List of top Mathematics Questions on Permutations

The letters of the word ``UDAYPUR'' are written in all possible ways with or without meaning and these words are arranged as in a dictionary. The rank of the word ``UDAYPUR'' is

The number of arrangements of the letters of the word BANANA so that the arrangement starts and ends with the same letter, is

There are 3 boys and 4 girls in a group. The number of ways they can sit in a row so that between any two boys there is a girl and between any two girls there is a boy, is

Let $S$ be the set of all 3-digit numbers containing the digits 3, 5 and 7 without repetition. The sum of all numbers in $S$ is

If \(^n P_5 = 360360\), then \(^n C_5 = \)

The number of 3-digit numbers greater than 500, that can be formed using the digits 3, 4, 5, and 7, with repetition, is

How many license plates can be made if the license plates contain 6 characters out of which the first two characters are distinct digits and the remaining 4 characters are distinct capital letters of the English alphabet?

20 delegates from 20 countries sit in a circle such that two particular delegates never sit together. In how many ways can they be seated?

The rank of the word ‘NEEDED’, when all letters of this word are permuted in all possible ways to form different 6-letter words and arranged in dictionary order, is

If number of circular permutations of 10 distinct things taken 5 at a time is \(m\) and number of linear permutations of 9 distinct things taken 4 at a time is \(n\), then \(m:n=\)

If number of circular permutations of 10 distinct things taken 5 at a time is \(m\) and number of linear permutations of 9 distinct things taken 4 at a time is \(n\), then \(m:n=\)

The rank of the word ‘NEEDED’, when all letters of this word are permuted in all possible ways to form different 6-letter words and arranged in dictionary order, is

If \[ {}^{n}P_{4}=5040 \] and \[ {}^{15}P_{r}=2730, \] then the value of \(n+r\) is:

The number of arrangements of the letters of the word SEARCH such that no letter remains in its original position is:

If \( 0 < r < s \le n \) and \( ^nP_r = ^nP_s \), then the value of \( (r - s) \) is :

The number of numbers greater than $5000$, less than $9000$ and divisible by $3$, that can be formed using the digits $0,1,2,5,9$, if repetition of digits is allowed, is

Five digit number is formed using the digits 0, 1, 2, 3, 4 and 5 without repetitions. Number of five digit numbers which are divisible by 10 is ________.

The number of integers greater than 7000 using 2, 4, 6, 7, 8 without repetition is ________.

The number of ways in which 6 boys and 4 girls can be seated around a round table such that 2 special boys and a special girl never sit together is

The domain of the function $f(x) = {^{7-x}\text{P}_{x-1}$ is

The feasible region for the constraints \( x - 2 \le y, x \ge y - 1, x \ge 2, y \le 4, x, y \ge 0 \), is

The domain of the function $f(x) = {^{7-x}\text{P}_{x-1}$ is

The feasible region for the constraints \( x - 2 \le y, x \ge y - 1, x \ge 2, y \le 4, x, y \ge 0 \), is