CDS (II) 2023 General Knowledge · Question 19 of 120

Correct — C, 1 and 2 only. Statement 1 is a fair description of the Bakhshali manuscript. It was dug out of a field in 1881 at Bakhshali, near Mardan in the old Gandhara country, it is written in the Sharada script, and its contents are mathematics — fractions, square roots, arithmetic and geometric progressions, along with simple, simultaneous, quadratic and indeterminate equations, each problem stated, solved and then checked. It is also one of the earliest documents anywhere to use a dot as a placeholder for zero, and it now sits in the Bodleian Library at Oxford. Statement 2 is right too. In the ganitapada of the Aryabhatiya, Aryabhata gives the rule that adding four to a hundred, multiplying by eight and adding sixty-two thousand yields the circumference of a circle of diameter twenty thousand — that is 62,832 divided by 20,000, which is 3·1416, correct to four decimal places. Statement 3 is where the item is decided: the Sharangadhara Samhita is a work of Ayurveda, not of politics. It is a medieval compendium famous for its pharmaceutical formulations and for the first textual account of diagnosis by the pulse, and it has nothing to do with the political system of ancient India.

• (a)1, 2 and 3 — The all-of-them pick. It fails on statement 3 alone — the Sharangadhara Samhita belongs to the medical literature, alongside the Charaka and Sushruta compendiums, and not to the literature of statecraft.
• (b)1 and 3 only — Keeps the false statement and throws out a true one. Aryabhata's value of 3·1416 is among the most quoted facts in the history of Indian mathematics, so statement 2 cannot be dropped.
• (d)2 only — Rejects statement 1, which is sound. The Sharada script, the mathematical subject matter and the progressions and square roots are all correctly attributed to the Bakhshali manuscript.

Indian mathematics is documented through a small set of texts that examiners return to. The Bakhshali manuscript is the oldest surviving Indian mathematical manuscript and the earliest Indian use of a placeholder dot for zero. Aryabhata's Aryabhatiya of 499 CE, in four sections, gives the value of pi, a table of sines, the rule for the area of a triangle and an explanation of eclipses by shadow. Brahmagupta's Brahmasphutasiddhanta sets out rules for arithmetic with zero and with negative numbers. Bhaskara II's Lilavati and Siddhanta Shiromani carry the tradition into the twelfth century.

Three statements from three different corners of ancient scholarship, and only one needs to be judged with care. Statements 1 and 2 are standard textbook lines. Statement 3 is a title test: any Samhita in the Indian tradition is overwhelmingly likely to be a medical or ritual compendium, and Sharangadhara sits with Charaka, Sushruta and Vagbhata among the physicians, so a work claimed to be about the political system should immediately look wrong. Two points of honesty about the printed statements. Aryabhata's word for his own value, asanna, means approaching, which suggests he knew it was an approximation and not exact — the paper's flat 'very accurate value' misses that. And the description of the Bakhshali language as Gatha, a refined form of old Prakrit, follows older scholarship, chiefly G. R. Kaye's edition; current descriptions call it a form of literary Sanskrit shaped by contemporary dialects. The point does not change which option is correct, but it is worth knowing that the stem is repeating a dated formula. The paper also prints the astronomer's name as 'Aryabhatta' with a double t, where the usual modern spelling is Aryabhata.

• The Bakhshali manuscript was found in 1881 near Mardan in the Gandhara region, is written in the Sharada script and is now in the Bodleian Library, Oxford.
• Its mathematics covers fractions, square roots, arithmetic and geometric progressions and several classes of equation, with each solution verified.
• It contains one of the earliest known uses of a dot as a placeholder for zero.
• Aryabhata's rule in the Aryabhatiya gives a circumference of 62,832 for a diameter of 20,000, that is pi = 3·1416, accurate to four decimal places.
• The Sharangadhara Samhita is a medieval Ayurvedic compendium, known for its pharmaceutical preparations and for the earliest textual treatment of pulse diagnosis.

• Accepting a Samhita as a political text; the word almost always marks a medical or ritual compendium.
• Crediting Aryabhata with inventing zero. He worked with a place-value system, but the symbol's history runs through other texts and inscriptions.
• Treating 3·1416 as an exact value; Aryabhata's own wording marks it as an approximation.

As a multi-statement item mixing texts, authors and subjects, or as a match between an ancient scholar and a specific finding or calculation.

• practice — not a real PYQ

  The Bakhshali manuscript, the oldest surviving Indian mathematical manuscript, is written in which one of the following scripts?

  • (a)Brahmi
  • (b)Kharoshthi
  • (c)Sharada
  • (d)Grantha

  Answer(c) Sharada — the script used in north-western India from about the eighth century onwards. The manuscript was found in 1881 near Mardan and is now at the Bodleian Library, Oxford.

• practice — not a real PYQ

  The Sharangadhara Samhita is a classical Indian text dealing primarily with

  • (a)statecraft and administration
  • (b)medicine and pharmacy
  • (c)grammar and phonetics
  • (d)astronomy and calendrics

  Answer(b) medicine and pharmacy — a medieval Ayurvedic compendium noted for its pharmaceutical formulations and for the earliest written account of pulse diagnosis.