$\begin{array}{1 1} 10 \\ 8 \\ 5\\ 12 \end{array}$

Answer : (b) 8

Explanation : In a GP

$S_{n}=\large\frac{a(r^n-1)}{r-1}\quad\;a=6,r=\large\frac{1}{2}$

$S_{n}=\large\frac{6(1-1/2^n)}{1-1/2}=\large\frac{765}{64}$

$1-(1/2)^n=\large\frac{765}{64*12}$

$(1/2)^n=1-\large\frac{765}{768}=\large\frac{3}{768}=\large\frac{1}{256}$

$(1/2)^n=\large\frac{1}{256}=(1/2)^8$

$n=8.$

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