1. Given that $n$ is a positive integer, the expansion of the binomial $\left(x^{2}+\frac{1}{x^{3}}\right)^{n}$ contains a term with $x^{7}$. Then the minimum value of $n$ is ( ).
(A) 4
(B) 5
(C) 6
(D) 7
$-1 . \mathrm{C}$.
Notice that, the general term formula of the required binomial expansion is
$$
T_{r+1}=\mathrm{C}_{n}^{r}\left(x^{2}\right)^{n-r}\left(\frac{1}{x^{3}}\right)^{r}=\mathrm{C}_{n}^{r} x^{2 n-5 r} .
$$

From $2 n-5 r=7(r \in \mathbf{N})$, we know that when $r=1$, $n$ has the minimum value 6.