My cousin hailed from a middle-class family and cleared BITSAT in one go. His father somehow managed to pay the fees for the first semester.
After joining he approached the SBI stall and found out about the educational loans they were offering. Ever since then whenever he received a fee demand form, he submitted it to the bank that took care of his entire college fee including food and accommodation. He did not have to spend any money except for his personal expenses. The scholarships are given solely on the basis of merit here.
However, BITS Pilani fees face a hike every year so I don’t think the ROI of non-CS branches is worth being considered by middle-class families.