I secured 10000 rank in aieee.So, should I go for a better college or a better branch?

Hi

You do not decide that whether to go for a good branch or a good college. You need to go for the best combination. You need to choose an appropriately decent college with a decent branch.

Getting a good branch in a non reputed college would do no gud and getting into a gud college wid a bad branch is also not done. So, go for the best combination. But always give the better college a priority than branch, but do balance them a bit.