CAT (QA) PYQs

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

The area of the quadrilateral bounded by the $Y$-axis, the line $x=5$, and the lines $|x-y|-|x-5|=2$, is

If x and y are real numbers such that $|x| + x + y = 15$ and $x + |y| - y = 20$, then $(x - y)$ equals