CAT (QA) PYQs

If $x$ and $y$ are real numbers such that $x^2 + (x - 2y − 1)^2 = - 4y(x + y)$, then the value $x - 2y$ is

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