10. In the arithmetic sequence $\left\{a_{n}\right\}$, if $\frac{a_{11}}{a_{10}}<-1$, and the sum of the first $n$ terms $S_{n}$ has a maximum value. Then when $S_{n}$ takes the smallest positive value, $n=(\quad)$.
(A) 1
(B) 10
(C) 19
(D) 20
10. C.

Let the common difference of the arithmetic sequence be $d$. Clearly, $d0, a_{11}0$.
Also, $S_{19}-S_{1}=9\left(a_{10}+a_{11}\right)<0$, so $n=19$.