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Combinatorics and Permutations in Indian Mathematics

Description: This quiz covers the concepts of combinatorics and permutations in Indian mathematics. It explores the contributions of Indian mathematicians in these fields and their applications in various areas.
Number of Questions: 15
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Tags: combinatorics permutations indian mathematics mathematical concepts
Attempted 0/15 Correct 0 Score 0

In the ancient Indian text, Lilavati, what is the term used for combinations?

  1. Samyoga

  2. Vyavakalpa

  3. Krama

  4. Varga


Correct Option: B
Explanation:

Vyavakalpa is the term used in Lilavati to refer to combinations.

Who is considered the father of Indian combinatorics?

  1. Aryabhata

  2. Bhaskara II

  3. Brahmagupta

  4. Varahamihira


Correct Option: C
Explanation:

Brahmagupta is widely regarded as the father of Indian combinatorics due to his significant contributions to the field.

What is the formula for calculating the number of permutations of n distinct objects?

  1. n!

  2. n + 1

  3. n - 1

  4. n^2


Correct Option: A
Explanation:

The formula for calculating the number of permutations of n distinct objects is n!, where n! represents the factorial of n.

In the context of Indian mathematics, what is the term used for permutations?

  1. Krama

  2. Vyavakalpa

  3. Samyoga

  4. Varga


Correct Option: A
Explanation:

Krama is the term used in Indian mathematics to refer to permutations.

Which Indian mathematician developed the concept of the Pascal's triangle?

  1. Aryabhata

  2. Bhaskara II

  3. Brahmagupta

  4. Varahamihira


Correct Option: B
Explanation:

Bhaskara II developed the concept of the Pascal's triangle, which is a triangular array of binomial coefficients.

What is the formula for calculating the number of combinations of n distinct objects taken r at a time?

  1. nCr

  2. nPr

  3. n!

  4. n + r


Correct Option: A
Explanation:

The formula for calculating the number of combinations of n distinct objects taken r at a time is nCr, where nCr represents the binomial coefficient.

Which Indian mathematician provided a systematic treatment of permutations and combinations in his work, the Lilavati?

  1. Aryabhata

  2. Bhaskara II

  3. Brahmagupta

  4. Varahamihira


Correct Option: B
Explanation:

Bhaskara II provided a systematic treatment of permutations and combinations in his work, the Lilavati.

What is the term used in Indian mathematics to refer to the arrangement of objects in a specific order?

  1. Krama

  2. Vyavakalpa

  3. Samyoga

  4. Varga


Correct Option: A
Explanation:

Krama is the term used in Indian mathematics to refer to the arrangement of objects in a specific order.

In the context of Indian mathematics, what is the term used for the selection of objects without regard to order?

  1. Krama

  2. Vyavakalpa

  3. Samyoga

  4. Varga


Correct Option: B
Explanation:

Vyavakalpa is the term used in Indian mathematics to refer to the selection of objects without regard to order.

Which Indian mathematician developed the concept of the Catalan numbers?

  1. Aryabhata

  2. Bhaskara II

  3. Brahmagupta

  4. Varahamihira


Correct Option: C
Explanation:

Brahmagupta developed the concept of the Catalan numbers, which are a sequence of natural numbers that occur in various combinatorial problems.

What is the formula for calculating the number of ways to arrange n distinct objects in a circle?

  1. n!

  2. n + 1

  3. n - 1

  4. (n-1)!


Correct Option: D
Explanation:

The formula for calculating the number of ways to arrange n distinct objects in a circle is (n-1)!, where (n-1)! represents the factorial of (n-1).

Which Indian mathematician provided a method for solving linear equations using permutations and combinations?

  1. Aryabhata

  2. Bhaskara II

  3. Brahmagupta

  4. Varahamihira


Correct Option: C
Explanation:

Brahmagupta provided a method for solving linear equations using permutations and combinations.

What is the term used in Indian mathematics to refer to the grouping of objects into subsets?

  1. Krama

  2. Vyavakalpa

  3. Samyoga

  4. Varga


Correct Option: C
Explanation:

Samyoga is the term used in Indian mathematics to refer to the grouping of objects into subsets.

Which Indian mathematician developed the concept of the Fibonacci numbers?

  1. Aryabhata

  2. Bhaskara II

  3. Brahmagupta

  4. Varahamihira


Correct Option: C
Explanation:

Brahmagupta developed the concept of the Fibonacci numbers, which are a sequence of numbers where each number is the sum of the two preceding ones.

What is the term used in Indian mathematics to refer to the division of a set of objects into equal parts?

  1. Krama

  2. Vyavakalpa

  3. Samyoga

  4. Varga


Correct Option: D
Explanation:

Varga is the term used in Indian mathematics to refer to the division of a set of objects into equal parts.

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