PrepWiser › Learn › Mathematics › Permutations & CombinationsPermutations & Combinations — JEE Main PYQs & Practice Questions Permutations & Combinations is a Mathematics chapter in the JEE Main syllabus. This page brings together 177 previous-year and practice questions on Permutations & Combinations, organised into 6 topics: Fundamental Principle of Counting, Permutations, Combinations, Circular Permutations, Distribution Problems and Rank of a Word. Most questions come with a step-by-step solution you can work through free in PrepWiser.
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Fundamental Principle of Counting The total number of functions, f:{1,2,3,4} →{1,2,3,4,5,6} such that f(1)+f(2)=f(3), is… The number of 4-digit numbers which are neither multiple of 7 nor multiple of 3 is… The number of ways of selecting two numbers a and b, a ∈{2,4,6, … ., 100} and b ∈{1,3,5… The number of 3 -digit numbers, that are divisible by 2 and 3 , but not divisible by 4… Total numbers of 3-digit numbers that are divisible by 6 and can be formed by using the… The largest n∈ ℕ, for which 7ⁿ divides 101!, is : A number is called a palindrome if it reads the same backward as well as forward. For… The total number of three-digit numbers, divisible by 3, which can be formed using the… A person has 3 shirts and 2 pants. The number of outfits possible is: The number of 3-digit odd numbers, whose sum of digits is a multiple of 7, is… Number of functions f:{1,2, …, 100} →{0,1}, that assign 1 to exactly one of the positive… A natural number has prime factorization given by n = 2ˣ3ʸ5ᶻ, where y and z are such… Number of 4-digit numbers that are less than or equal to 2800 and either divisible by 3… The total number of four digit numbers such that each of first three digits is divisible… The total number of 3-digit numbers, whose greatest common divisor with 36 is 2, is… If the number of seven-digit numbers, such that the sum of their digits is even, is m ·… The number of 4-digit numbers that can be formed from digits 1,2,3,4,5 (repetition… The number of times the digit 3 will be written when listing the integers from 1 to 1000… The largest value of n, for which 40ⁿ divides 60!, is The total number of 4-digit numbers whose greatest common divisor with 54 is 2, is… Permutations If the digits are not allowed to repeat in any number formed by using the digits 0, 2… The total number of six digit numbers, formed using the digits 4, 5, 9 only and… The number of words (with or without meaning) that can be formed from all the letters of… The number of 4 letter words (with or without meaning) that can be formed from the… Numbers are to be formed between 1000 and 3000 , which are divisible by 4 , using the… If the number of five digit numbers with distinct digits and 2 at the 10ᵗʰ place is 336… The number of three-digit even numbers, formed by the digits 0, 1, 3, 4, 6, 7 if the… If ¹P₁ + 2.²P₂ + 3.³P₃ + .... + 15.¹⁵P₁₅ = ^qPᵣ - s,0 ≤ s ≤ 1, then ^(q + s)Cᵣ₋ₛ is… The number of words, which can be formed using all the letters of the word "DAUGHTER"… If the number of words, with or without meaning, which can be made using all the letters… The number of ways, 5 boys and 4 girls can sit in a row so that either all the boys sit… The number of 4-letter words, with or without meaning, each consisting of 2 vowels and 2… The sum of all the four-digit numbers that can be formed using all the digits 2, 1, 2, 3… The number of ways, of forming a queue of 4 boys and 3 girls such that all the girls are… The number of integers, greater than 7000 that can be formed, using the digits 3, 5, 6… The number of words, with or without meaning, that can be formed by taking 4 letters at… The total number of three-digit numbers, with one digit repeated exactly two times, is… If ²ⁿ⁺¹ Pₙ₋₁: ²ⁿ⁻¹ Pₙ=11: 21, then n²+n+15 is equal to : How many 3-digit numbers can be formed using digits 1, 2, 3, 4 (repetition not allowed)? The total number of 5-digit numbers, formed by using the digits 1, 2, 3, 5, 6, 7 without… Combinations Some couples participated in a mixed doubles badminton tournament. If the number of… The number of triplets (x, y, z), where x, y, z are distinct non negative integers… From 6 men and 5 women, a committee of 4 is formed with exactly 2 men. The number of… There are ten boys B₁, B₂, ......., B₁₀ and five girls G₁, G₂, ........, G₅ in a class… If the sides AB, BC and CA of a triangle ABC have 3, 5 and 6 interior points… C(n, 2) = 10. Then n = x. Let ABC be a triangle. Consider four points p₁,p₂,p₃,p₄ on the side AB , five points… Let P₁, P₂, ......, P₁₅ be 15 points on a circle. The number of distinct triangles… C(10, 3) = The number of ways five alphabets can be chosen from the