funding - Do universities typically cover publication fees associated with open access publications?

I am an undergraduate student in a private Indian university. Last semester I worked on a research project with another undergrad student and under the mentorship of a PhD scholar.

We have submitted a paper to an Elsevier journal which charges a mandatory open-access fee of $500 on acceptance of the paper. In such cases, does the university typically cover these costs or are they borne by the authors of the paper?

Which department of the university should I contact to ask for funding for the same?