IPMAT Indore (SA) PYQs

The sum of a given infinite geometric progression is 80 and the sum of its first two terms is 35. Then the value of $n$ for which the sum of its first $n$ terms is closest to 100, is

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

If the sum of the first $21$ terms of the sequence: $\ln \frac{a}{b}, \ln \frac{a}{b \sqrt{b}}, \ln \frac{a}{b^{2}}, \ln \frac{a}{b^{2} \sqrt{b}}, \ldots$ is $\ln \frac{a^{m}}{b^{n}}$, then the value of $m+n$ is $\qquad$