IPMAT Indore 2020 (MCQ) PYQs

The inequality $\log_{2} \frac{3x - 1}{2 - x} < 1$ holds true for

Let $a = \dfrac{(\log_7 4)(\log_7 5 - \log_7 2)}{\log_{7} 25 (\log_7 8 - \log_7 4)}$. Then the value of $5^a$ is

The numbers $2^{2024}$ and $5^{2024}$ are expanded and their digits are written out consecutively on one page. The total number of digits written on the page is