A) \[\frac{{{(a+b)}^{r}}}{r\,!}\]
B) \[\frac{{{b}^{r}}}{r\,!}\]
C) \[\frac{{{e}^{a}}{{b}^{r}}}{r\,!}\]
D) \[{{e}^{a+{{b}^{r}}}}\]
Correct Answer: C
Solution :
\[S={{e}^{a+bx}}={{e}^{a}}.{{e}^{bx}}={{e}^{a}}\left\{ 1+\frac{bx}{1\ !}+\frac{{{(bx)}^{2}}}{2\ !}+..... \right\}\] The coefficient of\[{{x}^{r}}={{e}^{a}}.\frac{{{b}^{r}}}{r\ !}\].
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