Explanation:

The original sentence is erroneous.

Reason: Usage of the phrasal verb 'go out' which means ‘be extinguished' is inappropriate in this sentence.

'Go by' which means ‘to accept what someone or something says when you are deciding what to do or think’ would be suitable in this context.

E.g.: Going by what Tim said, we should be there by mid-afternoon.

Hence ‘go by’ should be used in place of ‘go out’ to make the sentence grammatically and contextually correct.

Among the given choices, only option B replaces the given bold part most appropriately.

The sentence after replacement becomes:

It wouldn’t be wise for India to go by America’s verbal assurance unless it is supported by actions.

Option B is hence the correct answer.