Change division to multiplication by the reciprocal:

\( \dfrac{3}{4} \div \dfrac{1}{2} = \dfrac{3}{4} \times \dfrac{2}{1} = \dfrac{6}{4} \).

Simplify \( \dfrac{6}{4} = \dfrac{3}{2} \).

Answer: \( \dfrac{3}{2} \).

\( \dfrac{5}{6} \div \dfrac{5}{12} = \dfrac{5}{6} \times \dfrac{12}{5} = \dfrac{60}{30} = 2 \).

Answer: 2.

\( \dfrac{7}{10} \div \dfrac{2}{5} = \dfrac{7}{10} \times \dfrac{5}{2} = \dfrac{35}{20} \).

Simplify \( \dfrac{35}{20} = \dfrac{7}{4} \).

Answer: \( \dfrac{7}{4} \).

\( \dfrac{2}{3} \div \dfrac{4}{9} = \dfrac{2}{3} \times \dfrac{9}{4} = \dfrac{18}{12} \).

Simplify \( \dfrac{18}{12} = \dfrac{3}{2} \).

Answer: \( \dfrac{3}{2} \).

Convert the mixed number:

\( 1\dfrac{1}{2} = \dfrac{3}{2} \).

Now divide:

\( \dfrac{3}{2} \div \dfrac{3}{4} = \dfrac{3}{2} \times \dfrac{4}{3} = \dfrac{12}{6} = 2 \).

The correct option is 2.