The greatest number among $$ 3^{50}, 4^{40}, 5^{30},  6^{20}$$ is

The simplest method to compare these four numbers is to express them as powers of the same exponent. This allows us to compare the bases, and the largest base will yield the greatest value when raised to that power. 

$$ 3^{50} = 243^{10} $$

$$4^{40} = 1024^{10}$$

$$5^{30} = 125^{10}$$

$$6^{20} = 36^{10}$$

1024 is greater than the rest , hence the greatest would be $$4^{40}$$.

So , the answer would be option (a) $$4^{40}$$.