IPMAT Indore 2019 (MCQ) PYQs

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

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 $\log_{(cos x)}(sin x) + \log_{(sin x)}(cos x) = 2,$ then the value of $x$ is