Define beta current gain of the transistor.

The transfer characteristic curve of a transistor, having input and output resistance $100 \mathrm{\Omega }$ and $100 \mathrm{k}\mathrm{\Omega }$ respectively, is shown in the figure. The voltage and power gain, are respectively:

Given below are two statements:

Statement I : $p-n$ junction diodes can be used to function as a transistor, simply by connecting two diodes, back to back, which acts as the base terminal

Statement II: In the study of transistors, the amplification factor $\beta$ indicates ratio of the collector current to the base current.

In the light of the above statements, choose the correct answer from the options given below.

In $\mathrm{CE}$ $\mathrm{NPN}$ transistor ${10}^{10}$ electrons enter the emitter in ${10}^{-6} \mathrm{s}$ when it is connected to the battery. About $5\%$ electrons recombine with holes in the base. The current gain of the transistor is __________

$\left(e=1.6\times {10}^{-19}\mathrm{C}\right)$