If the term independent of $x$ in the expansion of $\left(\sqrt{x}-\frac{k}{x^2}\right)^{10}$ is 405 , then $k=$

The number of rational terms in the binomial expansion $(\sqrt[4]{5}+\sqrt[5]{4})^{100}$ is

The coefficient of $x^{50}$ in the expansion of $(1+x)^{101}\left(1-x+x^2\right)^{100}$ is