Identify the segment in the sentence which contains the grammatical error.
Scarcely she had heard the news when she fainted.

“Scarcely”, like “hardly” and “no sooner”, is followed by an auxiliary verb + subject + main verb. This inversion is required when these words occur at the beginning of a clause.

Correct pattern: Scarcely + auxiliary verb + subject + past participle … when + clause.
Example: “Scarcely had I reached the station when the train left.”

In the given sentence the order is “Scarcely she had …”, where the subject “she” precedes the auxiliary “had”. This violates the inversion rule.

The error therefore lies in the segment “Scarcely she had”. The correct sentence should be:
“Scarcely had she heard the news when she fainted.”

Option A which is: Scarcely she had — is the erroneous segment.