The number of elements in the relation $\mathrm{R}=\left\{(x, y): 4 x^2+y^2<52, x, y \in \mathbf{Z}\right\}$ is

Let $f$ and $g$ be functions satisfying $f(x+y)=f(x) f(y), f(1)=7$ and $g(x+y)=g(x y), g(1)=1$, for all $x, y \in \mathbf{N}$. If $\sum\limits_{x=1}^{\mathrm{n}}\left(\frac{f(x)}{\mathrm{g}(x)}\right)=19607$, then n is equal to :

If $X=\left[\begin{array}{l}x \\ y \\ z\end{array}\right]$ is a solution of the system of equations $A X=B$, where $\operatorname{adj} A=\left[\begin{array}{ccc}4 & 2 & 2 \\ -5 & 0 & 5 \\ 1 & -2 & 3\end{array}\right]$ and $\mathrm{B}=\left[\begin{array}{l}4 \\ 0 \\ 2\end{array}\right]$, then $|x+y+z|$ is equal to :

The area of the region $\mathrm{A}=\left\{(x, y): 4 x^2+y^2 \leqslant 8\right.$ and $\left.y^2 \leqslant 4 x\right\}$ is: