A) \[\frac{{{e}^{a}}{{b}^{n}}}{n!}\]
B) \[\frac{{{(b.a)}^{n}}}{n!}\]
C) \[\frac{{{e}^{b}}.{{b}^{n}}}{(n-1)!}\]
D) \[\frac{{{a}^{n}}{{b}^{n-1}}}{n!}\]
Correct Answer: A
Solution :
We know that, \[{{e}^{x}}=1+\frac{x}{1!}+\frac{{{x}^{2}}}{2!}+\frac{{{x}^{3}}}{3!}+.....\] Put \[x=(a+bx),\] \[{{e}^{a+bx}}=1+\frac{a+bx}{1!}+\frac{{{(a+bx)}^{2}}}{2!}+\frac{{{(q+bx)}^{3}}}{3!}+.....\] \[\therefore \]Coefficient of\[{{x}^{n}}\]in \[{{e}^{a+bx}}={{e}^{a}}\frac{{{(b)}^{n}}}{n!}\]
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