The book 'Leelavati' belongs to the field of Mathematics is :

Question

Accepted Answer

The book 'Leelavati' is a renowned work in the field of mathematics, specifically focusing on arithmetic. Here is a detailed explanation supporting why Option 2 is the correct answer:

1. **Justification for Option 2 (Arithmetic):**
   - 'Leelavati' is a famous mathematical treatise written by the Indian mathematician Bhaskara II in the 12th century. The book is primarily focused on arithmetic and is known for its comprehensive coverage of basic arithmetic operations, including addition, subtraction, multiplication, and division. It also delves into more complex topics such as fractions, proportions, and the rule of three. The text is notable for its practical approach to teaching arithmetic, often using poetic verses and real-life examples to explain mathematical concepts.

2. **Explanation for why other options are incorrect:**

- **Option 1 (Algebra):**
     - While Bhaskara II did contribute significantly to algebra, particularly in his other work called 'Bijaganita,' 'Leelavati' itself is not primarily focused on algebra. 'Leelavati' is more concerned with arithmetic problems and solutions, making Option 1 incorrect in this context.

- **Option 3 (Chapter on spheres):**
     - The concept of spheres and related geometric topics are not the primary focus of 'Leelavati.' Although Bhaskara II's works do cover various aspects of geometry, including spheres, these are not the central theme of 'Leelavati.' Therefore, Option 3 is incorrect.

- **Option 4 (Mathematics of planets):**
     - The mathematics of planets, or astronomy, is covered in another of Bhaskara II's works called 'Siddhanta Shiromani,' which includes sections on planetary motion and celestial calculations. 'Leelavati' does not focus on this area, making Option 4 incorrect.

In conclusion, 'Leelavati' is best categorized under arithmetic, as it primarily deals with arithmetic operations and problems, justifying why Option 2 is the correct answer.