Data Structures Algorithms-II MCQs

Page No. 53

What is meant by integer partition?


a representing an integer as sum of positive and negative real numbers

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b representing an integer as sum of positive and negative integers

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crepresenting an integer as sum of positive integers

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drepresenting an integer as sum of positive real numbers

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Number of elements in the power set of set S={1,2,2} will be?


a2

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b4

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c6

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d8

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View Answer 6

Number of elements in the power set of set S={1,2,3} will be?


a 2

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b 4

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c6

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d8

✓


View Answer 8

Let A={1,2,3} B={2,3,4} C={1,3,5} D={2,3}. Find the cardinality of sum of all the sets.


a6

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b5

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c4

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d7

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View Answer 5

. ____________ is an arithmetic function that calculates the total number of positive integers less than or equal to some number n, that are relatively prime to n.


aEuler’s phi function

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bEuler’s omega function

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cCauchy’s totient function

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d Legrange’s function

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Using the inclusion-exclusion principle, find the number of integers from a set of 1-100 that are not divisible by 2, 3 and 5.


a 22

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b25

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c 26

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d 33

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View Answer 26

Counting intersections can be done using the inclusion-exclusion principle only if it is combined with De Morgan’s laws of complementing.


atrue

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b false

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cA & B

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dNone of these

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View Answer true

Which of the following statement is incorrect with respect to generalizing the solution using the inclusion-exclusion principle?


a including cardinalities of sets

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bexcluding cardinalities of pairwise intersections

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c excluding cardinalities of triple-wise intersections

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dexcluding cardinalities of quadraple-wise intersections

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With reference to the given Venn diagram, what is the formula for computing |AUBUC| (where |x, y| represents intersection of sets x and y)?


a|A U B U C|=|A|+|B|+|C|-|A,B|-|A,C|-|B,C|+|A, B,C|

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b|A, B,C|=|A|+|B|+|C|-|A U B|-|A U C|-|B U C|+|A U B U C|

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c|A, B,C|=|A|+|B|+|C|+|A,B|-|A,C|+|B,C|+|A U B U C|

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d|A U B U C|=|A|+|B|+|C| + |A,B| + |A,C| + |B,C|+|A, B,C|

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According to inclusion-exclusion principle, a n-tuple wise intersection is included if n is even.


aTrue

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bFalse

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cA & B

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dNone of these

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View Answer False

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