Choose the correct sentence out of the following :

The correct answer is Option (4) → Sudipta soon realized she was not cut out for PhD.

A phrasal verb is a verb joined with a small word such as up, out or together. The two words together have a new meaning.

Be cut out for something means to have the right qualities or abilities for a particular job or activity. It is mostly used in the negative. Sudipta soon understood that she did not have the temperament or skills needed for a PhD.
Example: He realised he was not cut out for a career in sales.

Why the Other Options are Incorrect?

Option 1: Sudipta soon realized she cut PhD down. — Incorrect. Cut down means to reduce something (cut down on sugar) or to fell a tree. "Cut PhD down" makes no sense.
Example: The doctor told him to cut down on salt.

Option 2: Sudipta soon realized she was not cut through for PhD. — Incorrect. Cut through means to go through something by the shortest way or to deal with something quickly. There is no phrase "cut through for".
Example: We cut through the park to reach the station.

Option 3: Sudipta soon realized PhD cut her up. — Incorrect. Cut up means to cut into pieces or, informally, to upset someone deeply. It does not express suitability.
Example: She was badly cut up by the news of his illness.