Correct option is (C) \(\frac 1 {\sqrt 3}\)
\(\cot 12^{\circ} \cdot \cot 38^{\circ} \cdot \cot 52^{\circ} \cdot \cot 60^{\circ} \cdot \cot 78^{\circ}\)
\(=\cot 12^{\circ} \cdot \cot 38^{\circ} \cdot \cot \left(90^{\circ}-38^{\circ}\right) \cdot \frac{1}{\sqrt{3}} \cdot \cot \left(90^{\circ}-12^{\circ}\right)\quad \left[\begin{array}{l} \because \cot \left(90^{\circ}-A\right)=\tan A \\ \quad\cot 60^{\circ}=\frac{1}{\sqrt{3}} \end{array}\right]\)
\(=\frac{1}{\tan12^{\circ}} \times \frac{1}{\tan 38^{\circ}} \times \tan 38^{\circ} \times \tan 12^{\circ} \times \frac 1{\sqrt 3}\)
\(=\frac 1 {\sqrt 3}\)
