RAS question
Brahmagupta, the mathematician who formalized rules for zero, worked at:
Correct answer: (C) Ujjain (Bhinmal).
Brahmagupta, the mathematician associated with formal rules for zero, worked at Ujjain and is also placed by Britannica at Bhillamala, modern Bhinmal, while writing the Brahma-sphuta-siddhanta.
Explanation
Brahmagupta is the figure to connect with Ujjain (Bhinmal), not with the other ancient centres listed in the options. He worked at Ujjain and wrote the Brahmasphutasiddhanta in 628 CE. Encyclopaedia Britannica places the Bhinmal side of the option by saying that the Brahma-sphuta-siddhanta was probably written while he was living in Bhillamala, modern Bhinmal. That matters because the same work is tied to the mathematical ideas named in the question: Brahmagupta defined zero as the result of subtracting a number from itself and gave rules for operations involving negative and positive numbers. His cyclic-quadrilateral result further marks him as a major ancient Indian mathematician-astronomer.
Why the other options are wrong
- (A) Pataliputra is not associated with Brahmagupta here; his work is tied to Ujjain/Bhillamala instead.
- (B) Taxila does not fit the evidence here, because the Brahma-sphuta-siddhanta is placed at Bhillamala and Brahmagupta is also tied to Ujjain.
- (D) Nalanda is a tempting ancient-learning-centre distractor, but Brahmagupta's work is not placed there.
Concept
This tests the RAS ancient Indian science-and-culture theme: matching major scholars with their works and centres. Brahmagupta recurs because zero, negative numbers and mathematical astronomy are standard markers of India's scientific tradition.