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Friday, 9 October

JEE Main Maths · Permutations and Combinations

Permutations and Combinations in JEE Main

Permutations and Combinations (Maths, Permutations and Combinations) came 50 times in 39 of the 42 JEE Main shifts Lumi analysed, across 22 distinct ideas. 28 of them came in 2024–26; it was last asked in 2026.

Questions
50
in 39 shifts
Ideas asked
22
12 asked more than once
Numerical answer
22
44% of its questions
Pattern
Asked most years
last asked 2026
Questions each year
06121’174’204’216’227’239’248’2511’26

In the shifts Lumi analysed for each year.

Difficulty and format
Easy 11Medium 35Hard 4

Format

  • Single correct28 Q
  • Numerical value22 Q
Ideas inside the topic
22 ideas
Where it sits

Part of Permutations and Combinations, which had 47 questions in all. Permutations and Combinations accounts for 106% of them. In Lumi's JEE taxonomy it belongs to Algebra.

Some questions sit in other chapters too: Binomial Theorem, Probability, Relations and Functions.

Every question

All 50 Permutations and Combinations questions

Newest first, each with its options and official answer.

  1. 2 Apr 2026, Shift 1 · Q6The number of seven-digit numbers, that can be formed by using the digits 1,2,3,51, 2, 3, 5 and 77 such that each digit is used at least once,…MediumSingle correct
  2. 2 Apr 2026, Shift 2 · Q7Let pnp_n denote the total number of triangles formed by joining the vertices of an nn-side regular polygon. If pn+1−pn=66p_{n+1} - p_n = 66,…EasySingle correct
  3. 4 Apr 2026, Shift 1 · Q4The number of functions f:{1,2,3,4}→{a,b,c}f:\{1,2,3,4\}\to\{a,b,c\}, which are not onto, is:EasySingle correct
  4. 4 Apr 2026, Shift 1 · Q8The number of ways, of forming a queue of 44 boys and 33 girls such that all the girls are not together, is:EasySingle correct
  5. 4 Apr 2026, Shift 2 · Q17Let A={(a,b,c):a,b,cA=\{(a,b,c):a,b,c are non-negative integers and a+b+2c=22}a+b+2c=22\}. Then n(A)n(A) is equal to:MediumSingle correct
  6. 5 Apr 2026, Shift 1 · Q21Let A={1,2,3,4,5,6}A = \{1, 2, 3, 4, 5, 6\}. The number of one-one functions f:A→Af: A \to A such that f(1)≥3f(1) \geq 3, f(3)≤4f(3) \leq 4 and f(2)+f(3)=5f(2) + f(3) = 5,…MediumNumerical value
  7. 5 Apr 2026, Shift 1 · Q22Two 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…MediumNumerical value
  8. 5 Apr 2026, Shift 2 · Q9A 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 :MediumSingle correct
  9. 6 Apr 2026, Shift 1 · Q7The number of 4-letter words, with or without meaning, each consisting of two vowels and two consonants that can be formed from the…MediumSingle correct
  10. 6 Apr 2026, Shift 2 · Q7A building has ground floor and 10 more floors. Nine persons enter in a lift at the ground floor. The lift goes up to the 10th^{\text{th}}…MediumSingle correct
  11. 8 Apr 2026, Shift 2 · Q9A 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…EasySingle correct
  12. 2 Apr 2025, Shift 1 · Q6The largest n∈Nn\in\mathbf{N} such that 3n3^n divides 50!50! is :EasySingle correct
  13. 2 Apr 2025, Shift 2 · Q6The 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…MediumSingle correctHas a figure
  14. 3 Apr 2025, Shift 1 · Q21If the number of seven-digit numbers, such that the sum of their digits is even, is m⋅n⋅10nm \cdot n \cdot 10^n;…MediumNumerical value
