CAT (QA) PYQs

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

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

Consider the pair of equations: $x^{2}-x y-x=22$ and $y^{2}-x y+y=34$. If $x>y$, then $x-y$ equals