IPMAT Indore 2025 (MCQ) PYQs

Suppose that a, b, and c are real numbers greater than 1. Then the value of $\dfrac{1}{1+\log_{a^2 b} \frac{c}{a}} + \dfrac{1}{1+\log_{b^2 c} \frac{a}{b}} + \dfrac{1}{1+\log_{c^2 a} \frac{b}{c}}$ is

If $\log _{\left(x^{2}\right)} y+\log _{\left(y^{2}\right)} x=1$ and $y=x^{2}-30$, then the value of $x^{2}+y^{2}$ is ___________.

The value of $(0.04^{log_{\sqrt{5}}(\frac{1}{4} + \frac{1}{8} + \frac{1}{16} + ...)})$ is __________.