  15. 3 Apr 2025, Shift 2 · Q7Line L1\mathrm{L_1} of slope 2 and line L2\mathrm{L_2} of slope 12\frac{1}{2} intersect at the origin O. In the first quadrant,…EasySingle correct
  16. 7 Apr 2025, Shift 1 · Q8From 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…MediumSingle correct
  17. 7 Apr 2025, Shift 1 · Q21For n≥2n \geq 2, let SnS_n denote the set of all subsets of {1,2,…,n}\{1, 2, \ldots, n\} with no two consecutive numbers. For example…MediumNumerical value
  18. 7 Apr 2025, Shift 2 · Q8Let pp be the number of all triangles that can be formed by joining the vertices of a regular polygon PP of nn sides and qq be the…MediumSingle correct
  19. 8 Apr 2025, Shift 2 · Q7There 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…EasySingle correct
  20. 6 Apr 2024, Shift 2 · Q5If 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…MediumSingle correct
  21. 6 Apr 2024, Shift 2 · Q6Let 0≤r≤n0\le r\le n. If n+1Cr+1:nCr:n−1Cr−1=55:35:21^{n+1}C_{r+1}:{}^{n}C_r:{}^{n-1}C_{r-1}=55:35:21, then 2n+5r2n+5r is equal to :MediumSingle correct
  22. 8 Apr 2024, Shift 1 · Q1Let [t][t] be the greatest integer less than or equal to tt. Let AA be the set of all prime factors of 2310 and f:A→Zf: A \to \mathbb{Z} be…MediumSingle correct
  23. 8 Apr 2024, Shift 1 · Q23The number of 3-digit numbers, formed using the digits 2, 3, 4, 5 and 7, when the repetition of digits is not allowed, and which are not…MediumNumerical value
  24. 9 Apr 2024, Shift 2 · Q23The number of integers, between 100 and 1000 having the sum of their digits equals to 14, is ______________.MediumNumerical value
  25. 29 Jan 2024, Shift 1 · Q22All the letters of the word "GTWENTY" are written in all possible ways with or without meaning and these words are written as in a…MediumNumerical value
  26. 30 Jan 2024, Shift 2 · Q23In an examination of Mathematics paper, there are 20 questions of equal marks and the question paper is divided into three sections : AA,…MediumNumerical value
  27. 31 Jan 2024, Shift 2 · Q5The number of ways in which 21 identical apples can be distributed among three children such that each child gets at least 2 apples, isEasySingle correct
  28. 31 Jan 2024, Shift 2 · Q6If for some m,nm,n; 6Cm+2(6Cm+1)+6Cm+2>8C3{}^6C_m+2\left({}^6C_{m+1}\right)+{}^6C_{m+2}>{}^8C_3 and n−1P3:nP4=1:8{}^{n-1}P_3:{}^nP_4=1:8, then nPm+1+n+1Cm{}^nP_{m+1}+{}^{n+1}C_m…MediumSingle correct
  29. 6 Apr 2023, Shift 1 · Q23The number of ways of giving 20 distinct oranges to 3 children such that each child gets at least one orange is ____________MediumNumerical value
  30. 8 Apr 2023, Shift 2 · Q5If the number of words, with or without meaning, which can be made using all the letters of the word MATHEMATICS in which C and S do not…MediumSingle correct
  31. 8 Apr 2023, Shift 2 · Q23Let R={a,b,c,d,e}R = \{a, b, c, d, e\} and S={1,2,3,4}S = \{1, 2, 3, 4\}. Total number of onto functions f:R→Sf: R \to S such that f(a)≠1f(a) \neq 1, is equal to…HardNumerical value
  32. 11 Apr 2023, Shift 1 · Q4The number of triplets (x,y,z)(x, y, z), where x,y,zx, y, z are distinct non negative integers satisfying x+y+z=15x + y + z = 15, isMediumSingle correct
  33. 11 Apr 2023, Shift 1 · Q30In an examination, 5 students have been allotted their seats as per their roll numbers. The number of ways, in which none of the students…EasyNumerical value
