9.21 The sum of the third from the beginning and the third from the end binomial coefficients in the expansion of $(\sqrt[4]{3}+\sqrt[3]{4})^{n}$ is 9900. How many rational terms are contained in this expansion?
9.21 The coefficients specified in the condition are equal to $C_{n}^{2}$. We have $2 \cdot \frac{n(n-1)}{2}=9900$, or $n(n-1)=100 \cdot 99$,

from which $n=100$. Then $T_{k+1}=C_{100}^{k} 3^{\frac{100-k}{4}} 4^{\frac{k}{3}} ;$ according to the condition, $\frac{k}{3}$ and $\frac{100-k}{4}$ are integers, i.e., $k$ is divisible by 12. For $n=100$, there are $\left[\frac{100}{12}\right]+1=9$ such numbers.

Answer: 9 terms.