A) 144
B) 288
C) 216
D) 576
E) (3)(211)
Correct Answer: D
Solution :
\[{{(1+3x+2{{x}^{2}})}^{6}}\] = \[{{[1+x(3+2x)]}^{6}}\] = \[1+{{\,}^{6}}{{C}_{1}}x(3+2x){{+}^{6}}{{C}_{2}}{{x}^{2}}{{(3+2x)}^{2}}\]\[{{+}^{6}}{{C}_{3}}{{x}^{3}}{{(3+2x)}^{3}}{{+}^{6}}{{C}_{4}}{{x}^{4}}{{(3+2x)}^{4}}\]\[{{+}^{6}}{{C}_{5}}{{x}^{5}}{{(3+2x)}^{5}}{{+}^{6}}{{C}_{6}}{{x}^{6}}{{(3+2x)}^{6}}\] Only \[{{x}^{11}}\] gets from \[^{6}{{C}_{6}}{{x}^{6}}{{(3+2x)}^{6}}\] \[\because \] \[^{6}{{C}_{6}}{{x}^{6}}{{(3+2x)}^{6}}=\,{{x}^{6}}{{(3+2x)}^{6}}\] \[\therefore \] Coefficient of \[{{x}^{11}}\] = \[^{6}{{C}_{5}}{{3.2}^{5}}=576\].
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