Junction Transistor question from JEE Main 2016

Answer: (b)

1. Correct relation: $\alpha = \frac{\beta}{1+\beta}$, i.e. $\frac{1}{\alpha} = \frac{1}{\beta} + 1$, so (a) and (c) are correct.
2. (b) $\alpha = \frac{\beta^2}{1+\beta^2}$ does not follow from $\alpha = \frac{\beta}{1+\beta}$, so it is incorrect.
3. (d) $\alpha = \frac{\beta}{1-\beta^2}$ is also not a valid relation.
4. The intended answer is (b).