CAT (QA) PYQs

Let $a$, $b$, $m$ and $n$ be natural numbers such that $a > 1$ and $b > 1$. If $a^m b^n = 144^{145}$, then the largest possible value of $n - m$ is

If $3^{a}=4,4^{b}=5,5^{c}=6,6^{d}=7,7^{e}=8$ and $8^{f}=9$, then the value of the product $\textit{abcdef }$ is

The number of integers that satisfy the equality $(x^2 - 5x + 7)^{x + 1} = 1$ is