Option 1: J. K. Rowling is a well-known author, known for her Harry Potter book series. However, she is not the author of the book `India Remembered`.
Option 2: Robert Dallek is an American historian and author, known for his biographies on American presidents. He is not the author of the book `India Remembered`.
Option 3: Pamela Mountbatten, also known as Countess Mountbatten of Burma, is the correct author of the book `India Remembered`. Pamela Mountbatten was the daughter of Lord Louis Mountbatten, the last Viceroy of India, and she wrote this book to share her experiences and memories of growing up in India during the time of the British Raj.
Option 4: Stephen Hawking was a renowned physicist, known for his work on black holes and cosmology. He is not the author of the book `India Remembered`.
Therefore, the correct answer is option 3, Pamela Mountbatten.