Engineering Entrance Exam

You might find it tough getting admission into the B. Tech IT program at Dwarkadas J. Sanghvi College of Engineering with an 89 percentile in the JEE since an expected cutoff for IT can be generally around 96 percentile or more for general category students.
Since you are applying under the Gujarati quota, which reserves 51% of the seats for Gujarati linguistic minority candidates, your chances might improve. The cutoff tends to be lower for Gujarati candidates, but the competition is not that weak. It would be advisable to look into the trends of the specific cutoffs for the current admission cycle and participate in the Maharashtra CAP counseling process for better insights.

A 92 percentile in JEE Mains can barely help you enter into an NIT, formulating a sweet proportion for' computer Science and electrical engineering branches. Well, there are still chances that you might get into some NITs and branches, even though they may be slightly messy in cutoffs or have lower openings with new institutions.

To improve your chances:

You aim for the new NITs or the ones with low cutoffs.
You can consider branches like Civil Engineering, Chemical Engineering, or Biotechnology, which have lower cut-offs as compared to core branches such as CSE or ECE. 
The final allocation of seats shall depend on your category of General, OBC, SC, etc., the opening and closing ranks and the NITs that you would be targeting. Keep watching the JoSAA counselling process to get the latest and most accurate information.

The chance of admission to a government college, given that your rank in JEE Mains is 213434, is very remote because the cut-off ranks to the government engineering colleges usually turn out much lower for them, more so in their popular branches. To exemplify this, it often lies within the cut-offs for general category students around 10,000 and 50,000 mark in NITs and IIITs respectively according to branches and college.
Cut off for government colleges in state like Madhya Pradesh and Uttar Pradesh is competitive yet may vary. According to the latest data, they require ranks much better than 213434 to even gain admission in government institutions, thereby you may have to get into private colleges or any other alternative if you actually want to pursue engineering.

Multiple rounds of counseling sessions are followed by the students admitted under the AUEET: Andhra University Engineering Entrance Test. Commonly, there will be two prominent rounds of counseling, while the initial rounds help fill seats on an open preference basis following merit ranking for seats, subsequent ones allow remaining vacancies and provide chances for students who newly entered into merit rankings.
With a rank of 2557, you could probably be offered a chance for entry into ECE (Electronics and Communication Engineering) or CSE (Computer Science Engineering), which could depend upon that year's competition level as well as seat availability within those streams.