The series of positive multiples of 3 is divided into sets : $$\{3\},\{6,9,12\},\{15,18,21,24,27\}, \ldots$$ Then the sum of the elements in the $$11^{\text {th }}$$ set is equal to ____________.

Let $$a, b$$ be two non-zero real numbers. If $$p$$ and $$r$$ are the roots of the equation $$x^{2}-8 \mathrm{a} x+2 \mathrm{a}=0$$ and $$\mathrm{q}$$ and s are the roots of the equation $$x^{2}+12 \mathrm{~b} x+6 \mathrm{~b}=0$$, such that $$\frac{1}{\mathrm{p}}, \frac{1}{\mathrm{q}}, \frac{1}{\mathrm{r}}, \frac{1}{\mathrm{~s}}$$ are in A.P., then $$\mathrm{a}^{-1}-\mathrm{b}^{-1}$$ is equal to _____________.

Let $$a_{1}=b_{1}=1, a_{n}=a_{n-1}+2$$ and $$b_{n}=a_{n}+b_{n-1}$$ for every

natural number $$n \geqslant 2$$. Then $$\sum\limits_{n = 1}^{15} {{a_n}.{b_n}} $$ is equal to ___________.

Let for $$f(x) = {a_0}{x^2} + {a_1}x + {a_2},\,f'(0) = 1$$ and $$f'(1) = 0$$. If a₀, a₁, a₂ are in an arithmatico-geometric progression, whose corresponding A.P. has common difference 1 and corresponding G.P. has common ratio 2, then f(4) is equal to _____________.