Mahavira's Contributions to Algebra

Description: Mahavira was an Indian mathematician who lived in the 9th century. He is best known for his work on algebra, which he called ganita. Mahavira's contributions to algebra include the development of new methods for solving equations, the use of negative numbers, and the development of a system of linear equations.
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What is the name of the book that Mahavira wrote on algebra?

  1. Ganita Sara Sangraha

  2. Lilavati

  3. Bijaganita

  4. Siddhanta Shiromani


Correct Option: A
Explanation:

Ganita Sara Sangraha is a book on algebra written by Mahavira in the 9th century. It is one of the earliest known works on algebra and contains many important contributions to the field.

What is the main topic of the Ganita Sara Sangraha?

  1. Arithmetic

  2. Geometry

  3. Algebra

  4. Trigonometry


Correct Option: C
Explanation:

The Ganita Sara Sangraha is a book on algebra. It covers a wide range of topics, including solving equations, using negative numbers, and developing a system of linear equations.

What is one of Mahavira's most important contributions to algebra?

  1. The development of new methods for solving equations

  2. The use of negative numbers

  3. The development of a system of linear equations

  4. All of the above


Correct Option: D
Explanation:

Mahavira made several important contributions to algebra, including the development of new methods for solving equations, the use of negative numbers, and the development of a system of linear equations.

What is one of Mahavira's methods for solving equations?

  1. The method of completing the square

  2. The method of substitution

  3. The method of elimination

  4. The method of false position


Correct Option: D
Explanation:

The method of false position is a method for solving equations that involves making an initial guess for the solution and then using that guess to find a better approximation. Mahavira was one of the first mathematicians to use this method.

What is the name of the system of linear equations that Mahavira developed?

  1. The Gaussian elimination method

  2. The Cramer's rule method

  3. The Gauss-Jordan elimination method

  4. The Laplace expansion method


Correct Option: C
Explanation:

The Gauss-Jordan elimination method is a method for solving systems of linear equations that involves using elementary row operations to transform the system into an equivalent system that is easier to solve. Mahavira was one of the first mathematicians to develop this method.

What is one of Mahavira's contributions to the use of negative numbers?

  1. He was the first mathematician to use negative numbers.

  2. He developed a system for representing negative numbers.

  3. He used negative numbers to solve equations.

  4. All of the above


Correct Option: D
Explanation:

Mahavira was one of the first mathematicians to use negative numbers. He developed a system for representing negative numbers and used them to solve equations.

What is the name of the symbol that Mahavira used to represent negative numbers?

  1. A minus sign (-)

  2. A dot (.)

  3. A bar (-)

  4. A circle (o)


Correct Option: B
Explanation:

Mahavira used a dot (.) to represent negative numbers. This symbol was later adopted by other mathematicians and is still used today.

What is one of Mahavira's contributions to the development of a system of linear equations?

  1. He was the first mathematician to develop a system of linear equations.

  2. He developed a method for solving systems of linear equations.

  3. He used systems of linear equations to solve problems in geometry.

  4. All of the above


Correct Option: D
Explanation:

Mahavira was one of the first mathematicians to develop a system of linear equations. He also developed a method for solving systems of linear equations and used them to solve problems in geometry.

What is the name of the problem that Mahavira used to illustrate the use of systems of linear equations?

  1. The problem of the two jars

  2. The problem of the three jars

  3. The problem of the four jars

  4. The problem of the five jars


Correct Option: A
Explanation:

Mahavira used the problem of the two jars to illustrate the use of systems of linear equations. The problem involves two jars that contain different amounts of water and asks how much water must be transferred from one jar to the other in order to make the amounts of water in the two jars equal.

What is the solution to the problem of the two jars?

  1. Transfer 3 units of water from the first jar to the second jar.

  2. Transfer 5 units of water from the first jar to the second jar.

  3. Transfer 7 units of water from the first jar to the second jar.

  4. Transfer 9 units of water from the first jar to the second jar.


Correct Option: B
Explanation:

The solution to the problem of the two jars is to transfer 5 units of water from the first jar to the second jar. This will make the amounts of water in the two jars equal.

What is one of Mahavira's contributions to the development of algebra?

  1. He developed new methods for solving equations.

  2. He used negative numbers to solve equations.

  3. He developed a system of linear equations.

  4. All of the above


Correct Option: D
Explanation:

Mahavira made several important contributions to the development of algebra, including the development of new methods for solving equations, the use of negative numbers to solve equations, and the development of a system of linear equations.

What is the name of the book that Mahavira wrote on algebra?

  1. Ganita Sara Sangraha

  2. Lilavati

  3. Bijaganita

  4. Siddhanta Shiromani


Correct Option: A
Explanation:

Ganita Sara Sangraha is a book on algebra written by Mahavira in the 9th century. It is one of the earliest known works on algebra and contains many important contributions to the field.

What is the main topic of the Ganita Sara Sangraha?

  1. Arithmetic

  2. Geometry

  3. Algebra

  4. Trigonometry


Correct Option: C
Explanation:

The Ganita Sara Sangraha is a book on algebra. It covers a wide range of topics, including solving equations, using negative numbers, and developing a system of linear equations.

What is one of Mahavira's most important contributions to algebra?

  1. The development of new methods for solving equations

  2. The use of negative numbers

  3. The development of a system of linear equations

  4. All of the above


Correct Option: D
Explanation:

Mahavira made several important contributions to algebra, including the development of new methods for solving equations, the use of negative numbers, and the development of a system of linear equations.

What is one of Mahavira's methods for solving equations?

  1. The method of completing the square

  2. The method of substitution

  3. The method of elimination

  4. The method of false position


Correct Option: D
Explanation:

The method of false position is a method for solving equations that involves making an initial guess for the solution and then using that guess to find a better approximation. Mahavira was one of the first mathematicians to use this method.

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