IIT

No Arvindhan, you will not get NITs but you will get a private college.

Sorry, but there is no ALLEN coaching classes in Nagpur but try for IIT-HOME: It is also the best coaching institute.

You can get colleges of your state, maybe even government ones. Try JEE college predictor to get more information and insight about college which you can get on the basis of your rank-
https://www.shiksha.com/b-tech/resources/jee-mains-college-predictor?utm_source=connect&utm_medium=CR_JEECP&utm_campaign=4067795.

It depends on the results of JEE Advanced. In order to get admission in IISC, you must score AIR rank under 50 and in IITs. It must be under 5000.

Hello Jerin,
The admission in IITs is based on the scores in JEE Advanced exams for which you can appear only on the completion of class 12th. In class 11th, you may start your preparations for the exams, and so you can have a chance to get IITs. All the best.

Hi Mainak,
For Bachelors in Computer Science and Engineering, there are a lot of other good colleges, where you can take admission. Some of them are:
IIIT Hyderabad
BIT Mesra
DAIICT
LNMIIT
PESIT
Jadavpur University
COMEDK Colleges like RVCE, BMSCE etc. Galgotias University, Thapar University, Amity University etc.

The admission mainly depends on JEE examination. To get into NITs, good score in JEE Mains is required. To get into IITs, good score in JEE Advanced is required.