If …, then the remainder when K is divided by 6 is :

Binomial Theorem

JEE Main 2022 · 25 Jun, Morning shift · Q2894

MathematicsMedium64×since 2002Q2894

{1 \over {2\,.\,{3^{10}}}} + {1 \over {{2^2}\,.\,{3^9}}} + \,\,.....\,\, + \,\,{1 \over {{2^{10}}\,.\,3}} = {K \over {{2^{10}}\,.\,{3^{10}}}}

, then the remainder when K is divided by 6 is :

JEE Main 2022 · 25 Jun, Morning shift · Q2894

MathematicsMedium64×since 2002Q2894

{1 \over {2\,.\,{3^{10}}}} + {1 \over {{2^2}\,.\,{3^9}}} + \,\,.....\,\, + \,\,{1 \over {{2^{10}}\,.\,3}} = {K \over {{2^{10}}\,.\,{3^{10}}}}

, then the remainder when K is divided by 6 is :