Dear aspirant,

As you told that you are not interested in any branch and considering you don't know the insights of this branch so let me tell you that for non core and higher packages you should go for the ece branch because technically the placements in the ece branch is pretty good as compared to the mechanical branch.

But if you have good grip on mechanics subject or fluid mechanics of thermodynamics and you have a liking for machines then you should go for that. Lastly its totally your call what you want to choose but as per my opinion due to your problems in family you would get a higher pay scale in the ece branch.