**Answer:**

Correct option is (C) 0.0177

**Solution:**

1.00 m aqueous solution means 1 mole of solute in 1 kg of water.

1 kg of water corresponds to ${1000\over18}=55.56$ moles.

The mole fraction of solute is ${1\over1+55.56}=0.0177$.

**Hence, the correct option is (C) 0.0177**