In an increasing geometric series, the sum of the second and the sixth term is $${{25} \over 2}$$ and the product of the third and fifth term is 25. Then, the sum of 4^th, 6^th and 8^th terms is equal to :

The value of the integral $$\int\limits_0^\pi {|{{\sin }\,}2x|dx} $$ is ___________.

The number of solutions of the equation log₄(x $$-$$ 1) = log₂(x $$-$$ 3) is _________.

The sum of 162^th power of the roots of the equation x³ $$-$$ 2x² + 2x $$-$$ 1 = 0 is ________.