Great quiz! The longest river flowing through India is the Brahmaputra (~4000 km) and not the Indus (~3600 km, disputed). But, for most of their courses, they flow in the neighbouring countries. The river with the longest length within India is the Ganges (2525 km).
Thanks, Aficionado. You are probably correct about the Brahmaputra being longer than the Indus. But there does seem to be some dispute about it. This source https://knowindia.gov.in/general-information/length-of-some-important-indian-rivers.php has them of equal length. So I do accept either answer.
Schiffi, you are right but I am following the convention of naming a river by it's estuary or outflow. It seems most logical since a river's name can change so many times over a long course.
YouLoveEagle, in my view, the length of a river is a Geographical concept and should be unaffected by human naming systems, however bizarre. As I said in the reply to the previous point, I follow the convention of naming the river by what it is called at the estuary. So the longest river that flows through the USA is the Mississippi, measured via its longest tributary, the Missouri.