The coefficient of ${x^n}$in expansion of $(1 + x)\,{(1 - x)^n}$ is

The term independent of $x$ in the expansion of ${\left( {2x - \frac{3}{x}} \right)^6}$ is

If the coefficients of $x^{-2}$ and $x^{-4}$ in the expansion of ${\left( {{x^{\frac{1}{3}}} + \frac{1}{{2{x^{\frac{1}{3}}}}}} \right)^{18}}\,,\,\left( {x > 0} \right),$ are $m$ and $n$  respectively, then $\frac{m}{n}$ is equal to 

Find a positive value of $m$ for which the coefficient of $x^{2}$ in the expansion $(1+x)^{m}$ is $6$

The sum of all those terms which are rational numbers in the expansion of $\left(2^{1 / 3}+3^{1 / 4}\right)^{12}$ is:

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