Combinatorics

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    Question 1

    How many onto (or surjective) functions are there from an n-element (n >= 2) set to a 2-element set?
     

    • 2(2n - 2)
       

    • 2n - 2
       

    • 2n - 1
       

    • 2n
       

    Question 2

    What is the possible number of reflexive relations on a set of 5 elements?
     

    • 225
       

    • 220
       

    • 215
       

    • 210
       

    Question 3

    There are 100 students. 85 choose Math, 80 choose Physics, 75 choose Chemistry, 70 choose Biology. What is the minimum number of students choosing all 4 subjects? Assume each student chosen at least one subject.
    • 15
    • 10
    • 5
    • Data is insufficient

    Question 4

    A dice is thrown. Let A be the event that the number obtained is greater than 5. Let B be the event that the number obtained is less than 5. Then P (AUB) is
    • 5/6
    • 2/6
    • 3/6
    • None of these

    Question 5

    Let G be a group of order 6, and H be a subgroup of G such that 1<|H|<6. Which one of the following options is correct?


    • Both G and H are always cyclic

    • G may not be cyclic, but H is always cyclic

    • G is always cyclic, but H may not be cyclic

    • Both G and H may not be cyclic

    Question 6

    There are 6 jobs with distinct difficulty levels, and 3 computers with distinct processing speeds. Each job is assigned to a computer such that:

    • The fastest computer gets the toughest job and the slowest computer gets the easiest job.
    • Every computer gets at least one job.

    The number of ways in which this can be done is ___________.

    • 65

    • 81

    • 36

    • 16

    Question 7

    The number of bit strings of length 8 that will either start with 1 or end with 00 is?

    • 32

    • 128

    • 160

    • 192

    Question 8

    How many substrings of different length (non-zero) can be formed from a character string of length n ?

    • n

    • n2

    • 2n

    • n(n+1)/2

    Question 9

    Two girls have picked 10 roses, 15 sunflowers and 14 daffodils. What is the number of ways they can divide the flowers amongst  themselves?
    • 1638
    • 2100
    • 2640
    • None of the above

    Question 10

    Which one the following is a closed form expression for the generating function of the sequence {an}, where an = 2n + 3 for all n = 0, 1, 2,...?

    2018cs


    • A

    • B

    • C

    • D

    There are 22 questions to complete.

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