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

The number of integer solutions of the equation $\left(x^{2}-10\right)^{\left(x^{2}-3 x-10\right)}=1$ is

If$\sqrt{5x+9}+\sqrt{5x-9} = 3(2+\sqrt{2})$, then $\sqrt{10x + 9}$ is equal to