NIT Calicut - National Institute of Technology Answered Questions

You can check the previous year's category wise cutoff's (category ranks) of these and other NITs at: https://josaa.nic.in/josaaorcrarchieve/Result/OpeningClosingRankArchieveN.aspx?Year=2017.
You would get an idea of your selection.
Best of luck.

Actually, there is nothing like better and best. It all depends on your interests and personality. Basically, IT is mostly related to computers, and it also has some basics in ECE. If you want to pursue a good career in the coding and software fields, you can choose IT. ECE is a subjective branch where you can learn a lot about devices and their functionalities. So, if you take your decision from a college perspective, I would prefer ECE at NIT-Calicut, as it is a premier institution and one of the top NITs. As I mentioned above, if you want to excel in the software field, IT at IIITM-Gwalior is better. You can get a lot of knowledge from seniors and from various clubs here.

Assuming you are from general category you need atleast 175+ marks to get a better seat in core and technical branches. Your board percentage will only lend you through the eligibility and the marks for Mains through the counseling. Try for other autonomous colleges to seek a better branch. Best of luck.

Yes, you have excellent marks for general Category in Mains. Between the two, I would suggest you to opt for the one which is nearest to you as these two do not hold a significant difference academically between them.
If both are around the same distance, I would suggest you NIT-Jaipur as the better one.
Also, try for SPA Bhopal over NIT Jaipur. Best of luck.

Placements of EEE at NIT Nagpur are very good. In fact, if you are very good at coding, you can sit for placements along with CSE people for the companies that come to hire them. However, the curriculum is very strenuous and for a good pointer, you'll have to study really hard. But all that will be worth in the long run.
All the best!