(a) The first data gives value of plate resistance
$r_{p} = \frac{\Delta V_{p}}{\Delta i_{p}} = \frac{10}{0.8 \times 10^{- 3}} = \frac{10^{5}}{8}\Omega$
Also $g_{m} = \frac{\Delta i_{p}}{\Delta V_{g}}\ $and $g_{m} = \frac{\mu}{r_{p}}$
$\Rightarrow \Delta V_{g} = \frac{\Delta i_{p} \times r_{p}}{\mu} = \frac{4 \times 10^{- 3} \times 10^{5}/8}{8} = 6.25\ V$