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didn't get you what you are saying.. could you please elaborate further.
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Thanks i got it now ! Actually i was interpreting the production wrongly based on string derivation !

S - > .S, dollar
S - > .Aa, dollar [Because of .S] ---------------------1
A  - > .Ab, a [Because of A at 1, and lookahead symbol will be first ( a, dollar) i.e a] ------ 2
A - > .c, a [Because of A at 1, and lookahead symbol will be first ( a, dollar ) i.e a]
A -> .Ab,b [Because of A at 2, and lookahead symbol will be first ( b, a ) i.e b]
A -> .c, b [Because of A at 2, and lookahead symbol will be first ( b, a ) i.e b]

So we can also write it as

S -> .S, dollar
S -> .Aa, dollar
A - > .Ab, a/b
A - > .c, a/b

Option c is correct here