If 1/(2. 3¹⁰) + 1/(2². 3⁹) +..... + 1/(2¹⁰. 3) = K/(2¹⁰. 3¹⁰), then the remainder when K is divided by 6 is:

Binomial Theorem and Its Simple Applications: JEE Main 2022 Mathematics question

JEE Main 2022 · 25 Jun, Morning shift · Q2894

JEE Main 202225 Jun, Morning shiftMathematicsMediumBinomial Theorem and Its Simple Applications131× since 2002

{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

JEE Main 202225 Jun, Morning shiftMathematicsMediumBinomial Theorem and Its Simple Applications131× since 2002

{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 :