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Yes, Go for it the finance background will play an very important role so go with the Finance specialisation.

IITG ECE is better because it is Old IIT.

Candidates who have qualified for TS ICET 2022 will be eligible to apply for counselling and the seats will be allotted to them based on the final merit list and choices filled by them. If your TS ICET 2022 rank is between 25,000 to 35,000, you will get admission into some of the reputed TS ICET 2022 participating colleges.
If a candidate is from a reserved category, the chances of their getting a seat with a rank over 30,000 or 35,000 in a TS ICET Participating College is quite decent. Unreserved seats will rarely get allotted to a candidate with more than 35,000 rank.

CAP registration for DTE has already started from 30th September 2022. You also apply now to get admission if you delay in applying you may loose chance of getting admission in your dream college. Apply on MAC CET DTE CAP rounds to get your request approved.

You can fill that based on NIRF Ranking 2020.