The coefficient of $x^{11}$ in the expansion of $(2 x^{2} + x - 3)^{6}$ is?

384

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192

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572

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64

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Solution

The correct option is B $192$
Solution -
Expand $(2 x^{2} + (x - 3))^{6}$
$=^{6} C_{1} (2 x^{2})^{6} +^{6} C_{1} (2 x^{2})^{5} (x - 3) + - - - - -^{6} C_{6} (x - 3)^{6}$ These terms will not have $x^{11}$ in them
$↓$
$6 \times 2^{6} x^{12} +^{6} C_{1} \times 2^{5} x^{10} (x - 3)$
coefficient of $x^{11} =^{6} C_{1} \times 2^{5}$
$= 6 \times 32$
$= 192$
B is correct

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