Question

In which following sentence,which word is an adverb used to modify an objective?

Answer 1

The word quite modifies the word late

Answer 2

I believe you meant 'adjective,' not 'objective.' 
In any case, there is only one adverb in the sentence, and that is the word quite. It modifies the adjective which follows it, which is the word late. You can ask the question - How late was it? And the answer would be - Quite. , which tells you it is the word that modifies it.