Goa

http://bitsadmission.com/cutoffscores.aspx
Go through this link for the complete information.

http://bitsadmission.com/cutoffscores.aspx
Go through this link for the complete information.

The placement record is good but to know the exact scenario for faculty and placements get in touch with the current students through social media or in person.

Priti, LPU students have also availed opportunities of Placements in government services through on-campus/off-campus placement drives. LPU provides ample opportunities to each and every of the eligible students to secure good placement. The university has been ranked high by outer agencies also wit

If you consider the teaching quality all the institutes are at par with each other. but if placements are taken into consideration you can consider IIT Delhi and NITK.

Yes, you can get easily in 2nd round or in spot round.

Goa University
Birla Institute of Technology and Science, Goa

I will definitely suggest you to consider BITS-Goa.
The infrastructure, environment, the alumni, placements everything will say you to consider BITS-Goa.
Go for it. Good luck.