If $$\alpha $$ and $$\beta $$ be two roots of the equation
x² – 64x + 256 = 0. Then the value of
$${\left( {{{{\alpha ^3}} \over {{\beta ^5}}}} \right)^{1/8}} + {\left( {{{{\beta ^3}} \over {{\alpha ^5}}}} \right)^{1/8}}$$ is :

If $$\sum\limits_{i = 1}^n {\left( {{x_i} - a} \right)} = n$$ and $$\sum\limits_{i = 1}^n {{{\left( {{x_i} - a} \right)}^2}} = na$$
(n, a > 1) then the standard deviation of n
observations x₁ , x₂ , ..., x_n is :

If {p} denotes the fractional part of the number p, then
$$\left\{ {{{{3^{200}}} \over 8}} \right\}$$, is equal to :

If f(x + y) = f(x)f(y) and $$\sum\limits_{x = 1}^\infty {f\left( x \right)} = 2$$ , x, y $$ \in $$ N, where N is the set of all natural number, then the value of $${{f\left( 4 \right)} \over {f\left( 2 \right)}}$$ is :