If 3 books on Physics, 2 books on Chemistry and 4 books on Mathematics are to be arranged on a shelf so that all the Physics books are together and all the Mathematics books are together, then the number of such arrangements is

If in a regular polygon, the number of diagonals are 54, then the number of sides of the polygon are

A linguistic club consists of 6 girls and 4 boys. A team of 4 members is to be selected from this group including the selection of a leader (from among these 4 members) for the team. If the team has to include at most one boy, the number of ways of selecting the team is

Five students are selected from $$n$$ students such that the ratio of number of ways in which 2 particular students are selected to the number of ways 2 particular students not selected is $$2: 3$$. Then, the value of $$n$$ is