Step 1: Understand the meaning of DOLOROUS.
Dolorous means feeling, expressing, or causing sorrow, grief, or pain; mournful. A dolorous face is one full of sadness, and a dolorous tale is one soaked in grief.
Step 2: Match it with the closest option.
Lachrymose describes someone who is tearful or given to weeping easily, or something that tends to induce tears. Since sorrow and the tendency to weep are closely linked in meaning, lachrymose sits nearest to dolorous among the given choices.
Step 3: Eliminate the other options.
Happy is a direct opposite of dolorous, so it cannot be right. Furious and Angry both describe rage, a completely different emotion from sorrow. Tempestuous describes something stormy or turbulently emotional, which suggests volatility rather than grief.
Step 4: Conclusion.
The word closest in meaning to dolorous is Lachrymose, option (b).