Plural or singular after "no"

What do you use after the word “no”? Plural or singular?

For example:- Which one of these is correct?

No exams or No exam?

Plus tell me this. Which one of these is correct?

There are no exams today.
There is no exam today.

I am also confused with the verbs that come before the word “no”. Please tell me

Both are OK.

There are no exams today.-- For all the students or for several courses
There is no exam today.-- For one course or for one student