alphabets of the word… The number of ways to select a cricket team of 11 from 15 players (including a captain)… Let pₙ denote the total number of triangles formed by joining the vertices of an n-side… Let S={(m,n):m,n∈ {1,2,3,…..,50}}. If the number of elements (m,n) in S such that 6ᵐ+9ⁿ… The value of C(8, 2) is x. Two players A and B play a series of games of badminton. The player, who wins 5 games… The number of diagonals in a hexagon is x. How many straight lines can be drawn through 10 points of which 4 are collinear? Let n > 2 be an integer. Suppose that there are n Metro stations in a city located along… There are 5 points P₁, P₂, P₃, P₄, P₅ on the side A B, excluding A and B, of a triangle… If ²ⁿ C₃: ⁿ C₃=10: 1, then the ratio (n²+3 n):(n²-3 n+4) is : Circular Permutations Distribution Problems The number of ways to distribute 30 identical candies among four children C₁, C₂, C₃ and… Let the set S={2,4,8,16, …, 512} be partitioned into 3 sets A, B, C with equal number of… The number of ways of getting a sum 16 on throwing a dice four times is ________. A person has three different bags and four different books. The number of ways, in which… The number of 6-letter words, with or without meaning, that can be formed using the… The number of ways, in which the letters A, B, C, D, E can be placed in the 8 boxes of… The number of ways in which 21 identical apples can be distributed among three children… Number of ways of arranging 8 identical books into 4 identical shelves where any number… The number of seven digit integers with sum of the digits equal to 10 and formed by… Let P be the set of seven digit numbers with sum of their digits equal to 11. If the… Eight persons are to be transported from city A to city B in three cars of different… The number of seven digit positive integers formed using the digits 1,2,3 and 4 only and… The students S₁, S₂, ....., S₁₀ are to be divided into 3 groups A, B and C such that… The total number of positive integral solutions (x, y, z) such that xyz = 24 is : Let A=[aᵢⱼ], aᵢⱼ ∈ ℤ ∩[0,4], 1 ≤ i, j ≤ 2. The number of matrices A such that the sum of… The number of ways, 16 identical cubes, of which 11 are blue and rest are red, can be… In an examination, 5 students have been allotted their seats as per their roll numbers… The number of ways of giving 20 distinct oranges to 3 children such that each child gets… Number of integral solutions to the equation x+y+z=21, where x ≥ 1,y≥3,z≥4, is equal to… The number of natural numbers, between 212 and 999, such that the sum of their digits is… Rank of a Word The letters of the word "UDAYPUR" are written in all possible ways with or without… All words, with or without meaning, are made using all the letters of the word MONDAY… The letters of the word OUGHT are written in all possible ways and these words are… If the letters of the word 'MOTHER' be permuted and all the words so formed (with or… 60 words can be made using all the letters of the word BHBJO, with or without meaning… If all the words with or without meaning made using all the letters of the word "NAGPUR"… All five letter words are made using all the letters A, B, C, D, E and arranged as in an… Let 5 digit numbers be constructed using the digits 0,2,3,4,7,9 with repetition allowed… If all the words with or without meaning made using all the letters of the word "KANPUR"… Five digit numbers are formed using the digits 1, 2, 3, 5, 7 with repetitions and are… If all the six digit numbers x₁ x₂ x₃ x₄ x₅ x₆ with 0< x₁ < x₂ < x₃ < x₄ < x₅ < x₆ are… The letters of the word 'MANKIND' are written in all possible orders and arranged in… If the letters of the word MATHS are permuted and all possible words so formed are… All the arrangements, with or without meaning, of the word FARMER are written excluding… All the letters of the word PUBLIC are written in all possible orders and these words… All the letters of the word "GTWENTY" are written in all possible ways with or without… More Mathematics chapters Frequently asked questions How many Permutations & Combinations questions are there for JEE Main? PrepWiser has 177 Permutations & Combinations questions for JEE Main, grouped into 6 topics such as Fundamental Principle of Counting, Permutations and Combinations.
Are these Permutations & Combinations questions from previous-year JEE Main papers? Yes — most are genuine previous-year questions from past JEE Main papers, and the rest are practice questions written to match the JEE Main pattern and difficulty.
Where can I see the answers and solutions to these Permutations & Combinations questions? Open any Permutations & Combinations question in PrepWiser (it is free) to attempt it; most come with a step-by-step solution.