List of top Mathematics Questions on Permutations

If \( 0 < r < s \le n \) and \( ^nP_r = ^nP_s \), then the value of \( (r - s) \) is :
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 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
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
In how many ways can 5 people be arranged in a row?
In a group of 3 girls and 4 boys, there are two boys \( B_1 \) and \( B_2 \). The number of ways in which these girls and boys can stand in a queue such that all the girls stand together, all the boys stand together, but \( B_1 \) and \( B_2 \) are not adjacent to each other, is:
How many 4-digit numbers can be formed using the digits 1, 2, 3, 4, 5 without repetition such that the number is divisible by 5?

Given, the function \( f(x) = \frac{a^x + a^{-x}}{2} \) (\( a > 2 \)), then \( f(x+y) + f(x-y) \) is equal to

In a paper there are 3 sections A, B and C which have 8, 6 and 6 questions each. A student have to attempt 15 questions such that they have to attempt at least 4 questions out of each sections. Then number of ways of attempting these questions are
Number of ways of arranging 5 officers in 4 rooms.
The number of ways to distribute 8 identical books into 4 distinct bookshelf is (where any bookshelf can be empty)
The number of ways of distributing \( 500 \) dissimilar boxes equally among \( 50 \) persons is
The number of 9 digit numbers, that can be formed using all the digits of the number 123412341 so that the even digits occupy only even places, is
The number of integers, greater than $7000$ that can be formed, using the digits $3,5,6,7,8$ without repetition, is
The number of numbers, strictly between 5000 and 10000 can be formed using the digits 1,3,5,7,9 without repetition, is

Consider the word INDEPENDENCE. The number of words such that all the vowels are together is?

7 boys and 5 girls are to be seated around a circular table such that no two girls sit together is?

The sum of all the four-digit numbers that can be formed using all the digits 2, 1, 2, 3 is equal to ______.

In what ratio must a shopkeeper mix peas and soyabean of ₹16 and ₹25 per kg respectively, so as to obtain a mixture of ₹19 per kg?
How many 3 digit even numbers can be formed from the digits (0-9) if repetition of digits are allowed?
The number of 3-digit odd numbers, whose sum of digits is a multiple of 7, is ________.
Let A be a 3 × 3 matrix having entries from the set {–1, 0, 1}. The number of all such matrices A having sum of all the entries equal to 5, is ______.