Which of the following is an ancient Indian treatise on problems related to Mathematics?

The correct answer is Lilavati.

Among the four options given, Lilavati is the ancient Indian treatise specifically devoted to problems related to Mathematics. Let us understand why this is correct and why the other options are not, by examining each choice carefully.

What is Lilavati?
Lilavati is a celebrated mathematical work composed by the renowned Indian mathematician and astronomer Bhaskaracharya (Bhaskara II) in the 12th century CE (around 1150 CE). It forms a part of his larger astronomical treatise called Siddhanta Shiromani. The word "Lilavati" literally means "the beautiful one" and is the name traditionally attributed to Bhaskara's daughter.

What does Lilavati cover?
The treatise is written in poetic Sanskrit verse and covers a wide range of mathematical topics, including:

- Arithmetic: Operations with whole numbers, fractions, and zero
- Algebra: Linear and quadratic equations
- Geometry: Properties of triangles, circles, and other figures
- Mensuration: Calculation of areas and volumes
- Combinatorics: Permutations and combinations
- Series and Progressions: Arithmetic and geometric progressions

Its problems are presented in an engaging, story-like narrative format — making it not only mathematically rich but also pedagogically elegant, even by modern standards.

Why are the other options incorrect?

- Nyaya Sutras: This is an ancient Indian philosophical text composed by the sage Akshapada Gautama. It deals with logic, epistemology, and the theory of knowledge — not mathematics.

- Mimamsa Sutras: Composed by the sage Jaimini, this text is one of the foundational works of the Mimamsa school of Hindu philosophy. It is concerned with the interpretation of Vedic rituals and dharma — not mathematics.

- Pramānavarttika: This is a classical Buddhist philosophical work by the scholar Dharmakirti (7th century CE). It deals with epistemology (theory of valid knowledge) and logic — not mathematics.

Conclusion:
Among all the options, only Lilavati by Bhaskaracharya is an ancient Indian treatise entirely devoted to mathematical problems and principles. It stands as a monumental contribution to the history of mathematics in India and the world, and is thus the correct answer to this question.