Explanation:

The Chairman of the Rajya Sabha holds a specific constitutional role, directly linked to another high office. - **Option A (Zakir Hussain):** Dr. Zakir Hussain served as the third President of India and was the second Vice President of India. As Vice President, he was the ex-officio Chairman of the Rajya Sabha, but he was not the *first*. - **Option B (Sardar Patel):** Sardar Vallabhbhai Patel was the first Deputy Prime Minister and Home Minister of India. He never served as the Chairman of the Rajya Sabha. - **Option C (Dr. Rajendra Prasad):** Dr. Rajendra Prasad was the first President of India. The President is not the Chairman of the Rajya Sabha. - **Option D (Dr. S. Radhakrishnan):** This is the correct answer. According to Article $64$ of the Indian Constitution, the Vice President of India is the ex-officio Chairman of the Rajya Sabha. Dr. Sarvepalli Radhakrishnan was the first Vice President of India, serving from $1952$ to $1962$. Consequently, he was the first Chairman of the Rajya Sabha, presiding over its sessions during his tenure as Vice President.