IPMAT Indore 2023 (MCQ) PYQs

The set of all values of $x$ satisfying the inequality $\log _{\left(x+\frac{1}{x}\right)}\left[\log _{2}\left(\frac{x-1}{x+2}\right)\right]>0$ is

If $4^{\log_2{x}} - 4x + 9^{\log_3{y}} - 16y + 68 = 0$, then $y - x$ equals:

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