(b) $\beta = \frac{I_{c}}{I_{b}} = \frac{I_{e} - I_{b}}{I_{b}} = \frac{I_{e}}{I_{b}} - 1\ \ or\ \ \ \frac{I_{e}}{I_{b}} = 1 + \beta$ or $I_{b} = \frac{I_{e}}{1 + \beta} = \frac{8.2}{1 + 40} = \frac{8.2}{41} = 0.20\ mA$.
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.