$latex \mathbf{\frac{1}{\sqrt{3}}}&s=1$
$latex \cot 10^{\circ}\cdot \cot 80^{\circ}\cdot \cot 20^{\circ}\cdot \cot 70^{\circ}\cdot \cot 60^{\circ}$
$latex = \cot 10^{\circ}\cdot \tan 10^{\circ}\cdot \cot 20^{\circ}\cdot \tan 20^{\circ}\cdot \cot 60^{\circ}$
$latex \left [ \because \tan\left ( 90^{\circ}- \Theta \right ) = \cot \Theta \right ]$
$latex \left [ \tan\Theta \cdot \cot \Theta = 1 \right ]$
$latex = 1\times 1\times \frac{1}{\sqrt{3}} \left [ \because \cot 60^{\circ} = \frac{1}{\sqrt{3}} \right ]&s=1$
$latex = \frac{1}{\sqrt{3}}&s=1$
Hence option [C] is correct answer.