• A. He is the man I was looking for. - Correct. "For" is the appropriate preposition.

• E. Mumbai is famous for its textiles. - Correct. "For" is the correct preposition to use with "famous."

Why the others are incorrect:

• B. I have eaten nothing since four days. - Incorrect. It should be "for four days." "Since" is used with a specific point in time (e.g., "since yesterday"), while "for" is used with a duration of time (e.g., "for four days").

• C. Camels are peculiarly adapted for life in the desert. - While "for" isn't grammatically wrong, "to" is the more common and natural preposition to use with "adapted." "Adapted to" is the preferred phrasing.

• D. There is no cure to common cold. - Incorrect. It should be "There is no cure for the common cold."