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Whats The Answer & How to solve such kind of Questions ?

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Best answer
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First they should have to mentioned start state here I assuming X as a start state because x is only state from which all other state are reachable, minimum length string generate by x is a

X->Y

Y-> A from here itself we can say answer is b

Now state X and Y assure that already one a is extra either at beginning or end or both side

State S,A,B ensure number of a= number of b

S,A,B cannot be reached without X hence option b is correct
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