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Mathematics - Permutation Combination

Practise 214 JEE Main previous year questions on Permutation Combination, compiled from papers spanning 2002 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 Main tests.

Permutation Combination has been asked in 25 of the 25 years of JEE Main papers analysed (2002–2026), with 214 questions in all. 21% of them were easy, 52% moderate and 27% tough. Most of its questions came from 2023, with 40 questions that year. In the last three years (2024–2026) it had 50 questions across 49 papers, about 1 per paper.

The chapter's 12 topics are not weighted equally: Permutation (48 questions, 22%), Combination (42 questions, 20%), and Selection of one or more item (39 questions, 18%) have been asked the most. Permutation has also led over the last five years, with 35 questions. Permutation has produced the most tough questions (16).

  1. 1A 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 i08 Apr, 2026 (E)Division and Distribution of Distinct Items
  2. 2The number of -letter words, with or without meaning, each consisting of two vowels and two consonants that can be formed from the letters o06 Apr, 2026 (M)Combination
  3. 3A building has ground floor and 10 more floors. Nine persons enter in a lift at the ground floor. The lift goes up to the floor. The number 06 Apr, 2026 (E)Combination
  4. 4Two players and play a series of games of badminton. The player, who wins games first, wins the series. Assuming that no game ends in a draw05 Apr, 2026 (M)Arrangement under Constraint
  5. 5A box contains blue, yellow and red balls. The number of ways, of drawing balls containing at least two balls of each colour, is :05 Apr, 2026 (E)Combination
  6. 6The number of ways of forming a queue of boys and girls such that all the girls are not together, is:04 Apr, 2026 (M)Permutation
  7. 7Let . Then is equal to:04 Apr, 2026 (E)Division of Identical items
  8. 8The number of seven-digit numbers, that can be formed by using the digits and such that each digit is used at least once, is :02 Apr, 2026 (M)Permutation
  9. 9Let denote the total number of triangles formed by joining the vertices of an -side regular polygon. If , then the sum of all distinct prime02 Apr, 2026 (E)Combination
  10. 10Let . Let 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 exa28 Jan, 2026 (M)Permutation
  11. 11Three persons enter in a lift at the ground floor. The lift will go upto floor. The number of ways, in which the three persons can exit the 28 Jan, 2026 (E)Permutation
  12. 12The number of numbers greater than 5000, less than 9000 and divisible by 3, that can be formed using the digits , if the repetition of the d24 Jan, 2026 (M)Permutation
  13. 13The largest value of , for which divides , is24 Jan, 2026 (E)Exponent of prime
  14. 14The letters of the word "UDAYPUR" are written in all possible ways with or without meaning and these words are arranged as in a dictionary. 24 Jan, 2026 (E)Permutation
  15. 15The number of 4 -letter words, with or without meaning, which can be formed using the letters PQRPQRSTUVP, is .23 Jan, 2026 (M)Permutation
  16. 16The number of ways, in which 16 oranges can be distributed to four children such that each child gets at least one orange, is23 Jan, 2026 (E)Division of Identical items
  17. 17Let S denote the set of 4-digit numbers such that and P denote the set of 5 -digit numbers having product of its digits equal to 20. Then is23 Jan, 2026 (E)Combination
  18. 18Let ABC be a triangle. Consider four points on the side AB, five points on the side , and four points on the side AC. None of these points i22 Jan, 2026 (M)Combination
  19. 19The number of strictly increasing functions from the set to the set such that for , is equal to :21 Jan, 2026 (M)Combination
  20. 20Let . If the number of elements in S such that is a multiple of 5 is and the number of elements ( ) in such that is a square of a prime numb21 Jan, 2026 (M)Division of Identical items
  21. 21The largest , for which divides 101!, is :21 Jan, 2026 (E)Factorial
  22. 22There are 12 points in a plane, no three of which are in the same straight line, except 5 points which are collinear. Then the total number 08 Apr, 2025 (E)Combination
  23. 23From a group of 7 batsmen and 6 bowlers, 10 players are to be chosen for a team, which should include atleast 4 batsmen and atleast 4 bowler07 Apr, 2025 (M)Combination
  24. 24For , let denote the set of all subsets of with no two consecutive numbers. For example , but . Then is equal to ________07 Apr, 2025 (M)Division of Identical items
  25. 25Let p be the number of all triangles that can be formed by joining the vertices of a regular polygon P of n sides and q be the number of all07 Apr, 2025 (E)Combination
  26. 26Let m and be two 2-digit numbers. Then the total numbers of pairs , such that , is ________04 Apr, 2025 (E)Permutation
  27. 27If the number of seven-digit numbers, such that the sum of their digits is even, is ; , then is equal to _______03 Apr, 2025 (M)Permutation
  28. 28Line of slope 2 and line of slope intersect at the origin O . In the first quadrant, are 12 points on line and are 9 points on line . Then t03 Apr, 2025 (E)Combination
  29. 29The number of sequences of ten terms, whose terms are either 0 or 1 or 2 , that contain exactly five 1 s and exactly three 2 s , is equal to02 Apr, 2025 (M)Permutation
  30. 30The largest such that divides 50 ! is:02 Apr, 2025 (M)Exponent of prime
  31. 31The number of ways, in which the letters , D, E can be placed in the 8 boxes of the figure below so that no row remains empty and at most on02 Apr, 2025 (E)Geometric Permutation
  32. 32Let P 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 29 Jan, 2025 (M)Permutation
  33. 33The number of 6-letter words, with or without meaning, that can be formed using the letters of the word MATHS such that any letter that appe29 Jan, 2025 (M)Permutation
  34. 34If all the words with or without meaning made using all the letters of the word "KANPUR" are arranged as in a dictionary, then the word at p29 Jan, 2025 (E)Permutation
  35. 35The number of different 5 digit numbers greater than 50000 that can be formed using the digits 0 , , such that the sum of their first and la28 Jan, 2025 (M)Permutation
  36. 36The number of natural numbers, between 212 and 999 , such that the sum of their digits is 15 , is28 Jan, 2025 (E)Permutation
  37. 37Group A consists of 7 boys and 3 girls, while group B consists of 6 boys and 5 girls. The number of ways, 4 boys and 4 girls can be invited 24 Jan, 2025 (E)Combination
  38. 38The number of words, which can be formed using all the letters of the word "DAUGHTER", so that all the vowels never come together, is23 Jan, 2025 (M)Arrangement under Constraint
  39. 39The number of ways, 5 boys and 4 girls can sit in a row so that either all the boys sit together or no two boys sit together, is -23 Jan, 2025 (E)Arrangement under Constraint
  40. 40From all the English alphabets, five letters are chosen and are arranged in alphabetical order. The total number of ways, in which the middl22 Jan, 2025 (M)Arrangement under Constraint
  41. 41In a group of 3 girls and 4 boys, there are two boys and . The number of ways, in which these girls and boys can stand in a queue such that 22 Jan, 2025 (E)Arrangement under Constraint
  42. 42The number of integers, between 100 and 1000 having the sum of their digits equals to 14 , is _________09 Apr, 2024 (E)Factorial
  43. 43The number of 3-digit numbers, formed using the digits and 7 , when the repetition of digits is not allowed, and which are not divisible by 08 Apr, 2024 (M)Permutation
  44. 44The number of ways five alphabets can be chosen from the alphabets of the word MATHEMATICS, where the chosen alphabets are not necessarily d08 Apr, 2024 (E)Selection of one or more item
  45. 45The number of triangles whose vertices are at the vertices of a regular octagon but none of whose sides is a side of the octagon is06 Apr, 2024 (M)Geometric Permutation
  46. 46Let . If , then is equal to:06 Apr, 2024 (E)Factorial
  47. 47If all the words with or without meaning made using all the letters of the word "NAGPUR" are arranged as in a dictionary, then the word at p06 Apr, 2024 (E)Permutation
  48. 48The number of ways of getting a sum 16 on throwing a dice four times is______05 Apr, 2024 (M)Division of Identical items
  49. 4960 words can be made using all the letters of the word BHBJO, with or without meaning. If these words are written as in a dictionary, then t05 Apr, 2024 (E)Arrangement under Constraint
  50. 50There are 5 points on the side , excluding and , of a triangle . Similarly there are 6 points on the side and 7 points on the side of the tr04 Apr, 2024 (M)Selection of one or more item

