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
     

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Question 2

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

  • 225
     

  • 220
     

  • 215
     

  • 210
     

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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
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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
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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

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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

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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

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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

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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
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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

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There are 22 questions to complete.

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