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

The middle term in the expansion of ${(1 + x)^{2n}}$ is

If the second, third and fourth term in the expansion of ${(x + a)^n}$ are $240, 720$ and $1080$ respectively, then the value of $n$ is

If the coefficients of $x^{7}$ and $x^{8}$ in the expansion of $\left(2+\frac{x}{3}\right)^{n}$ are equal, then the value of $n$ is equal to $.....$

The term independent of $x$ in the binomial expansion of $\left( {1 - \frac{1}{x} + 3{x^5}} \right){\left( {2{x^2} - \frac{1}{x}} \right)^8}$ is

The term independent of $x$ in the expression of $\left(1-x^{2}+3 x^{3}\right)\left(\frac{5}{2} x^{3}-\frac{1}{5 x^{2}}\right)^{11}, x \neq 0$ is