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Friday, 9 October

JEE Main Maths · Class 11

Permutations and Combinations: JEE Main previous year questions

Permutations and Combinations had 47 questions in the 42 JEE Main shifts Lumi analysed, about 1.0 a shift, asked in 40 of 42 shifts. It ranks 14 of 22 Maths chapters by questions; 6% of its questions were hard.

Questions
47
in 40 of 42 shifts
A shift, on average
1.0
of 25 Maths questions
Since 2024
+0.1
0.9 a shift in 2017–23, 1.1 in 2024–26
Numerical answer
23
49% of its questions

Year by year

How often it came

Questions in the analysed shifts of each year. Years differ in how many shifts Lumi analysed, so read the bars with the shift count.

Questions each year
05101’173’205’214’226’2310’249’259’26

2017: 1 shifts · 2020: 4 shifts · 2021: 4 shifts · 2022: 4 shifts · 2023: 4 shifts · 2024: 8 shifts · 2025: 8 shifts · 2026: 9 shifts

Difficulty by year
  • 20171
  • 20203
  • 20215
  • 20224
  • 20236
  • 202410
  • 20259
  • 20269
  • Easy
  • Medium
  • Hard

Inside the chapter

Topics and the ideas that repeat

1 topics and 18 distinct ideas; 11 ideas were asked more than once. Most questions are single correct and calculation.

Topics, by questions

5 questions had no close topic in our taxonomy and are counted for the chapter only.

Ideas asked most
11 repeat

Study it on Lumi

Permutations and Combinations: the interactive lesson

Every question

All 47 Permutations and Combinations questions

Newest first. Each opens with its options and the official answer.

2026 9 questions

  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 · 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
  4. 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
  5. 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
  6. 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
  7. 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
  8. 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
  9. 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

2025 9 questions

  1. 2 Apr 2025, Shift 1 · Q9The number of sequences of ten terms, whose terms are either 0 or 1 or 2, that contain exactly five 1s and exactly three 2s, is equal to :EasySingle correct
  2. 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
  3. 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
  4. 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
  5. 4 Apr 2025, Shift 2 · Q22Let m and n, (m<n)(m<n), be two 2-digit numbers. Then the total numbers of pairs (m,n)(m,n), such that gcd⁡(m,n)=6\gcd(m,n)=6, is __________.HardNumerical value
  6. 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
  7. 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
  8. 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
  9. 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

2024 10 questions

  1. 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
  2. 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
  3. 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
  4. 9 Apr 2024, Shift 2 · Q21Let A={(x,y):2x+3y=23, x,y∈N}A=\{(x, y): 2x+3y=23,\ x, y\in\mathbb{N}\} and B={x:(x,y)∈A}B=\{x: (x, y)\in A\}. Then the number of one-one functions from AA to BB is equal…MediumNumerical value
  5. 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
  6. 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
  7. 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
  8. 31 Jan 2024, Shift 1 · Q23The total number of words (with or without meaning) that can be formed out of the letters of the word 'DISTRIBUTION' taken four at a time,…MediumNumerical value
  9. 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
  10. 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

2023 6 questions

  1. 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
  2. 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
  3. 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
  4. 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
  5. 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
  6. 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

2022 4 questions

  1. 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
  2. 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
  3. 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
  4. 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

2021 5 questions

  1. 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
  2. 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
  3. 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
  4. 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
  5. 18 Mar 2021, Shift 1 · Q88The number of times the digit 3 will be written when listing the integers from 1 to 1000 is __________.MediumNumerical value

2020 3 questions

  1. 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
  2. 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
  3. 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

2017 1 questions

  1. 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

Pattern: Asked most years.