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

Five persons $$\mathrm{A}, \mathrm{B}, \mathrm{C}, \mathrm{D}$$ and $$\mathrm{E}$$ are seated in a circular arrangement. If each of them is given a cap of one of the three colours red, blue and green, then the number of ways of distributing the caps such that the persons seated in adjacent seats get different coloured caps, is