A) \[^{40}{{C}_{4}}\]
B) \[^{10}{{C}_{4}}\]
C) 210
D) 310
Correct Answer: D
Solution :
\[{{(1+x+{{x}^{3}}+{{x}^{4}})}^{10}}={{(1+x)}^{10}}\,{{(1+{{x}^{3}})}^{10}}\] \[=(1+{}^{10}{{C}_{1}}\,.\,x+{}^{10}{{C}_{2}}\,.\,{{x}^{2}}+.....)\]\[(1+{}^{10}{{C}_{1}}\,.\,{{x}^{3}}+{}^{10}{{C}_{2}}\,.\,{{x}^{6}}+.....)\] \[\therefore \]Coefficient of \[{{x}^{4}}\] \[=\,{}^{10}{{C}_{1}}.{}^{10}{{C}_{1}}+{}^{10}{{C}_{4}}=310\].
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