He asked (1) certain boy (2) to enter (3) the Director's office. (4) No error…

The adjective 'certain' can mean 'a particular but unnamed' person or thing (e.g. 'a certain person'). Used this way before a singular countable noun, it still obeys the ordinary rule for singular countable nouns: the noun phrase needs a determiner, usually the indefinite article 'a'/'an' -- placing an adjective in front of the noun does not remove that requirement.

In this sentence, segment (2) reads "certain boy": the adjective 'certain' sits directly before the singular countable noun 'boy' with no article, which is ungrammatical. The article must be restored, giving "a certain boy." The corrected sentence reads: "He asked a certain boy to enter the Director's office."

• (1) "He asked" correctly opens the sentence with the pattern 'ask + object + to-infinitive' (ask someone to do something); no error here.

• (3) "to enter" correctly supplies the to-infinitive required by that same pattern; no error here.

• (4) "the Director's office" correctly combines the possessive 's with the definite article 'the' to specify one particular office; no error here.

• Since exactly one segment is ungrammatical, 'No error' (5) cannot be the right choice either.

Therefore, the error lies in segment (2), "certain boy," and the correct choice is (2).