CAT (QA) PYQs

Let x, y, and z be real numbers satisfying

$4(x^2 + y^2 + z^2) = a$

$4(x - y - z) = 3+ a$

Then a equals

The product of two positive numbers is $616$. If the ratio of the difference of their cubes to the cube of their difference is $157: 3$, then the sum of the two numbers is

If $(a+b \sqrt{n})$ is the positive square root of $(29-12 \sqrt{5})$, where $a$ and $b$ are integers, and $n$ is a natural number, then the maximum possible value of $(a+b+n)$ is