IPMAT Indore (MCQ) 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 ________.

Given that $1 + \frac{1}{2^2} + \frac{1}{3^2} + \frac{1}{4^2} + ... = \frac{\pi^2}{6}$, the value of $1 + \frac{1}{3^2} + \frac{1}{5^2} + \frac{1}{7^2} + ...$ is

If $f(n)= 1 + 2 + 3 +\cdots+(n+1)$ and $g(n)= \sum_{k=1}^{k=n} \dfrac{1}{f(k)}$, then the least value of $n$ for which $g(n)$ exceeds the value $\dfrac{99}{100}$ is: