (dots in the picture) in some order. We say tha2023 (Paper 2)Selection of one or more item
- 7The number of 4 -digit integers in the closed interval 2022 , 4482 formed by using the digits 0 , 2 , 3 , 4 , 6 , 7 is ______.2022 (Paper 1)Arrangement under Constraint
- 8Consider 4 boxes, where each box contains 3 red balls and 2 blue balls. Assume that all 20 balls are distinct. In how many different ways ca2022 (Paper 2)Permutation
- 9Let S 1 = i , j , k : i , j , k 1 , 2 , , 10 S 2 = i , j : 1 i j + 2 10 , i , j 1 , 2 , , 10 S 3 = i , j , k , l : 1 i j k l , i , j , k , l2021 (Paper 2)Selection of one or more item
- 10An engineer is required to visit a factory for exactly four days during the first 15 days of every month and it is mandatory that no two vis2020 (Paper 2)Arrangement under Constraint
- 11In a hotel, four rooms are available. Six persons are to be accommodated in these four rooms in such a way that each of these rooms contains2020 (Paper 2)Division and Distribution of Distinct Items
- 12Five persons A , B , C , D and E are seated in a circular arrangement. If each of them is given a hat of one of the three colours red, blue 2019 (Paper 2)Arrangement under Constraint
- 13The number of 5 digit numbers which are divisible by 4 , with digits from the set { 1,2 , 3,4 , 5 } and the repetition of digits is allowed,2018 (Paper 1)Arrangement under Constraint
- 14In 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 girls G 1 , G 2 , G 3 , G 4 , 2018 (Paper 2)Combination
- 15Words 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 words where no letter is repeated;2017 (Paper 1)Arrangement under Constraint
- 16A debate club consists of 6 girls and 4 boys. A team of 4 members is to be selected from this club including the selection of a captain (fro2016 (Paper 1)Combination
- 17Let 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 stand consecutively in the que2015 (Paper 1)Arrangement under Constraint
- 18Let 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 such distinct arrangements n 1 2014 (Paper 1)Arrangement under Constraint
- 19Let n 2 be an integer. Take n distinct points on a circle and join each pair of points by a line segment. Colour the line segment joining ev2014 (Paper 1)Geometric Permutation
- 20Three boys and two girls stand in a queue. The probability that the number of boys ahead of every girl is atleast one more than the number o2014 (Paper 2)Arrangement under Constraint
- 21Six cards and six envelopes are numbered 1, 2, 3, 4, 5, 6 and cards are to be placed in envelopes so that each envelope contains exactly one2014 (Paper 2)Dearrangement
- 22Paragraph: Box contains three cards bearing numbers ; box contains five cards bearing numbers ; and box contains seven cards bearing numbers2014 (Paper 2)Combination
- 23The total number of ways in which 5 balls of different colours can be distributed among 3 persons so that each person gets at least one ball2012 (Paper 1)Division and Distribution of Distinct Items
- 24Let denote the number of all -digit positive integers formed by the digits 0,1 or both such that no consecutive digits in them are 0 . Let t2012 (Paper 2)Arrangement under Constraint
- 25Let denote the number of all -digit positive integers formed by the digits 0,1 or both such that no consecutive digits in them are 0 . Let t2012 (Paper 2)Arrangement under Constraint
- 26The number of seven digit integers, with sum of the digits equal to 10 and formed by using the digits 1,2 and 3 only, is2009 (Paper 1)Arrangement under Constraint
- 27Paragraph: Let be the set of all symmetric matrices all of whose entries are either 0 or 1 . Five of these entries are 1 and four of them ar2009 (Paper 1)Arrangement under Constraint
- 28Consider all possible permutations of the letters of the word ENDEANOEL. Match the Statements/Expressions in Column I with the Statements/Ex2008 (Paper 2)Arrangement under Constraint
- 29The letters of the word are permuted and all the permutations are arranged in an alphabetical order as in an English dictionary. The number 2007 (Paper 2)Permutation
- 30If are prime numbers and are the positive integers such that LCM of is , then the number of ordered pairs is2006Selection of one or more item
Frequently Asked Questions
1.How many questions are available for Permutation Combination?
This chapter includes 30 questions compiled from JEE Advanced papers spanning 2006 to 2026.
2.Are these questions only from JEE Advanced, or from other exams too?
These are JEE Advanced questions specifically for the Permutation Combination chapter. Questions from other exams like JEE Main or NTA Abhyas (JEE Main) are organised separately under their respective exam sections.
3.Is Permutation Combination an important chapter for JEE Advanced Mathematics?
Permutation Combination has appeared in 18 of the 21 years of JEE Advanced papers covered here, with 30 questions across 23 papers - about one per paper it appears in.
4.What is the difficulty level of Permutation Combination questions in JEE Advanced?
Of the 30 questions analysed for this chapter, 27% are easy, 37% moderate and 37% tough. 2014 had the most, with 5 questions.
5.Which topics in Permutation Combination should I focus on?
These topics have carried the most weightage in Permutation Combination:
- Arrangement under Constraint - 15 questions (50%)
- Combination - 4 questions (13%)
- Selection of one or more item - 3 questions (10%)
- Arrangement under Constraint has produced the most tough questions (5).
6.Is Permutation Combination's weightage in JEE Advanced going up or down?
Across all 23 papers analysed, Permutation Combination has averaged about 1.3 questions per paper. In the last three years (2024–2026), that average has fallen, at about 0.7 questions per paper. Use the year-wise numbers on this page for the exact trend before you decide how much time to give it.