The question requires us to match the authors with their respective books. Let`s go through each option to understand the matching:

Option 1: Bal Gangadhar Tilak and "The Arctic Home in the Vedas." This match is correct.

Option 2: Dadabhai Naoroji and "Hind Swaraj." This match is incorrect. Dadabhai Naoroji did not write "Hind Swaraj." Therefore, a correction is needed.

Alert - The correct answer should be 2.

Option 3: Mahatma Gandhi and "The Discovery of India." This match is correct.

Option 4: Jawaharlal Nehru and "Poverty and Un-British Rule in India." This match is correct.

Therefore, the correct match is:

1. Bal Gangadhar Tilak - "The Arctic Home in the Vedas"

2. Dadabhai Naoroji - (Correction needed)

3. Mahatma Gandhi - "The Discovery of India"

4. Jawaharlal Nehru - "Poverty and Un-British Rule in India"