Q$1.$ The following data were obtained from a liquid$-$limit test on a highly plastic clay:

Two plastic$-$limit determinations had water contents of $41\mathrm{.}4\%$ and $39\mathrm{.}8\%.$ Determine:

a$).$ the LL$,$ PL$,$ and the PI of the soil.

b$).$ the liquidity index $($LI$)$ if the natural water content is $120\mathrm{.}6\%.$

c$).$ the void ratio at the liquid limit $($assume $G_s=2\mathrm{.}7).$

d$).$ what would be the expected behaviour of such soil under applied shear stress?