CAT Exam 2021 Slot 2 Solved Paper

$2.25\le 2+2^{\mathit{n}+2}\le 202$
$2.25-2\le 2+2^{\mathit{n}+2}-2\le 202-2$
$0.25\le 2^{\mathit{n}+2}\le 200$
${\log }_{2}0.25\le \mathit{n}+2\le {\log }_{2}200$
$-2\le \mathit{n}+2\le 7.\mathit{x}\mathit{x}$
$-4\le \mathit{n}\le 7.\mathrm{xx}-2$
$-4\le \mathit{n}\le 5.\mathrm{xx}$
Possible integers$=-4,-3,-2,-1,0,1,2,3,4,5$ If we see the second expression that is provided, i.e
$3+3^{\mathit{n}+1}$,it can be implied that n should be at least $-1$ for this expression to be an integer.
So, $\mathit{n}=-1,0,1,2,3,4,5$
Hence, there are a total of 7 values.