Final answer:
The Gupta Empire achieved the development of the concept of zero, the use of a decimal system, and patronized the creation of Buddhist cave paintings at Ajanta.
Step-by-step explanation:
The development of the concept of zero, the use of a decimal system, and the Buddhist cave paintings at Ajanta are all achievements of the Gupta Empire. During the Gupta Empire, Indian mathematicians invented the number zero and used decimals and zero as a mark for precise measurements. The Gupta Dynasty also patronized artists who created beautiful sculptures in the Ajanta caves, showcasing the sophistication of the art during that time.