Which of the following sentences uses the determiner correctly?

The correct answer is Option (2) → The lake has become so dirty that few fishermen cast their nets in it now.

Few and a few:

• Few means hardly any. It has a negative sense. A few means some and has a positive sense. Both go with countable plural nouns.
• The lake is “so dirty”, so hardly any fishermen use it now. So “few fishermen” is correct.

Why the Other Options are Incorrect?

Option 1: The hill road is so narrow that a few drivers dare to take it after dark. — Incorrect. “So narrow” points to a negative result, hardly any drivers. That needs “few”, not “a few”.
Corrected: The hill road is so narrow that few drivers dare to take it after dark.

Option 3: Few friends came over to help, so we finished packing the house in an hour. — Incorrect. The result is good (“finished ... in an hour”), so some friends did come. That needs “a few”.
Corrected: A few friends came over to help, so we finished packing the house in an hour.

Option 4: There was few traffic on the highway, so we reached Shimla before noon. — Incorrect. “Traffic” is uncountable, so it takes “little”, not “few”.
Corrected: There was little traffic on the highway, so we reached Shimla before noon.