If $\frac{1}{4}\times \frac{2}{6}\times \frac{3}{8}\times \frac{4}{10}\times \frac{5}{12}\times...... \frac{31}{64} = \frac{1}{2^{x}}$, then what would be the value of x :
[A]36
[B]37
[C]32
[D]31

36
The given expression is,
$\frac{1}{4}\times \frac{2}{6}\times \frac{3}{8}\times \frac{4}{10}\times \frac{5}{12}\times...... \frac{31}{64} = \frac{1}{2^{x}}$
$=> \frac{1}{2}\times \frac{1}{2}\times \frac{1}{2}\times .....$to 30 terms $\times \frac{1}{64} = \frac{1}{2^{x}}$
$=> \frac{1}{2^{30}}\times \frac{1}{2^{6}} = \frac{1}{2^{x}}$
$=> \frac{1}{2^{36}} = \frac{1}{2^{x}}$
$=> x = 36$
Hence option [A] is the right answer.