what I should vs. which I should

Question

A: I have three exams this week. I don't know what/ which(one) I should study first.

B: Making a study schedule might help.

Which is the right choice? and why is it?

Answer 1

If we are limited to the words as supplied, then which is incorrect. However, a simple addition makes it grammatical:

I have three exams. I don't know which [of them] to study for.

We don't "study an exam". We study for an exam.

I have three exams. I don't know what [thing] to study.

what is an empty room. There, it can hold anything that can be studied. Unlike which, what does not refer back to an antecedent.

Here are three kittens. Which do you like best?

Here are three kittens. Which of them do you like best?

The two sentences above are equivalent in meaning.

Here are three kittens. I know what they like to play with: yarn.

Here, what is an unspecified thing, and when it is modified by "they like to play with", what refers to thing-they-like-to-play-with.

The kittens knocked a vase over. I didn't know what to say to them.

There, what is also a thing, broadly understood. When it is modified by "to say", it refers to thing-that-can-be-said.

As you can see from these examples, what does not refer back to an earlier noun.

Answer 2

"Which." You are choosing from a set of three options; it is not an indefinite open set that you are picking from if the answer to the question is one of the three.
If it were an indefinite open set (e.g. the answer of what to study could be any possible point or sub-topic), "what" would sound more natural.

In either case, you will be understood here.

Answer 3

"Which" is the best, because there are limited options.