The rational number between $\dfrac{1}{3}$ and $\dfrac{1}{2}$ is:

1. $\dfrac{3}{7}$ and $\dfrac{3}{8}$

2. $\dfrac{2}{5}$ and 0

3. $\dfrac{1}{6}$ and $\dfrac{2}{3}$

4. $\dfrac{2}{3}$ and $\dfrac{3}{2}$

As we know that, for any two rational numbers $\dfrac{a}{b}$ and $\dfrac{c}{d}$, $\Big(\dfrac{a + c}{b + d}\Big)$ is also a rational number with its value lying between $\dfrac{a}{b}$ and $\dfrac{c}{d}$.

The rational number between $\dfrac{1}{3}$ and $\dfrac{1}{2}$ is $\Big(\dfrac{1 + 1}{3 + 2}\Big)$

= $\Big(\dfrac{2}{5}\Big)$

The rational number between $\dfrac{1}{3}$ and $\dfrac{2}{5}$ is $\Big(\dfrac{1 + 2}{3 + 5}\Big)$

= $\Big(\dfrac{3}{8}\Big)$

The rational number between $\dfrac{1}{2}$ and $\dfrac{2}{5}$ is $\Big(\dfrac{1 + 2}{2 + 5}\Big)$

= $\Big(\dfrac{3}{7}\Big)$

$\dfrac{3}{7}$ and $\dfrac{3}{8}$ are two rational number between $\dfrac{1}{3}$ and $\dfrac{1}{2}$

Hence, option 1 is the correct option.