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The coefficient of

Question:

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

  1. $-84$

  2. 84

  3. 126

  4. -126


Correct Option: 1,

Solution:

$(1+x)(1-x)^{10}\left(1+x+x^{2}\right)^{9}$

$\left(1-x^{2}\right)\left(1-x^{3}\right)^{9}$

${ }^{9} C_{6}=84$

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