Matching each case to its actual, well-known subject matter is the quickest route through this question, since only one of the four cases is directly associated with breaking down the formal quasi-judicial versus administrative divide.
Since the quoted words describe the reasoning specifically associated with A.K. Kraipak, that is the case being asked about.
Ridge v. Baldwin and A.K. Kraipak are the two cases most likely to be confused here, since both are celebrated for expanding the reach of natural justice, and separating their distinct contributions resolves the question.
Once Ridge v. Baldwin's narrower contribution is distinguished from A.K. Kraipak's broader articulation of the principle quoted in the question, A.K. Kraipak stands out as the case being referred to.
Therefore, the correct answer is A.K. Kraipak v. Union of India AIR 1970 SC 150.