Choose the option that contains the incorrect pair of homonym(s).

The correct answer is Option (1) → Beside, Besides

Homonyms in this sense are words that sound alike but differ in meaning (and often in spelling). Beside means next to, and besides means in addition to or apart from. The two do not sound alike, since "besides" ends in an extra /z/ sound; they are two related words often confused, not a homonym pair.
Example: She sat beside me, and besides Ravi, nobody else came.

Why the Other Options are Incorrect?

Option 2: Cite, site — Incorrect. Correct use: they sound the same: to cite is to quote or mention as proof; a site is a place where something is built or happens. So it is a correct pair.
Example: The engineer cited the report while visiting the building site.

Option 3: Bear, Bare — Incorrect. Correct use: they sound the same: to bear is to put up with (also a large wild animal); bare means uncovered. So it is a correct pair.
Example: I cannot bear walking on the hot sand with bare feet.

Option 4: Duel, Dual — Incorrect. Correct use: they sound the same: a duel is a fight between two people; dual means having two parts. So it is a correct pair.
Example: The hero of the dual-role film fights a duel with his twin.