CAT (QA) PYQs

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

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 $\left(x^2+\frac{1}{x^2}\right)=25$ and $x>0$, then the value of $\left(x^7+\frac{1}{x^7}\right)$ is