IIM-K (BMSAT) 2025 (QA) PYQs

The set of real values of $x$ for which the inequality $\log _{27} 8 \leq \log _{3} x \lt 9^{\frac{1}{\log _{2} 3}}$ holds is

Suppose that $\log_2[\log_3 (\log_4a)] = \log_3 [\log_4 (\log_2b)] = \log_4 [\log_2 (\log_3c)] = 0$ then the value of $a + b + c$ is

If $\log_3(x^2 - 1)$, $\log_3(2x^2 + 1)$ and $\log_3(6x^2 + 3)$ are the first three terms of an arithmetic progression, then the sum of the next three terms of the progression is