CAT (QA) PYQs

If $(x+6\sqrt{2})^{\frac{1}{2}} - (x-6\sqrt{2})^{\frac{1}{2}} = 2\sqrt{2}$, then x equals

Given that $x^{2018}y^{2017} = 1/2$ and $x^{2016}y^{2019} = 8$, the value of $x^2 + y^3$ is

Let $n$ and $m$ be two positive integers such that there are exactly $41$ integers greater than $8^m$ and less than $8^n$, which can be expressed as powers of $2$. Then, the smallest possible value of $n + m$ is