List of top Mathematics Questions on Permutation and Combination asked in JEE Main

A person has three different bags and four different books. The number of ways, in which he can put these books in the bags so that no bag is empty, is:
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 :
The number of ways of forming a queue of 4 boys and 3 girls such that all the girls are not together, is:
The number of seven-digit numbers that can be formed by using the digits \(1,2,3,5,7\) such that each digit is used at least once, is:
If \( \alpha, \beta \) are roots of the equation \( 12x^2 - 20x + 3 = 0 \), \( \lambda \in \mathbb{R} \). If \( \frac{1}{2} \leq |\beta - \alpha| \leq \frac{3}{2} \), then the sum of all possible values of \( \lambda \) is:
The number of ways, 5 boys and 4 girls can sit in a row so that either all the boys sit together or no two boys sit together 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:

Let  R = {(1, 2), (2, 3), (3, 3)}} be a relation defined on the set \( \{1, 2, 3, 4\} \). Then the minimum number of elements needed to be added in \( R \) so that \( R \) becomes an equivalence relation, is:

The number of words that can be formed using all the letters of the word "DAUGHTER" such that all the vowels never come together, is: