Let f(x) = 2¹⁰.x + 1 and g(x)=3¹⁰.x $$-$$ 1. If (fog) (x) = x, then x is equal to :

If (27)⁹⁹⁹ is divided by 7, then the remainder is :

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 :

If all the words, with or without meaning, are written using the letters of the word QUEEN and are arranged as in English dictionary, then the position of the word QUEEN is :