ISI2016-DCG-21

Question

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

• A. $-70$
• B. $70$
• C. $35$
• D. None of these

Answer 1

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

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

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

$\implies -2\times ^7C_3=-70$