Hello,
Yes, you can get some branches in SSN, CEG, MIT with a rank of 4000 in TNEA in BC category according to last year's cutoffs( visit this link to check out last year's cutoffs:
https://images.careers360.mobi/sites/default/files/TNEA-2018-ROUND-1-Opening-Closing-Ranks.pdf).
To predict which branch you can get in these colleges through TNEA, go to this link:
https://engineering.careers360.com/tnea-college-predictor
Best Wishes
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