Choose the most appropriate option to fill in the blank in the given…

The correct answer is Option (4) → by

Note: The given answer is as per the official NTA Answer Key. However, more than one answer is possible here: Option (4) "by" and Option (3) "with" both make a correct sentence, as explained below.

Option 1: of — Incorrect. Of shows belonging or relation; "fascinated of" is not English.
Example: The colour of the sky changed at sunset.

Option 2: at — Incorrect. At follows adjectives of reaction such as surprised at or angry at; "fascinated at" is not used.
Example: He was surprised at the result.

Option 3: with — Can also be considered as correct. Dictionaries give both fascinated by and fascinated with for being strongly attracted to something; "fascinated with the jewellery" is correct, especially for a continuing interest.
Example: He has been fascinated with old coins since childhood.

Option 4: by — Correct (Answer as per NTA). Fascinated means so strongly attracted that one cannot look away, and fascinated by is the most common form. The daughter was held by the beauty of the jewellery and insisted on trying on a tiara.
Example: The children were fascinated by the magician's tricks.