Regular Expression from Finite Automata

Question

Can someone please explain me how could we derive the RE from FA's ... Here-- https://gateoverflow.in/464/gate2008-52

PS- Obviously the answer can be easily obtained using parsing, but how can we derive the regular expression?? Ardent is too lengthy for exam point of view, so explanation with some other technique like state elimination will be appreciated...

Answer 1

Sometimes state elimination become lengthy it depend on the questions nature