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


b representing an integer as sum of positive and negative integers


crepresenting an integer as sum of positive integers


drepresenting an integer as sum of positive real numbers



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


a2


b4


c6


d8


View Answer 6

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


a 2


b 4


c6


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


b5


c4


d7


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


bEuler’s omega function


cCauchy’s totient function


d Legrange’s function



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


b25


c 26


d 33


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


b false


cA & B


dNone of these


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


bexcluding cardinalities of pairwise intersections


c excluding cardinalities of triple-wise intersections


dexcluding cardinalities of quadraple-wise intersections



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|


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


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


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



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


aTrue


bFalse


cA & B


dNone of these


View Answer False

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