The term independent of $$x$$ in the expansion of $${\left( {1 - x} \right)^2} \cdot {\left( {x + \frac{1}{x}} \right)^{10}}$$    is

Solution :
Expression $$ = \frac{1}{{{x^{10}}}}\left( {1 - 2x + {x^2}} \right){\left( {1 + {x^2}} \right)^{10}}$$
$$ = \frac{1}{{{x^{10}}}}{\left( {1 + {x^2}} \right)^{10}} - \frac{2}{{{x^9}}}{\left( {1 + {x^2}} \right)^{10}} + \frac{1}{{{x^8}}}{\left( {1 + {x^2}} \right)^{10}}.$$
∴ the term independent of $$x = {\,^{10}}{C_5} - 2 \times 0 + {\,^{10}}{C_4}.$$