A) 144
B) 288
C) 216
D) 576
Correct Answer: D
Solution :
[d] \[{{(1+3x+2{{x}^{6}})}^{6}}={{[1+x(3+2x)]}^{6}}\] \[=1{{+}^{6}}{{C}_{1}}x(3+2x){{+}^{6}}{{C}_{2}}{{x}^{2}}{{(3+2x)}^{2}}{{+}^{6}}{{C}_{3}}{{x}^{3}}{{(3+2x)}^{3}}\] \[{{+}^{6}}{{C}_{4}}{{x}^{4}}{{(3+2x)}^{4}}{{+}^{6}}{{C}_{5}}{{x}^{5}}{{(3+2x)}^{5}}{{+}^{6}}{{C}_{6}}{{x}^{6}}{{(3+2x)}^{6}}\] We get \[{{x}^{11}}\]only from \[^{6}{{C}_{6}}{{x}^{6}}{{(3+2x)}^{6}}\]Hence, coefficient of \[{{x}^{11}}\]is \[^{6}{{C}_{5}}\times 3\times {{2}^{5}}=576.\]
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