CAT (QA) PYQs

In how many ways can a pair of integers $(x, a)$ be chosen such that $x^2 - 2 | x | + | a - 2 | = 0$?

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

The shortest distance of the point $\left(\frac{1}{2}, 1\right)$ from the curve $y=|x-1|+|x+1|$ is