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Q.

The coefficient of $x^{18}$ in the product $(1 + x) (1 - x)^{10} {(1 + x + x^{2})}^{9}$ is

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a

-84

b

84

c

126

d

-126

answer is B.

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Detailed Solution

$(1 + x) (1 - x)^{10} {(1 + x + x^{2})}^{9} = (1 - x^{2}) (1 - x)^{9} {(1 + x + x^{2})}^{9} = (1 - x^{2}) {(1 - x^{3})}^{9}$

$∴$ Coefficient of $x^{18}$ is $^{9} C_{6} =^{9} C_{3} = \frac{9 \times 8 \times 7}{6} = 84$ .

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