The correct option is C Has been living
Let’s examine the sentence: “He is living in this house for the past ten years.” The sentence states that the action of living in the house started ten years ago and is continuing in the present day. Hence, the tense of the sentence should be present perfect continuous. The present perfect continuous tense (also known as the present perfect progressive tense) shows that something started in the past and is continuing at the present time. The present perfect continuous is formed using the construction has/have been + the present participle. So, the verbs required by the sentence are “has been living” and not “is living.” Hence, the correct sentence would be, “He has been living in this house for the past ten years.” So, Option C is the correct answer.