IPMAT Indore 2021 (SA) PYQs

The terms of a geometric progression are real and positive. If the $p$-th term of the progression is $q$ and the $q$-th term is $p$, then the logarithm of the first term is

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 ________.

Assume that all positive integers are written down consecutively from left to right as in 1234567891011...... The 6389th digit in this sequence is