A) \[990\]
B) \[605\]
C) \[810\]
D) None of these
Correct Answer: A
Solution :
We have,\[{{(1+x+{{x}^{2}}+{{x}^{3}})}^{11}}\] \[={{\{(1+x)(1+{{x}^{2}})\}}^{11}}\] \[={{(1+x)}^{11}}{{(1+{{x}^{2}})}^{11}}\] \[=(1{{+}^{11}}{{C}_{1}}x{{+}^{11}}{{C}_{2}}{{x}^{2}}{{+}^{11}}{{C}_{3}}{{x}^{3}}{{+}^{11}}{{C}_{4}}{{x}^{4}}+...)\] \[(1{{+}^{11}}{{C}_{3}}{{x}^{2}}{{+}^{11}}{{C}_{2}}{{x}^{4}}{{+}^{11}}{{C}_{3}}{{x}^{6}}+...)\] Coefficient of\[{{x}^{4}}{{=}^{11}}{{C}_{2}}{{+}^{11}}{{C}_{4}}{{+}^{11}}{{C}_{1}}^{11}{{C}_{2}}\] \[=55+330+605=990\]
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