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

Let $0 \leq a \leq x \leq 100$ and $f(x)=|x-a|+|x-100|+|x-a-50|$. Then the maximum value of $f(x)$ becomes $100$ when $a$ is equal to