A) 1/2
B) 1/4
C) 1/20
D) 1/10
Correct Answer: C
Solution :
\[(1-x){{\log }_{e}}(1-x)\] \[=(1-x)\left[ -x-\frac{{{x}^{2}}}{2}-\frac{{{x}^{3}}}{3}-\frac{{{x}^{4}}}{4}-\frac{{{x}^{5}}}{5}-......\infty \right]\] Hence coefficient of \[{{x}^{5}}=\frac{1}{4}-\frac{1}{5}=\frac{1}{20}\].
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