A) 132
B) 144
C) \[-132\]
D) \[-144\]
Correct Answer: D
Solution :
We have \[{{(1-x-{{x}^{2}}+{{x}^{3}})}^{6}}={{(1-x)}^{6}}{{(1-{{x}^{2}})}^{6}}\] coefficient of \[{{x}^{7}}\] in \[{{\left( 1-x-{{x}^{2}}+{{x}^{3}} \right)}^{6}}{{=}^{6}}{{C}_{1}}.{{-}^{6}}{{C}_{3}}{{-}^{6}}{{C}_{2}}{{+}^{6}}{{C}_{5}}{{.}^{6}}{{C}_{1}}\] \[=6\times 20-20\times 15+6\times 6\] \[=-144\]
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