In the expansion of ${(1 + 3 x + 2 x^{2})}^{6}$ , the coefficient of $x^{11}$ is

144

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288

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216

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576

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Solution

The correct option is A 576
$= (2 x^{2} + 3 x + 1)^{6}$
$= (2 x^{2} + 2 x + x + 1)^{6}$
$= (2 x + 1)^{6} (x + 1)^{6}$
$x^{11}$ can be formed by $x^{5} \times x^{6}$
or $x^{6} \times x^{5}$
Coefficient of $x^{11} = 6_{C_{5}} (2)^{5} \times 6_{C_{6}} + 6_{C_{6}} (2)^{6} \times 6_{C_{5}}$
$= 32 \times 18$
$= 576$
$D$ is correct

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