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Jee Main 2025 — Medium JEE math MCQ

Let $S = N \cup \{0\}$. Define a relation $R$ from $S$ to $R$ by $R = \{ (x, y) : \log_e y = x \log_e \left( \frac{2}{3} \right), x \in S, y \in R \}$ Then, the sum of all the elements in the range of $R$ is equal to
  1. A. $\frac{10}{9}$
  2. B. $\frac{5}{2}$
  3. C. $\frac{\sqrt{3}}{2}$
  4. D. $\frac{1}{3}$

Solution

The correct option is **D**. (D. $\frac{1}{3}$)

MATH

medium • PYQ Reworded
Question
Read carefully, then pick the best option.
Let S=N∪{0}S = N \cup \{0\}. Define a relation RR from SS to RR by R={(x,y):log⁡ey=xlog⁡e(23),x∈S,y∈R}R = \{ (x, y) : \log_e y = x \log_e \left( \frac{2}{3} \right), x \in S, y \in R \} Then, the sum of all the elements in the range of RR is equal to
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Jee Main 2025 — Medium JEE Mathematics MCQ | MyGoalPrep