IPMAT Indore 2022 (MCQ) PYQs

The value of $(0.04^{log_{\sqrt{5}}(\frac{1}{4} + \frac{1}{8} + \frac{1}{16} + ...)})$ 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 $\log_4 x = a$ and $\log_{25} x = b$, then $\log_x 10$ is