IIM-K (BMSAT) 2025 (QA) PYQs

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

A boy agrees to work at the rate of one rupee on the first day, two rupees on the second day, four rupees on third day and

so on, thus getting on any day twice the amount he received just the day before. How many rupees will the boy earn in all, if

he started working on the $5^{th}$ of March and completed the work on the $28^{th}$ of March?

The sum of the first 5 terms of a geometric progression is the same as the sum of the first 7 terms of the same progression. If the sum of the first 9 terms is 24, then the 4th term of the progression is