CAT (QA) PYQs

If $m$ and $n$ are integers such that $(m+2n)(2m+n) = 27$, then the maximum possible value of $2m-3n$ is

How many pairs $(m, n)$ of positive integers satisfy the equation $m^2 + 105 = n^2$?

Suppose $a,b,c$ are three distinct natural numbers, such that $3ac = 8(a+b)$. Then, the smallest possible value of $3a+2b+c$ is