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Question: Answered & Verified by Expert
If $\mathrm{x}_{\mathrm{i}}>0, \mathrm{y}_{\mathrm{i}}>0(\mathrm{i}=1,2,3, \ldots \ldots \mathrm{n})$ are the values of two variable $X$ and Y with geometric mean Pand Q respectively, then the geometric mean of $\frac{\mathrm{X}}{\mathrm{Y}}$ is
MathematicsSequences and SeriesNDANDA 2018 (Phase 2)
Options:
  • A $\frac{\mathrm{P}}{\mathrm{Q}}$
  • B antilog $\left(\frac{\mathrm{P}}{\mathrm{Q}}\right)$
  • C $\mathrm{n}(\log \mathrm{P}-\log \mathrm{Q})$
  • D $\mathrm{n}(\log \mathrm{P}+\log \mathrm{Q})$
Solution:
1868 Upvotes Verified Answer
The correct answer is: antilog $\left(\frac{\mathrm{P}}{\mathrm{Q}}\right)$
$\left(x_{1} x_{2} \ldots \ldots \ldots x_{n}\right)^{1 / n}=\mathrm{P}$
$\left(y_{1} y_{2} \ldots \ldots . y_{n}\right)^{1 / n}=\mathrm{Q}$
$\left(\frac{x_{1} \cdot x_{2} \ldots \ldots \ldots \ldots x_{n}}{y_{1} \cdot y_{2} \ldots \ldots \ldots . y_{n}}\right)^{1 / n}=\frac{\left(x_{1} \cdot x_{2} \ldots \ldots \ldots \ldots x_{n}\right)^{1 / n}}{\left(y_{1} y_{2} \ldots \ldots \ldots . y_{n}\right)^{1 / n}}=\frac{\mathrm{P}}{\mathrm{Q}}$

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