  34. 13 Apr 2023, Shift 2 · Q6All words, with or without meaning, are made using all the letters of the word MONDAY. These words are written as in a dictionary with…EasySingle correct
  35. 13 Apr 2023, Shift 2 · Q22Total numbers of 3-digit numbers that are divisible by 6 and can be formed by using the digits 1, 2, 3, 4, 5 with repetition, is ______MediumNumerical value
  36. 25 Jul 2022, Shift 1 · Q1The total number of functions, f:{1,2,3,4}→{1,2,3,4,5,6}f:\{1,2,3,4\}\rightarrow\{1,2,3,4,5,6\} such that f(1)+f(2)=f(3)f(1)+f(2)=f(3), is equal to :MediumSingle correct
  37. 25 Jul 2022, Shift 1 · Q22The letters of the word 'MANKIND' are written in all possible orders and arranged in serial order as in an English dictionary. Then the…MediumNumerical value
  38. 28 Jul 2022, Shift 1 · Q21Let S be the set of all passwords which are six to eight characters long, where each character is either an alphabet from {A,B,C,D,E}\{A,B,C,D,E\}…MediumNumerical value
  39. 24 Jun 2022, Shift 1 · Q21The number of one-one functions f:{a,b,c,d}→{0,1,2,…,10}f:\{a, b, c, d\}\to\{0, 1, 2, \ldots, 10\} such that 2f(a)−f(b)+3f(c)+f(d)=02f(a)-f(b)+3f(c)+f(d)=0 is ______.HardNumerical value
  40. 24 Jun 2022, Shift 1 · Q22In an examination, there are 5 multiple choice questions with 3 choices, out of which exactly one is correct. There are 3 marks for each…MediumNumerical value
  41. 29 Jun 2022, Shift 1 · Q30Let b1b2b3b4b_1b_2b_3b_4 be a 4-element permutation with bi∈{1,2,3,……,100}b_i \in \{1, 2, 3, \ldots\ldots, 100\} for 1≤i≤41 \le i \le 4 and bi≠bjb_i \ne b_j for…MediumNumerical value
  42. 3 Aug 2021, Shift 2 · Q82If six letter words (with or without meaning) are formed using A, B, C, D, E and F, then the number of words, in which exactly one of…MediumNumerical value
  43. 25 Jul 2021, Shift 1 · Q89There are 5 students in class 10, 6 students in class 11 and 8 students in class 12. If the number of ways, in which 10 students can be…HardNumerical value
  44. 16 Mar 2021, Shift 2 · Q73Consider a rectangle ABCD having 5, 7, 6, 9 points in the interior of the line segments AB, CD, BC, DA respectively. Let α\alpha be the…MediumSingle correct
  45. 18 Mar 2021, Shift 1 · Q65The sum of all the 4-digit distinct numbers that can be formed with the digits 1, 2, 2 and 3 is :MediumSingle correct
  46. 8 Jan 2020, Shift 1 · Q75An urn contains 5 red marbles, 4 black marbles and 3 white marbles. Then the number of ways in which 4 marbles can be drawn so that at the…EasyNumerical value
  47. 9 Jan 2020, Shift 2 · Q68If 10 different balls are to be placed in 4 distinct boxes at random, then the probability that two of these boxes contain exactly 2 and 3…MediumSingle correct
  48. 2 Sep 2020, Shift 1 · Q71If the letters of the word 'MOTHER' be permuted and all the words so formed (with or without meaning) be listed as in a dictionary, then…MediumNumerical value
  49. 6 Sep 2020, Shift 2 · Q72The number of words (with or without meaning) that can be formed from all the letters of the word "LETTER" in which vowels never come…MediumNumerical value
  50. 2 Apr 2017 (offline) · Q66A man X has 7 friends, 4 of them are ladies and 3 are men. His wife Y also has 7 friends, 3 of them are ladies and 4 are men. Assume X and…HardSingle correct