CAT (QA) PYQs

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

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

If $a, b, c$ are non-zero and $14^a = 36^b = 84^c$, then $6b \left( \frac{1}{c} - \frac{1}{a} \right)$ is equal to