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Your marks don't even clear the cutoff so getting admission in NMIMS ain't possible for you.

Yes, you can apply as BBA is nothing to do with maths actually.

Hi,
The new counseling for B.Ed colleges will start in May of June 2020.

You can get placement in mechanical engineering in NIT if you have strong hold in any one topic of your course like thermodynamics, fluid mechanics, dynamics, etc. If you have no strong hold in any one topic of your course, then there is no chance of placement. Also, you have to maintain minimum 8 CGPA for good placement.