Data Structure Questions and Answers-Generating Partitions

 

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Data Structure Questions and Answers-Generating Partitions

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Question 1
What is meant by integer partition?
A
representing an integer as sum of positive and negative real numbers
B
representing an integer as sum of positive and negative integers
C
representing an integer as sum of positive integers
D
representing an integer as sum of positive real numbers
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Question 1 Explanation: 
Integer partition is the way of representing an integer as sum of positive integers. Partitions differing only in their order are considered to be same.

Question 2
How many partitions will be formed for the integer 3?
A
2
B
3
C
4
D
8
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Question 2 Explanation: 
We need to find the combinations of positive integers which give 3 as their sum. These will be {3}, {2, 1}, {1, 1, 1}. Thus the correct answer is 3.

Question 3
What is meant by number theory?
A
study of integers
B
study of complex numbers
C
numerology
D
theory of origination of mathematics
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Question 3 Explanation: 
Number theory is a branch of mathematics that deals with the study of integers. Partitioning of a number comes under the study of number theory.

Question 4
Which of the following is true according to Ramanujan's congruence?
A
No. of partitions are divisible by 5 for a number 3 more than a multiple of 5
B
No. of partitions are divisible by 5 for a number 4 more than a multiple of 5
C
No. of partitions are divisible by 5 for a number 2 more than a multiple of 5
D
No. of partitions are divisible by 5 for a number 1 more than a multiple of 5
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Question 4 Explanation: 
Ramanujan's congruence are some relations found for the no. of partitions of an integer. According to it, the number of partitions of an integer is divisible by 5 if that integer is 4 more than a multiple of 5.

Question 5
The no. of partitions of which of the following integer will be divisible by 5?
A
3
B
5
C
9
D
6
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Question 5 Explanation: 
According to Ramanujan's congruence number of partitions of an integer is divisible by 5 if that integer is 4 more than a multiple of 5. So out of the given options 9 is the only integer which satisfies this condition.

There are 5 questions to complete.

 

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