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 D $576$
${(\frac{1 + 3}{a} + \frac{2 x^{2}}{b})}^{6}$
using binomial expansion
$^{6} C_{r} (1 + 3 x)^{6 - r} (2 x^{2})^{r}$
Power of $x$ will be $11$ only when $r = 5$
$^{6} C_{5} \times 3 \times 2^{5}$
$= 576$

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