The coefficient of $x^4$ in the expansion of $(1-x+x^2-x^3)^4$ is

The term independent of $x$ in the expansion of $\left(\frac{x+1}{x^{2/3}+1-x^{1/3}}-\frac{x-1}{x-x^{1/2}}\right)^{10}, x>1$ is:

Let $a_n$ denote the term independent of $x$ in the expansion of $\left[x+\frac{\sin(1/n)}{x^2}\right]^{3n}$. Then $\lim_{n \to \infty} \frac{a_n \cdot n!}{^{3n}P_n}$ equals

The term independent of $x$ in the expansion of $\left(\sqrt{x}-\frac{2}{\sqrt{x}}\right)^{18}$ is

The term independent of $x$ in the expansion of ${\left( {2x + \frac{1}{{3x}}} \right)^6}$ is

In the expansion of $\left(\sqrt[3]{2}+\frac{1}{\sqrt[3]{3}}\right)^n, n \in N$,if the ratio of the $15^{\text{th}}$ term from the beginning to the $15^{\text{th}}$ term from the end is $\frac{1}{6}$,then the value of ${}^n C_3$ is: