NIT

Not all the NITs are better than VIT.
The starting top 6-7 NIT are definitely better than VIT but if you get to choose between rest of the NITs and VIT choose VIT. Make sure you choose VIT, Vellore and not any other if you also want to enjoy the college life because the placement and all are same for each branch but the campus life you have in Vellore can't be compared to any other campus.
Coming to get a good score, just keep your basics clear the paper for VITEEE is easier than Mains.

Class 12th Score:
1-Language,
2-Physics,
3-Mathematics,
4-Any one of (Chemistry, Biology, Biotechnology, Technical Vocational Subject),
5-Any other subject. At least 45% marks (40 % in case of candidate belonging to reserved category) in each of the subjects. Regards.

Please specify in which NIT you wish to apply and also which branch of M.Sc. you want to apply?

For IIT, it is 75% and is the easiest part of it. If you want to join IIT, you need to crack JEE Mains and JEE Advanced as a good rank in advanced can get you a seat in IIT. Though you must be eligible for NIT if you get your expected marks, but to get a seat there, you need to perform well in JEE Mains.
All the best.

You have not mentioned the course for which you want admission. As for B.Tech you need to qualify JEE Mains and a good rank in the exam can fetch you a seat, for M.Tech you need to have a good rank in GATE for different courses offered there are different entry scheme.

You are eligible for NITs like MNIT Jaipur, NIT Silchar, and NIT Kurukshetra but not for NIT Warangal because for pursuing MBA from NIT Warangal one must have an engineering background.

Batch 2016-18 is 50% placed as of now with an average package of 6 LPA. ROI is good.

Please go ahead and call them back.
All the best.

First of all, congratulations, for scoring 480 marks in GATE. With that score, I am sure you can apply in all IITs and NITs. Still, you have to wait till they announce their cut-off list. It changes every year.

For top NITS, above 100 marks is required.