Area of S =

$$a \in R$$ (the set of all real numbers), a $$\ne$$ $$-$$1,

$$\mathop {\lim }\limits_{n \to \infty } {{({1^a} + {2^a} + ... + {n^a})} \over {{{(n + 1)}^{a - 1}}[(na + 1) + (na + 2) + ... + (na + n)]}} = {1 \over {60}}$$, Then a = ?

Let $$\omega$$ be a complex cube root of unity with $$\omega$$ $$\ne$$ 1 and P = [p_ij] be a n $$\times$$ n matrix with p_ij = $$\omega$$^{i + j}. Then P² $$\ne$$ 0, when n = ?

The function $$f(x) = 2\left| x \right| + \left| {x + 2} \right| - \left| {\left| {x + 2} \right| - 2\left| x \right|} \right|$$ has a local minimum or a local maximum at x =