Yes you could have applied but the rejistrations are over now.  Bit still some seats are reserved in management quota you can apply for that.
But for that may be you have to give a higher fees.
You can apply for many ither colleges that are as good as VIT.
All the best

ya surely u should apply for VITEE 2018 as it is the entry to VIT Vellore and Chennai campus. VIT is one the best private engineering college in India. They will ask questions similar to JEE examination.

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