JEE Main 2022 · 25 Jun · Shift 1 · Mathematics Q8

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MathematicsSingle correct+4 / -1Question 8 of 90

If $\dfrac1{2\cdot3^{10}}+\dfrac1{2^2\cdot3^9}+\dots+\dfrac1{2^{10}\cdot3}=\dfrac K{2^{10}\cdot3^{10}}$ , then the remainder when K is divided by 6 is :

Answer and worked solution

Official answer: D

Clear denominators. Multiplying by $2^{10}3^{10}$ : $K=\displaystyle\sum_{k=1}^{10}2^{10-k}3^{k-1}=\frac{3^{10}-2^{10}}{3-2}=59049-1024=58025$ .

Mod 6. $58025=6\times9670+5$ .

(D)

Topics:Geometric progression Number systems

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JEE Main 2022 · 25 Jun · Shift 1, Mathematics question 8