A) \[\frac{{{3}^{11}}-1}{11}\]
B) \[\frac{{{2}^{11}}-1}{11}\]
C) \[\frac{{{11}^{3}}-1}{11}\]
D) \[\frac{{{11}^{2}}-1}{11}\]
Correct Answer: A
Solution :
We have \[{{(1+x)}^{10}}={{C}_{0}}+{{C}_{1}}x+{{C}_{2}}{{x}^{2}}+...+{{C}_{10}}{{x}^{10}}\] Integrating both sides from 0 to 2, we get \[\frac{{{3}^{11}}-1}{11}=2{{C}_{0}}+\frac{{{2}^{2}}}{2}{{C}_{1}}+\frac{{{2}^{3}}}{3}{{C}_{2}}+....+\frac{{{2}^{11}}}{11}{{C}_{10}}\].
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