IPMAT Indore 2024 (MCQ) PYQs

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 product of the roots of the equation $\log_{2} 2^{(\log_{2}x)^{2}} -5 \log_{2}x+6=0$ is

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