In India, the Permanent House refers to the Rajya Sabha (Council of States). The Vice President of India serves as the ex-officio Chairman of the Rajya Sabha, making the Vice President the Chairperson of the Permanent House.
Thus, the correct answer is the Vice President of India. In Indian polity, the Vice President holds the position of Chairman of Rajya Sabha, which is a unique role distinct from the Speaker of the Lok Sabha.