CAT (QA) PYQs

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

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

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