The area of the region enclosed between the circles $x^2+y^2=4$ and $x^2+(y-2)^2=4$ is:

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:

Let the line $x=-1$ divide the area of the region $\left\{(x, y): 1+x^2 \leq y \leq 3-x\right\}$ in the ratio $m: n, \operatorname{gcd}(m, n)=1$. Then $m+n$ is equal to

If the area of the region $\{(x, y) : 1-2x \leq y \leq 4-x^2,\; x \geq 0,\; y \geq 0 \}$ is $\dfrac{\alpha}{\beta}$, $\alpha, \beta \in \mathbb{N}, \gcd(\alpha,\beta)=1$, then the value of $(\alpha+\beta)$ is: