In order to replace the underlined part of the sentence with the correct form of the verb, we must understand the tense of sentence.
The given sentence is a general statement as it explains us about a rule. The word 'nowadays' explains that the sentence is in present tense. Hence, we will replace the underlined sentence with simple present tense of the verb.
Option A - 'Has played' is used to describe a completed action in the present, which is called 'present perfect tense.' As the sentence states a general fact, we must use the simple present tense. Hence, option A is incorrect.
Option B - 'Play' is plural form of the verb which can be used with a plural subject in present tense. As the given subject in the sentence is a singular subject, we can't use a plural verb. Hence, option B is incorrect.
Option D - 'Has been playing' is present perfect continuous tense. 'Has been' explain us the action started in the past and the participle form of the verb (playing) explains us that the action is continuing. Hence, option D is incorrect.
Option C - 'Plays' is the third person form of the verb 'play', which agrees with the third person subject 'internet'. It is in simple present tense. Hence, option C is the correct answer.
'Nowadays, internet plays an important role in education.'