If $$4^x-3^{x-1 / 2}=3^{x+1 / 2}-2^{2 x-1}$$, then the value of $$x$$ is

The total number of permutations of $$n$$ different things taken not more than $$r$$ at a time, when each thing may be repeated any number of times is

How many chords can be drawn through 21 points on a circle?

If a polygon of $$n$$ sides has 560 diagonals, then $$n=$$