The correct answer is option 1: 1 2 4 1 3.

Let`s evaluate each option to understand the matching of authors with their respective books:

Option 1:

- Author I, Sekhar Bandyopadhyay, matches with Book 1, "Jawaharlal Nehru: A Biography, Vol-I, 1889-1947."

- Author II, Sarvepalli Gopal, matches with Book 2, "From Plassey to Partition: A History of Modern India."

- Author III, David Hardiman, matches with Book 4, "Gandhi in His Time and Ours."

- Author IV, Gyanendra Pandey, matches with Book 1, "The Ascendancy of the Congress in Uttar Pradesh, 1926-1934."

Option 2:

- Author I is matched with the incorrect book.

- Author II is matched with the incorrect book.

- Author III is matched with the incorrect book.

- Author IV is matched with the correct book.

Option 3:

- Author I is matched with the incorrect book.

- Author II is matched with the incorrect book.

- Author III is matched with the incorrect book.

- Author IV is matched with the correct