jee-main 2022 Q62

jee-main · India · session1_25jun_shift1 Geometric Sequences and Series Finite Geometric Sum and Term Relationships
If $\frac { 1 } { 2 \cdot 3 ^ { 10 } } + \frac { 1 } { 2 ^ { 2 } \cdot 3 ^ { 9 } } + \ldots + \frac { 1 } { 2 ^ { 10 } \cdot 3 } = \frac { K } { 2 ^ { 10 } \cdot 3 ^ { 10 } }$, then the remainder when $K$ is divided by 6 is
(1) 2
(2) 3
(3) 4
(4) 5
If $\frac { 1 } { 2 \cdot 3 ^ { 10 } } + \frac { 1 } { 2 ^ { 2 } \cdot 3 ^ { 9 } } + \ldots + \frac { 1 } { 2 ^ { 10 } \cdot 3 } = \frac { K } { 2 ^ { 10 } \cdot 3 ^ { 10 } }$, then the remainder when $K$ is divided by 6 is\\
(1) 2\\
(2) 3\\
(3) 4\\
(4) 5