Disinterested has second meaning too: having or feeling no interest in something; uninterested(According to Google). Which has a common synonym “InDifferent” with “NonChalant”.
NonChalant: (of a person or manner) feeling or appearing casually calm and relaxed; not displaying anxiety, interest, or enthusiasm. (Which seems to match with disinterested).
What is the subtle difference am I missing here? Will GRE include such close pairs in SE questions?
@gregmat Please help in same.