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 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

In how many ways can 5 people be arranged in a row?

All the letters of the word LETTER are arranged in all possible ways and the words (with or without meaning) thus formed are arranged in dictionary order. Then the rank of the word TETLER is:

5 men and 4 women are seated in a row. If the number of arrangements in which one particular man and one particular woman are together is $ \alpha $, and the number of arrangements in which they are not together is $ \beta $, then $ \frac{\alpha}{\beta} = $

5-digit numbers are formed by using the digits 0, 1, 2, 3, 5, 7 without repetition and all of them are arranged in ascending order. Then the rank of the number 70513 is:

The number of positive integers less than 10000 which contain the digit 5 at least once is

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?

From the word "CURVE", how many 3-letter words can be formed out of all 2-letter or more combinations (with all distinct letters)? Find probability of getting a 3-letter word.

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.

Among the 5 married couples, if the names of 5 men are matched with the names of their wives randomly, then the probability that no man is matched with the name of his own wife is ?

If all the numbers which are greater than 6000 and less than 10000 are formed with the digits $ 3,5,6,7,8 $ without repetition of the digits, then the difference between the number of odd numbers and the number of even numbers among them is:

The number of ways of arranging all the letters of the word "COMBINATIONS" around a circle so that no two vowels come together is

If the number of circular permutations of 9 distinct things taken 5 at a time is $n_1$, and the number of linear permutations of 8 distinct things taken 4 at a time is $n_2$, then what is $\frac{n_1}{n_2}$?

A man has 7 relatives, 4 of them are ladies and 3 gents; his wife has 7 other relatives, 3 of them are ladies and 4 gents. The number of ways they can invite them to a party of 3 ladies and 3 gents so that there are 3 of man's relatives and 3 of wife's relatives, is

Among the 4-digit numbers that can be formed using the digits $\{1,2,3,4,5,6\}$ without repeating any digit, the number of such numbers which are divisible by 6 is \;?

With respect to the roots of the equation $ 3x^3 + bx^2 + bx + 3 = 0 $, match the items of List-I with those of List-II.

The number of ways in which 4 different things can be distributed to 6 persons so that no person gets all the things is \;?

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 rank of the word "TABLE" counted from the rank of the word "BLATE" in dictionary order is:

Among the 4-digit numbers formed using the digits $ 0, 1, 2, 3, 4 $ when repetition of digits is allowed, the number of numbers which are divisible by 4 is: