A) \[144\]
B) \[288\]
C) \[216\]
D) \[576\]
Correct Answer: D
Solution :
\[{{(1+3x+2{{x}^{2}})}^{6}}={{\{1+x(3+2x)\}}^{6}}\] \[=1{{+}^{6}}{{C}_{1}}\times (3+2x){{+}^{6}}{{C}_{2}}{{x}^{2}}{{(3+2x)}^{2}}\]\[{{+}^{6}}{{C}_{3}}{{x}^{3}}{{(3+2x)}^{3}}{{+}^{6}}{{C}_{4}}{{x}^{4}}{{(3+2x)}^{4}}\]\[{{+}^{6}}{{C}_{5}}x{{(3+2x)}^{5}}{{+}^{6}}{{C}_{6}}{{x}^{6}}{{(3+2x)}^{6}}\] Only \[{{x}^{11}}\] gets form\[^{6}{{C}_{6}}{{x}^{6}}{{(3+2x)}^{6}}\] \[\because \] \[^{6}{{C}_{6}}{{x}^{6}}{{(3+2x)}^{6}}={{x}^{6}}{{(3+2x)}^{6}}\] \[\therefore \] Coefficient of\[{{x}^{11}}{{=}^{6}}{{C}_{5}}3\cdot {{2}^{5}}=576\]
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