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, in sq. units, enclosed by the lines $x = 2$, $y = |x - 2| + 4$, the $X-$axis and the $Y-$axis is equal to

The area of the closed region bounded by the equation $| x | + | y | = 2$ in the two-dimensional plane is