If $ 2^{10}+2^{9} \cdot 3^{1}+2^{8} \cdot 3^{2}+\ldots .+2 \cdot 3^{9}+3^{10}=S-2^{11} $, then $ \mathrm{S} $ is equal to : [JEE Main 2020, 5 Sep (Shift 1)]

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If \( 2^{10}+2^{9} \cdot 3^{1}+2^{8} \cdot 3^{2}+\ldots .+2 \cdot 3^{9}+3^{10}=S-2^{11} \), then \( \mathrm{S} \) is equ…

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