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MBA cannot be done without some math. An MBA student needs analytical knowledge of basic math concepts such as arithmetic, algebra, geometry, and statistics. Finance specialisation involves lot of arithmetic so you can choose some other options where Maths is comparatively lesser. However please keep in mind, a good MBA should be comfortable with numerical abilities.
1. Human Resource Management
2. Marketing.

Good you please proceed for BBA no need to fear for maths, BBA is completely business accounts not engineering maths.

Yes, in placement some companies can set the criteria for class 10th and class 12th marks (Generally above 60%) along with the B.Tech CGPA. However, this is not necessary for all, most of the companies focus on B.Tech CGPA.

NIMS University accepts JEE Main scores for B.Tech admissions. NIMS also conducts NIMS Entrance test for B.Tech admissions. The basic eligibility criteria of B.Tech courses are given below. Eligibility: 10+2 with minimum 50% marks in PCM. For more details please visit the NIM University website.

Hello Souvik, it's tough to say as to how cutoff percentiles will play out in this year's JEE Mains. I am attaching last year's cutoff percentiles for different categories. You will need to decide as to whether your percentile is good enough for your aim of not. Cut-off for JEE Advance
Candidates having at least 90.3765335 percentile will be eligible to appear for JEE Advanced. For EWS students the cut-off is 70.2435518, for OBC it is 72.8887969, SC - 50.1760245, ST - 39.0696101, PwD - 0.06185224
Best wishes to you.

No, you are just left behind by.50 percentage of getting CSE /ECE in any NIT because 85 to 95 Percentage is required fir the same.