IPMAT Indore 2019 (MCQ) PYQs

The number of terms common to both the arithmetic progressions $2, 5, 8, 11, ..., 179$ and $3, 5, 7, 9, ..., 101$ 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 $\qquad$

If $\frac{1}{1^2} + \frac{1}{2^2} + \frac{1}{3^2} + \ldots$ up to $\infty = \frac{\pi^2}{6}$, then the value of $\frac{1}{1^2} + \frac{1}{3^2} + \frac{1}{5^2} + \ldots$ up to $\infty$ is