JEE 2020 Mathematics : Permutation and Combination

In a chess tournament, all participants were to play one game with the other. Two players fell ill after having played 3 games each. If total number of games played in the tournament is equal to 84, then total number of participants in the beginning was equal to:

Number of ways in which four letter of the word ‘DEGREE’ can be selected is

If letters of the word ‘KUBER’ are written in all possible orders and arranged as in a dictionary, then rank of the word ‘KUBER’ will be:

A is a set containing n elements. A subset P of A is chosen. The set A is reconstructed by replacing the elements of P. A subset Q of A is again chosen. The number of ways of chosen P and Q such that P ∩Q = ϕ is

Five balls of different colors are to be placed in three boxes of different sizes. Each box can hold all five balls. The number of ways in which we can place the balls in the boxes (order is not considered in the box) so that no box remains empty is

Total number of ways of selecting two numbers from the set {1, 2, 3, 4, …., 3n} so that their sum is divisible by 3 is equal to:

There are 20 people among whom two are brothers. The number of ways in which we can arrange them around a circle so that there is exactly one person between those brothers is

Total number of 4-digit number that are greater than 3000, that can be formed using the digits 1, 2, 3, 4, 5, 6 (no digit is being repeated in any number) is equal to: