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The value of the term independent of $x$ in the expansion of $(1-x)^{2}(x+\frac{1}{x})^{7}$ is

  1. $-70$
  2. $70$
  3. $35$
  4. None of these
in Combinatory by Boss (16.8k points)
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1 Answer

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

$=(1-2x+x^2)\left(\binom{7}{0}\frac{1}{x^7}+\binom{7}{1}\frac{1}{x^5}+\binom{7}{2}\frac{1}{x^3}+\binom{7}{3}\frac{1}{x}+\binom{7}{0}x+\ldots\right)$

The only term independent of x will be coefficient of $(-2x)(^7C_3(1/x))$

$\implies -2\times ^7C_3=-70$
by Boss (11.8k points)
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