If 1/4 × 2/6 × 3/8 × 410 × 512 × . . . . . × 3164 = 12^x then the value of x is?

Answer: Option C

$$\frac{1}{4}\times$$ $$\frac{2}{6}\times$$ $$\frac{3}{8}\times$$ $$\frac{4}{10}\times$$ $$\frac{5}{12}\times$$ . . . . . $$\times \frac{31}{64}$$ $$=\frac{1}{2^x}$$
Denominator of first term is cut by the numerator of next terms, second term to the next one and so on.
$$\begin{array}{rl}& \Rightarrow {\left(\frac{1}{2}\right)}^{30}\times {\left(\frac{1}{2}\right)}^6=\frac{1}{2^x}\\ & \Rightarrow {\left(\frac{1}{2}\right)}^{30+6}=\frac{1}{2^x}\\ & \Rightarrow \frac{1}{2^{36}}=\frac{1}{2^x}\\ & \Rightarrow x=36\end{array}$$