IPMAT Rohtak 2020 (QA) PYQs

A new sequence is obtained from the sequence of positive integers $(1,2,3, \ldots)$ by deleting all the perfect squares. Then the $2022^{\text {nd }}$ term of the new sequence is ________.

The value of $(\frac{1}{\sqrt{9}-\sqrt{8}} - \frac{1}{\sqrt{8}-\sqrt{7}} + \frac{1}{\sqrt{7}-\sqrt{6}} - \frac{1}{\sqrt{6}-\sqrt{5}} + \frac{1}{\sqrt{5}-\sqrt{4}})$ is

The sum up to $10$ terms of the series $1 \cdot 3 + 5 \cdot 7 + 9 \cdot 11 + ...$ is