Hello student look all these three college Are best in itself but NIT Trichy is more preferable among students because of a government college and Being one of the best NIT. to get admission into NIT trichy you need to appear in jee main. Application form for jee main April examination starts from 07th of February and shall remain open till 07th of March 2020.

While you need to appear in BITSAT for Bits and VITEEE for VIT respectively.

Feel free to comment if you have any doubt

Good luck