GATE EC 2020 Set 1 Q33 — BJT and MOSFET Amplifiers

The base of an $\text{npn BJT T1}$  has a linear doping profile $N_{B}\left ( x \right )$ as shown below. The base of another $\text{npn BJT T2}$ has a uniform doping $N_{B}$ of $10^{17}cm^{-3}$. All other parameters are identical for both the devices. Assuming that the hole density profile is the same as that of doping, the common-emitter current gain of $\text{T2}$ is