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RAS question

Consider the following about Brahmagupta's contributions to mathematics: 1. Brahmagupta was the first to give explicit rules for arithmetic operations involving zero, including the result of dividing a number by zero 2. Brahmagupta formulated a formula for the area of a cyclic quadrilateral, known today as Brahmagupta's formula 3. Brahmagupta's major work is the Brahmasphutasiddhanta (628 CE) How many of the above statements are correct?

Correct answer: (C) All three.

All three statements are correct: Brahmagupta gave explicit arithmetic rules involving zero, formulated the cyclic-quadrilateral area formula now called Brahmagupta's formula, and wrote the Brahmasphutasiddhanta in 628 CE.

  1. (A)

    Only one

  2. (B)

    Only two

  3. (C)

    All three

  4. (D)

    No statement is correct

Explanation

Brahmagupta's mathematical importance is tied to the Brahmasphutasiddhanta, written in 628. In that work, he defined zero as the result of subtracting a number from itself and stated rules such as adding or subtracting zero leaving a number unchanged, and multiplying by zero giving zero. He also tried to extend arithmetic to division by zero; his statement that zero divided by zero is zero was wrong, but it still shows a systematic attempt to handle zero arithmetically. The geometry statement is also correct: the same work gives the area formula for a cyclic quadrilateral, now known as Brahmagupta's formula. Since all three listed statements match these points, the answer is all three.

Why the other options are wrong

  • (A) Only one cannot be correct because the zero-arithmetic rules, the cyclic-quadrilateral area formula, and the 628 CE Brahmasphutasiddhanta statement are all supported.
  • (B) Only two is too low because Brahmagupta's flawed 0/0 result does not make the broader statement about his explicit zero-arithmetic rules false.
  • (D) None is impossible because the cited biography records the Brahmasphutasiddhanta, its zero rules, and its formula for the area of a cyclic quadrilateral.

Concept

This tests ancient Indian mathematics within the history of science, especially how mathematical texts are linked to named scholars and specific works. RAS often returns to such points because Rajasthan-linked centres such as Bhillamala connect cultural history with scientific achievements.

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