A) 15
B) 30
C) 16
D) 32
E) 17
Correct Answer: A
Solution :
\[{{(2{{x}^{2}}-x-1)}^{5}}={{a}_{0}}+{{a}_{1}}x+{{a}_{2}}{{x}^{2}}\] \[+....+{{a}_{10}}{{x}^{10}}\] \[\therefore \]For \[x=1\] \[0={{a}_{0}}+{{a}_{1}}+{{a}_{2}}+....+{{a}_{10}}\] ?.(i) For\[x=-1\] \[{{(2+1-1)}^{2}}={{a}_{0}}-{{a}_{1}}+{{a}_{2}}+....+{{a}_{10}}\] ?. (ii) On adding Eqs. (i) and (ii) \[0+{{(2)}^{5}}=2({{a}_{0}}+{{a}_{2}}+...+{{a}_{10}})\] \[\Rightarrow \] \[\frac{32}{2}={{a}_{0}}+{{a}_{2}}+....+{{a}_{10}}\] \[\Rightarrow \] \[16-1={{a}_{2}}+....+{{a}_{10}}\] \[\Rightarrow \] \[{{a}_{2}}+{{a}_{3}}+....+{{a}_{10}}=15\]
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