Let f : R $$ \to $$ R be a function defined by
f(x) = max {x, x²}. Let S denote the set of all points in R, where f is not differentiable. Then :

Let z = x + iy be a non-zero complex number such that $${z^2} = i{\left| z \right|^2}$$, where i = $$\sqrt { - 1} $$ , then z lies on the :

Consider the data on x taking the values
0, 2, 4, 8,....., 2ⁿ with frequencies
ⁿC₀ , ⁿC₁ , ⁿC₂ ,...., ⁿC_n respectively. If the
mean of this data is $${{728} \over {{2^n}}}$$, then n is equal to _________ .

Suppose that a function f : R $$ \to $$ R satisfies
f(x + y) = f(x)f(y) for all x, y $$ \in $$ R and f(1) = 3.
If $$\sum\limits_{i = 1}^n {f(i)} = 363$$ then n is equal to ________ .