Frequently Asked Questions

1.How many questions are available for Permutation Combination?

This chapter includes 214 questions compiled from JEE Main papers spanning 2002 to 2026.

2.Are these questions only from JEE Main, or from other exams too?

These are JEE Main questions specifically for the Permutation Combination chapter. Questions from other exams like NTA Abhyas (JEE Main) or JEE Advanced are organised separately under their respective exam sections.

3.Is Permutation Combination an important chapter for JEE Main Mathematics?

Permutation Combination has appeared in 25 of the 25 years of JEE Main papers covered here, with 214 questions across 173 papers - about one per paper it appears in.

4.What is the difficulty level of Permutation Combination questions in JEE Main?

Of the 214 questions analysed for this chapter, 21% are easy, 52% moderate and 27% tough. 2023 had the most, with 40 questions.

5.Which topics in Permutation Combination should I focus on?

These topics have carried the most weightage in Permutation Combination:

  • Permutation - 48 questions (22%)
  • Combination - 42 questions (20%)
  • Selection of one or more item - 39 questions (18%)
  • Permutation has produced the most tough questions (16).
6.Is Permutation Combination's weightage in JEE Main going up or down?

Across all 173 papers analysed, Permutation Combination has averaged about 1.2 questions per paper. In the last three years (2024–2026), that average has fallen, at about 1.0 questions per paper. Use the year-wise numbers on this page for the exact trend before you decide how much time to give it.