A) \[0\]
B) \[1\]
C) \[128\]
D) \[64\]
Correct Answer: A
Solution :
Given \[{{(x-1)}^{7}}={{a}_{7}}{{x}^{7}}+{{a}_{6}}{{x}^{6}}+......+{{a}_{1}}x+{{a}_{0}}\]Since the given polynomial terms are in expression, form Pacal?s triangle we get the coefficients of 1st four terms. Symmetrical to those of the last four terms. \[\Rightarrow \]\[{{(x-1)}^{7}}={{x}^{7}}-7{{x}^{6}}+21{{x}^{5}}-35{{x}^{4}}+35{{x}^{3}}-\] \[21{{x}^{2}}+7x-1=0\] \[\Rightarrow \]\[{{a}_{7}}+{{a}_{6}}+{{a}_{5}}.....+{{a}_{1}}+{{a}_{0}}\] \[=1-7+21-35+35-21+7-1=0\]
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