Correct option is C ) [ L^{2}T^{-2} ]
Explaination::
The velocity of light in vacuum is
c = \({1 \over {\sqrt {{\mu _0}{\varepsilon _0}} }}\)
\(\therefore[{1 \over {{\mu _0}{\varepsilon _0}}}]\) = [c^{2}] = [L^{2}T^{-2}]
\(\therefore\) Dimension of \({1 \over {{\mu _0}{\varepsilon _0}}}\)= [L^{2}T^{-2}]