\[(a)\;e=\frac{1}{\sqrt 3} \quad (b)\;e=\frac{1}{3} \quad (c)\;e=\sqrt 3 \quad (d)\;e=3\]

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Comparing velocities before and after collision parallel to the plane surface

$v \sin 60^{\circ}=u \sin 30^{\circ}$

Comparing components of velocity normal to the surface

$v \cos 60=eu \cos 30^{\circ}$

$\cot 60=e \cot 30^{\circ}$

$e=\large\frac{\cot 60}{\cot 30}$

$e= \large\frac{\Large\frac{1}{\sqrt 3}}{\sqrt 3}$

$e=\large\frac{1}{3}$

Hence b is the correct answer

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