A) \[\frac{71}{120}\]
B) \[-\frac{71}{120}\]
C) \[\frac{31}{40}\]
D) \[-\frac{31}{40}\]
Correct Answer: B
Solution :
\[(1-2x+3{{x}^{2}}){{e}^{-x}}\] \[=(1-2x+3{{x}^{2}})\left\{ 1-\frac{x}{1\ !}+\frac{{{x}^{2}}}{2\ !}-\frac{{{x}^{3}}}{3\ !}+....... \right\}\] \[\therefore \] The coefficient of \[{{x}^{5}}\] \[=1\left( -\frac{1}{5\ !} \right)+(-2)\,\left( \frac{1}{4\ !} \right)+3\left( -\frac{1}{3\ !} \right)\] \[=1+\left( \frac{1}{1.2}-\frac{1}{2.3} \right)+\left( \frac{1}{3.4}-\frac{1}{4.5} \right)+....\].
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