Step 1: Understanding the Concept:
Varāhamihira (c. 505–587 CE) was a polymath from Ujjain who summarized the astronomical and astrological knowledge of ancient India. He is credited with writing definitive works in all three branches of Jyōtiṣa: Siddhānta (Astronomy), Saṃhitā (Mundane/General Astrology), and Hōrā (Predictive Astrology).
Step 2: Detailed Explanation:
Let's analyze the authorship of the books listed:
1. Br̥hajjātakam (B): This is Varāhamihira's masterpiece in natal astrology. It is considered the most authoritative text on interpreting birth charts.
2. Laghujātakam (D): A concise version of the above, also authored by him, providing simplified rules for beginners.
3. Br̥hatsaṃhitā (E): A monumental encyclopedia covering eclipses, planetary movements, rainfall, agriculture, architecture, and omens. It is the definitive text for Mundane Astrology.
4. Līlāvatī (A): This was written by Bhāskarācārya II (12th century). It is a famous treatise on arithmetic and geometry.
5. Āryabhaṭīyam (C): This was written by Āryabhaṭa I (late 5th century), covering mathematics and astronomy.
Therefore, the correct set authored by Varāhamihira is B, D, and E. His works are characterized by high mathematical precision and a deep synthesis of earlier 'Siddhāntas'. He was one of the 'Navaratnas' (Nine Gems) in the court of Vikramāditya, and his contributions elevated Jyōtiṣa to a formal academic discipline. In addition to these, he also wrote the *Pañcasiddhāntikā*, which is our only source for the five ancient astronomical systems of India.
Step 3: Final Answer:
The books by Varāhamihira are Br̥hajjātakam, Laghujātakam, and Br̥hatsaṃhitā (B, D, E).