Answer
$7.0\times10^{-4}\,s$
Work Step by Step
$\omega=\frac{2\pi}{T}=\frac{1}{\sqrt {LC}}$
$\implies T=2\pi\sqrt {LC}$
$\frac{T}{4}$ time is taken to attain full charge.
$\implies t=\frac{T}{4}=\frac{2\pi\sqrt {LC}}{4}=\frac{\pi\sqrt {50\times10^{-3}H\times4.0\times10^{-6}F}}{2}=7.0\times10^{-4}\,s$
