Sure, here is the translated text:

```
I. Fill-in-the-Blanks (8 points per question, total 64 points)
1. Given the sets
$$
A=\{x \mid 5 x-a \leqslant 0\}, B=\{x \mid 6 x-b>0\}
$$

where $a, b \in \mathbf{N}_{+}$.
If $A \cap B \cap \mathbf{N}=\{2,3,4\}$, then the number of integer pairs $(a, b)$ is . $\qquad$
```
-1.30 .
Notice that, $A \cap B=\left(\frac{b}{6}, \frac{a}{5}\right]$. From the problem, we know $1 \leqslant \frac{b}{6}<2$, and $4 \leqslant \frac{a}{5}<5$. Therefore, $b \in\{6,7, \cdots, 11\}, a \in\{20,21, \cdots, 24\}$. Hence, the number of integer pairs $(a, b)$ is 30.