To match List I with List II, let`s analyze the contributions of each individual mentioned in List I.

I. Visakhadatta: Visakhadatta is known for his work in drama. He is an ancient Indian playwright who wrote the famous Sanskrit play called "Mudrarakshasa." The play revolves around political intrigue and power struggle during the time of Chandragupta Maurya. Therefore, Visakhadatta is associated with drama.

II. Varahamihira: Varahamihira was an Indian astronomer, mathematician, and astrologer who lived during the 6th century. He made significant contributions to the field of astronomy, particularly in the study of celestial movements and calculations. He wrote the famous astronomical work called "Panchasiddhantika" which discusses five astronomical systems. Varahamihira`s contributions firmly establish his association with astronomy.

III. Charaka: Charaka was an ancient Indian physician and is considered one of the pioneers of Ayurveda, the traditional system of medicine in India. He is believed to have lived around the 1st century BCE and authored the renowned medical treatise known as the "Charaka Samhita." His work covers a wide range of medical topics, including diagnosis, treatment, and principles of Ayurveda. Thus, Charaka is connected with medicine.

IV. Brahmagupta: Brahmagupta was an Indian mathematician and astronomer who lived during the 7th century CE. He made significant contributions to mathematics, especially in the field of number theory and algebra. Brahmagupta`s most famous work is the "Brahmasphutasiddhanta," which presents mathematical formulas and solutions. Although he had an interest in astronomy as well, his contributions to mathematics were more significant. Hence, Brahmagupta is associated with mathematics.

Considering the information above, we can match the individuals in List I with their respective fields in List II as follows:

I. Visakhadatta - (B) Drama

II. Varahamihira - (C) Astronomy

III. Charaka - (A) Medicine

IV. Brahmagupta - (D) Mathematics

Based on this analysis, we can see that Option 3: I - B, II - C, III - A, IV - D is the correct answer.