A) 32
B) 26
C) 29
D) 24
Correct Answer: D
Solution :
\[{{\left( x-\sqrt{{{x}^{3}}-1} \right)}^{6}}+{{\left( x-\sqrt{{{x}^{3}}-1} \right)}^{6}}\] \[{{+}^{6}}{{C}_{6}}{{({{x}^{3}}-1)}^{3}}]\] \[=2{{[}^{6}}{{C}_{0}}{{x}^{6}}+{}^{6}{{C}_{2}}{{x}^{7}}-{}^{6}{{C}_{2}}{{x}^{4}}+{}^{6}{{C}_{4}}{{x}^{8}}+{}^{6}{{C}_{4}}{{x}^{2}}\] \[-2\,\,{}^{6}{{C}_{4}}{{x}^{5}}+({{x}^{9}}-1-3{{x}^{6}}+3{{x}^{3}})]\] \[\Rightarrow \]Sum of coefficient of even powers of x \[=2[115+15+1513]=24\]You need to login to perform this action.
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