CAT (QA) PYQs

The largest real value of a for which the equation $|x + a| + |x - 1| = 2$ has an infinite number of solutions for $x$ is

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