Step 1: Understanding the Concept:
Indian Jyotish literature is vast, spanning thousands of years. Authors wrote comprehensive Siddhantas (theory), Karana texts (manuals for practical calculation), and Bhashyas (commentaries).
Step 2: Detailed Matching of Authors and Books:
1. Pratibha-bodhakam (A): This is a work by Sudhakara Dvivedi, a prolific mathematician and astronomer of the 19th-20th century who edited and revived many ancient texts. (A matches III).
2. Karana-kutuhalam (B): Written by Bhaskaracharya II (the author of Siddhanta Shiromani) in 1183 CE. It is a Karana text based on a specific epoch. (B matches IV).
3. Brahmasphutasiddhanta (C): The masterpiece of Brahmagupta (7th Century CE), famous for being the first text to treat 'zero' as a number and providing the solution for quadratic equations. (C matches II).
4. Grahalaghavm (D): Written by Ganesh Daivajna (16th Century CE). It is currently the most popular text for making traditional almanacs (Panchangs) in India. (D matches I).
Step 3: Verification:
Sequence: A-III, B-IV, C-II, D-I. This corresponds to Option (2).
Step 4: Final Answer:
The matches identify the authors of these pivotal texts in the Indian astronomical tradition.