Let I be an identity matrix of order 2 $$\times$$ 2 and P = $$\left[ {\matrix{ 2 & { - 1} \cr 5 & { - 3} \cr } } \right]$$. Then the value of n$$\in$$N for which Pⁿ = 5I $$-$$ 8P is equal to ____________.

Let f : R $$ \to $$ R satisfy the equation f(x + y) = f(x) . f(y) for all x, y $$\in$$R and f(x) $$\ne$$ 0 for any x$$\in$$R. If the function f is differentiable at x = 0 and f'(0) = 3, then

$$\mathop {\lim }\limits_{h \to 0} {1 \over h}(f(h) - 1)$$ is equal to ____________.

Let $${}^n{C_r}$$ denote the binomial coefficient of x^r in the expansion of (1 + x)ⁿ. If $$\sum\limits_{k = 0}^{10} {({2^2} + 3k)} {}^{10}{C_k} = \alpha {.3^{10}} + \beta {.2^{10}},\alpha ,\beta \in R$$, then $$\alpha$$ + $$\beta$$ is equal to ___________.

Let P(x) be a real polynomial of degree 3 which vanishes at x = $$-$$3. Let P(x) have local minima at x = 1, local maxima at x = $$-$$1 and $$\int\limits_{ - 1}^1 {P(x)dx} $$ = 18, then the sum of all the coefficients of the polynomial P(x) is equal to _________.