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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

1. approximately $2.0$ times that of $\text{T1}$.
2. approximately $0.3$ times that of $\text{T1}$.
3. approximately $2.5$ times that of $\text{T1}$.
4. approximately $0.7$ times that of $\text{T1}$.