If 2^{10} + 2^{9} cdot 3^{1} + 2^{8} cdot 3^{ | vedclass

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(C) The given expression is a geometric progression with first term $a = 2^{10}$,common ratio $r = \frac{3}{2}$,and number of terms $n = 11$.The sum o

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$3^{11}$

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(C) The given expression is a geometric progression with first term $a = 2^{10}$,common ratio $r = \frac{3}{2}$,and number of terms $n = 11$.The sum of the geometric progression is given by $S' = a \frac{r^n - 1}{r - 1}$.Substituting the values: $S' = 2^{10} \frac{(\frac{3}{2})^{11} - 1}{\frac{3}{2} - 1} = 2^{10} \frac{\frac{3^{11}}{2^{11}} - 1}{\frac{1}{2}} = 2^{11} \left( \frac{3^{11} - 2^{11}}{2^{11}} \right) = 3^{11} - 2^{11}$.Given that $S' = S - 2^{11}$,we have $3^{11} - 2^{11} = S - 2^{11}$.Therefore,$S = 3^{11}$.

If $2^{10} + 2^{9} \cdot 3^{1} + 2^{8} \cdot 3^{2} + \ldots + 2^{1} \cdot 3^{9} + 3^{10} = S - 2^{11}$,then $S$ is equal to

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