Permutations & Combinations — JEE Maths Practice Questions & Solutions

12 questions on Permutations & Combinations with full step-by-step solutions, including past-year (PYQ) problems. Free to practice.

mediumPYQ · JEE Main 2026

The number of $4$-letter words, with or without meaning, each consisting of two vowels and two consonants that can be formed from the letters of the word INCONSEQUENTIAL, without repeating any letter, is

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mediumPYQ · JEE Main 2026

The number of seven-digit numbers that can be formed by using the digits $1, 2, 3, 5$ and $7$ such that each digit is used at least once, is

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mediumPYQ · JEE Main 2026

The number of ways of forming a queue of $4$ boys and $3$ girls such that all the girls are not together, is

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mediumPYQ · JEE Main 2026

Two players $A$ and $B$ play a series of games of badminton. The player who wins $5$ games first wins the series. Assuming no game ends in a draw, the number of ways in which player $A$ wins the series is

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mediumPYQ · JEE Main 2026

A 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:

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hard

If $S$ is the sum of all the possible integral values of $x$ satisfying the equation

$$20\left[\frac{x^3-5x^2+6x}4-{}^{x-1}C_5\right]-4\left[{}^{x-1}C_4-4\left({}^{x-1}C_3\right)\right] > 0,$$

then the number of divisors of $S$ is

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hard

Suppose $A$ is the set of the first $3$ natural numbers. Taking $X$, $Y$ as non-empty subsets of $A$, the number of ordered set pairs $\left(X,Y\right)$ such that $\max\left(X\right)>\min\left(Y\right)$ is $2^{p}$; then $p$ is equal to

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hard

Let $N$ be the number of words which can be formed using all the letters of the word "DARJEELING" so that there are at least two consonants between any two vowels. Then match List I with List II:

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medium

If $N$ is the number of ways in which $10$ biscuits can be distributed to five beggars seated in a row such that no two consecutive beggars remain without biscuit, then $\dfrac N{100}$ is

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medium

There are four colour-shifting balls of colours $C_1$, $C_2$, $C_3$ and $C_4$ initially. Each ball can change into any other colour or can regain its own colour at every second. The number of ways theircolours can change, if the maximum possible number of arrangements of all four balls is to be possible after $1$ second, is equal to

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medium

$7$ points are given in a plane (as shown in the below figure): points $1$, $2$, $3$ lie on one straight line and points $3$, $4$, $5$, $6$, $7$ lie on another straight line, the two lines meeting at point $3$. Then using these $7$ points

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medium

Let $n = x_1x_2x_3\ldots x_9$ be formed using the digits $1,2,\ldots,9$, each digit being used once only. If $n_1$ is the number of possible $n$ for which $1<\left|x_3-x_4\right|<5$ and $n_2$ is the number of possible $n$ for which $\left|x_3-x_4\right| = 1$, then $\left[\dfrac{n_1}{n_2}\right]$ is equal to (where $[\,\cdot\,]$ is G.I.F.

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