List of top Mathematics Questions on permutations and combinations asked in JEE Main

Number of seven digits numbers which can be formed by using all the digits 1, 2, 3, 4, 5 with at least one digit repeated is _____.

If all the letters of the word 'UDAYPUR' are arranged in all possible permutations and these permutations are listed in dictionary order, then the rank of the word 'UDAYPUR' is

Number of ways of distributing 16 identical oranges among 4 persons such that each one gets at least one orange is:

If the product \[ \left( \frac{1}{\binom{15}{0}} + \frac{1}{\binom{15}{1}} \right) \left( \frac{1}{\binom{15}{1}} + \frac{1}{\binom{15}{2}} \right) \cdots \left( \frac{1}{\binom{15}{12}} + \frac{1}{\binom{15}{13}} \right) \] is equal to \[ \frac{\alpha^{13}}{\binom{14}{0} \binom{14}{1} \binom{14}{2} \cdots \binom{14}{12}}, \] then \( 30\alpha \) is equal to:

If all the letters of the word 'UDAYPUR' are arranged in all possible permutations and these permutations are listed in dictionary order, then the rank of the word 'UDAYPUR' is

The number of ways 16 oranges distributed to 4 children, each gets at least one.

Let \( S=\{1,2,3,4,5,6,7,8,9\} \). Let \( x \) be the number of 9-digit numbers formed using the digits of the set \( S \) such that only one digit is repeated and it is repeated exactly twice. Let \( y \) be the number of 9-digit numbers formed using the digits of the set \( S \) such that only two digits are repeated and each of these is repeated exactly twice. Then:

Let A = \{-2, -1, 0, 1, 2, 3, 4\. Let R be a relation on A defined by xRy if and only if \(2x + y \le 2\). Let \(l\) be the number of elements in R. Let \(m\) and \(n\) be the minimum number of elements required to be added in R to make it reflexive and symmetric relations respectively. Then \(l + m + n\) is equal to :}

A lift is going up to the \(10^{\text{th}}\) floor. Number of ways in which \(3\) people can exit the lift at {three different floors, if the lift will not stop at I$^{\text{st}}$, II$^{\text{nd}}$ and III$^{\text{rd}}$ floors, is: }

Let S denote the set of 4-digit numbers abcd such that $a>b>c>d$ and P denote the set of 5-digit numbers having product of its digits equal to 20. Then $n(S) + n(P)$ is equal to ___

If \( A = \{ 1, 2, 3, 4, 5, 6 \}, B = \{ 1, 2, 3, 4, 5, 6, 7, 8, 9 \} \), then the number of strictly increasing functions from \( A \to B \) such that \( f(i) \neq i \) for \( i = 1, 2, 3, 4, 5, 6 \) is

\[ \left(\frac{1}{^{15}C_0}+\frac{1}{^{15}C_1}\right) \left(\frac{1}{^{15}C_1}+\frac{1}{^{15}C_2}\right) \cdots \left(\frac{1}{^{15}C_{12}}+\frac{1}{^{15}C_{13}}\right) = \frac{\alpha^{13}}{^{14}C_0\cdot {}^{14}C_1\cdot {}^{14}C_2\cdots {}^{14}C_{12}} \] If so, then find the value of \(30\alpha\).

Number of 4 letter words with or without meaning formed from the letters of the word PQRSTTUVV is:

Let \( S \) be the number of 4-digit numbers \( abcd \), where \[ a>b>c>d \] and let \( P \) be the number of 5-digit numbers \( abcde \), where the product of digits is 20. Find \( S + P \):

If the number of seven-digit numbers, such that the sum of their digits is even, is $ m \cdot n \cdot 10^a $; $ m, n \in \{1, 2, 3, ..., 9\} $, then $ m + n $ is equal to