(a) Here $\mathrm{\Delta}V_{c} = 0.5\ V,\ \mathrm{\Delta}i_{c} = 0.05mA = 0.05 \times 10^{- 3}A$
Output resistance is given by
$R_{out} = \frac{\mathrm{\Delta}V_{c}}{\mathrm{\Delta}i_{c}} = \frac{0.5}{0.05 \times 10^{- 3}} = 10^{4}\Omega = 10k\Omega$