Can an Indian who has been a permanent American resident for the past 10 years apply for a green card for his brother who is an Indian resident?

No, US permanent residents can only apply for immediate relatives (spouse and unmarried children under 18) regardless of how many years they have been a permanent resident. If the US permanent resident would like to petition for his/her brother, he/she must first become a US citizen through naturalization (which he/she may after 5 years of being a PR). US citizens may petition for spouses, children, siblings, and parents.