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JEE Advanced Permutations and Combinations questions with solutions

Counting principles, arrangements and selections. 18 questions from our 2016–2025 JEE Advanced pattern papers, from the Class 11 Mathematics syllabus. Each has the answer and a full solution.

Also practise: Permutations and Combinations for JEE Main

JEE Advanced 2025

Find the number of six-digit numbers, all of whose digits belong to \1,2,3,4\, in which each of the digits 1,2,3,4 appears at least once and which…JEE Advanced 2025 Paper 1 · hard
Which of the following statements is(are) correct?JEE Advanced 2025 Paper 2 · hard

JEE Advanced 2024

A string of length 7 is formed using the letters A, B, C such that it begins with A, no two adjacent letters are the same, and all three letters…JEE Advanced 2024 Paper 1 · medium
The number of distinct five-letter arrangements (words, meaningful or not) that can be formed from the letters of the word ENGINEER, in which both…JEE Advanced 2024 Paper 2 · hard
Ten identical sweets are to be distributed among five children, each child receiving at most 3 sweets (a child may receive none). The number of ways…JEE Advanced 2024 Paper 2 · hard

JEE Advanced 2023

Let N be the number of ordered pairs (a,b) of positive integers with a<b and lcm(a,b)=360. Find N.JEE Advanced 2023 Paper 1 · medium
Let N be the number of onto functions f:\1,2,3,4,5\→\1,2,3\ satisfying f(1)≠ f(2). Find N.JEE Advanced 2023 Paper 1 · medium
Match each counting problem in List-I with its answer in List-II. List-I (P) The number of arrangements of all letters of BANANA in which no two A's…JEE Advanced 2023 Paper 1 · medium
The number of ordered triples (a,b,c) of integers with 0≤ a,b,c≤7 and a+b+c=15 isJEE Advanced 2023 Paper 2 · medium

JEE Advanced 2022

Match the counting statements in List-I with the numbers in List-II. List-I (P) Number of real solutions of |x^2-4|=x+2 (Q) Number of ordered pairs…JEE Advanced 2022 Paper 1 · hard
A shopkeeper distributes 12 identical sweets among 4 distinct children so that each child gets at least 1 and at most 5 sweets. The number of ways to…JEE Advanced 2022 Paper 2 · medium

JEE Advanced 2020

All arrangements of the seven letters of the word BALLOON (using all letters) are considered.JEE Advanced 2020 Paper 1 · hard
The number of ordered triples (a,b,c) of positive integers with a+b+c=20 and each of a,b,c≤ 9 isJEE Advanced 2020 Paper 1 · medium

JEE Advanced 2019

All distinct arrangements of the eight letters of the word CALCULUS are written down.JEE Advanced 2019 Paper 1 · hard

JEE Advanced 2018

Ten identical balls are distributed among four distinct boxes so that every box receives at least 1 and at most 4 balls. Find the number of…JEE Advanced 2018 Paper 1 · medium
Find the number of 7-digit strings formed using only the digits 1,2,3, in which each of the three digits appears at least once and the sum of all the…JEE Advanced 2018 Paper 2 · medium

JEE Advanced 2017

Find the number of ordered pairs (m,n) of positive integers satisfying 1/m+1/n+1/mn=1/6.JEE Advanced 2017 Paper 1 · medium

JEE Advanced 2016

The number of ways of distributing 10 identical balls among 4 distinct boxes so that every box receives at least 1 ball and no box receives more than…JEE Advanced 2016 Paper 2 · medium

Other Mathematics topics

Area Under Curves 13 Binomial Theorem 10 Complex Numbers 24 Conic Sections 34 Differential Equations 18 Differentiation and Application of Derivatives 20 Indefinite and Definite Integrals 18 Limits 19 Matrices and Determinants 28 Probability 38 Quadratic Equations 12 Sequences and Series 11 Sets, Relations and Functions 8 Straight Lines and Circles 10 Three Dimensional Geometry 22 Trigonometry and Inverse Trigonometric Functions 18 Vector Algebra 9