IPMAT Indore (MCQ) PYQs

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

If $x, y, z$ are positive real numbers such that $x^{12} = y^{16} = z^{24}$ and the three quantities $3 \log_y x, 4 \log_z y, n \log_x z$ are in arithmetic progression, then the value of $n$ is