CAT (QA) PYQs

If r a constant such that $|x^2 - 4x - 13| = r$ has exactly three distinct real roots, then the value of r is

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