CAT (QA) PYQs

Let $S$ be the set of all points $(x, y)$ in the x-y plane such that $|x|+|y| \le 2$ and $|x| \ge 1$. Then, the area, in square units, of the region represented by $S$ equals:

The number of distinct integer solutions $(x, y)$ of the equation $|x + y| + |x - y| = 2$, is

The number of integer solutions of equation $2|x|\left(x^{2}+1\right)=5 x^{2}$ is