CAT (QA) PYQs

If $x$ is a real number, then $\sqrt{\log_e \frac{4x-x^2}{3}}$ is a real number if and only if

For all possible integers $n$ satisfying $2.25 \leq 2+2^{n+2} \leq 202$, the number of integer values of $3+3^{n+1}$ is

If y is a negative number such that $2^{y^2log_3 5} = 5^{\log_2 3}$, then y equals