Here is some information to assist you in choice-making-
IIT Dhanbad Mechanical is the best option among the three. This college has a rich legacy and a strong brand value. Apart from that, it offers good placements with brands like Tata visiting the campus for recruitment purposes.
But if you have an interest in Electrical, you can opt for IIT Tirupati. Unlike before, the college is now functioning from its permanent campus. The permanent campus is destined to house 12,500 students. It is under construction in phases, but it already houses 1500+ students at present.
Therefore, IIT Dhanbad Mechanical is the best choice. But if Electrical interests you, opt for IIT Tirupati Electrical.
If you are interested in programming, you can definitely go for IIIT Allahabad and IIIT Bangalore. According to my friends studying there, they both have an excellent coding culture.
The points below give a brief overview of the present coding culture of IIIT Bangalore, which will increase the level of interest for a programming geek in the institute.
Therefore, even being in a nascent stage, students from IIIT Bangalore enjoy the top-level programming culture and so, there are huge scopes for such geeks in the institute.