Is it true that a B-school with low fees provides average placements and a B-School with high fees provides better placements?

It's not necessary. Do good search before final selection.

Dear Abhishek, Placement totally depends on student's performance and his/her confidence. B-Schools are only the facilitator to arrange the company in the campus. So, decide the B-School depending on all the factors like Faculty, Research, Location, Case Studies and not only on Fees. All the best.