1. In the polynomial of $x$ obtained by expanding $(\sqrt{3} x+\sqrt[3]{2})^{100}$, the number of terms with rational coefficients is ( ).
(A) 50
(B) 17
(C) 16
(D) 15
-、1. The general term of the expansion of $\mathrm{B}(\sqrt{3} x+\sqrt[3]{2})^{100}$ is
$$
T_{r+1}=C_{100}^{r} 3^{50-\frac{r}{2}} \cdot 2^{\frac{r}{3}} x^{100-r} \text {. }
$$

Since $C_{100}^{\prime}$ is an integer, to make the coefficient of a certain term in the polynomial of $x$ a rational number, it is only necessary that $\frac{r}{2}, \frac{r}{3}$ are both integers, hence $r$ must be a multiple of 6. There are $\left[\frac{100}{6}\right]+1$ $=17$ multiples of 6 between 0 and 100.