If the sum of the first n terms of the series $$\,\sqrt 3 + \sqrt {75} + \sqrt {243} + \sqrt {507} + ......$$ is $$435\sqrt 3 ,$$ then n equals :

If the arithmetic mean of two numbers a and b, a > b > 0, is five times their geometric mean, then $${{a + b} \over {a - b}}$$ is equal to :

For any three positive real numbers a, b and c,

9(25$${a^2}$$ + b²) + 25(c² - 3$$a$$c) = 15b(3$$a$$ + c).
Then

If   A > 0, B > 0   and    A + B = $${\pi \over 6}$$,

then the minimum value of tanA + tanB is :