JEE Math Practice Question
Let $\mathrm{S}=\mathbf{N} \cup\{0\}$. Define a relation R from S to $\mathbf{R}$ by : $$ \mathrm{R}=\left\{(x, y): \log _{\mathrm{e}} y=x \log _{\mathrm{e}}\left(\frac{2}{5}\right), x \in \mathrm{~S}, y \in \mathbf{R}\right\} . $$ Then, the sum of all the elements in the range of $R$ is equal to :
- A.$\frac{3}{2}$
- B.$\frac{10}{9}$
- C.$\frac{5}{2}$
- D.$\frac{5}{3}$
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