$($a$)$ The following results $($Table $2)$ were obtained during a liquid limit test on a saturated clay sample:

Table $2$

Determine the liquid limit$.$ If the plastic limit of the same soil sample was $\backslash (38\backslash \%\backslash )$ and the natural water content was $\backslash (45\backslash \%\backslash )$ determine the plasticity index and liquidity index and classify the soil.