The correct answers are: On no account will late assignments be accepted, even if your dog ate your laptop. Under no circumstances are students permitted to text during my notoriously long lectures. Nowhere else will you find a more rigorous and intellectually demanding academic experience.

Negative prepositional phrases (like on no account, under no circumstances, in no way) and negative adverbs of place (like nowhere) require the auxiliary verb or the "to be" verb to be placed before the subject.

Incorrect Options:

• In no way I will tolerate... fails to invert the subject and auxiliary. It should be: "In no way will I tolerate..."

• Not only you must read... fails to invert the subject and modal verb. It should be: "Not only must you read..."