A) 1/12
B) 7/12
C) 5/12
D) None of these
Correct Answer: B
Solution :
\[{{e}^{2x}}-2{{e}^{x}}+1=1+\frac{2x}{1\ !}+\frac{{{(2x)}^{2}}}{2\ !}+\frac{{{(2x)}^{3}}}{3\ !}+\frac{{{(2x)}^{4}}}{4\ !}+......\]\[-2\left\{ 1+\frac{x}{1\ !}+\frac{{{x}^{2}}}{2\ !}+\frac{{{x}^{3}}}{3\ !}+\frac{{{x}^{4}}}{4\ !}+..... \right\}+1\] \[\therefore \] The coefficient of \[{{x}^{4}}\]\[=\frac{{{2}^{4}}}{4\ !}-2.\frac{1}{4\ !}=\frac{2}{4\ !}({{2}^{3}}-1)=\frac{7}{12}\].
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