CAT (QA) PYQs

The number of distinct integers $n$ for which $\log_{1/4}(n^2 - 7n + 11) > 0$, is

If $x$ and $y$ are positive real numbers such that $\log_{x}\left(x^{2}+12\right)=4$ and $3 \log _{y} x=1$, then $x+y$ equals

Let $x$ and $y$ be positive real numbers such that $\log _{5}(x+y)+\log _{5}(x-y)=3$, and $\log _{2} y-\log _{2} x=1-\log _{2} 3$. Then $x y$ equals