c
For common emitter, the current gain is

\(\beta=\left(\frac{\Delta \mathrm{I}_{\mathrm{C}}}{\Delta \mathrm{I}_{\mathrm{B}}}\right)_{\mathrm{V}_{\mathrm{CE}}}\)

i.e., at a given potential difference of \(\mathrm{CE},\)

\({\beta=\frac{\left(10 \times 10^{-3}-5 \times 10^{-3}\right) A}{\left(200 \times 10^{-6}-100 \times 10^{-6}\right) A}} \)

\({=\frac{5 \times 10^{-3}}{100 \times 10^{-6}}=50}\)