jee-main 2025 Q19

jee-main · India · session1_29jan_shift2 Geometric Sequences and Series Sum of an Infinite Geometric Series (Direct Computation)

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

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

Paper Questions

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