Combinatorics

Question 11

How many 4-digit even numbers have all 4 digits distinct?

• 4536
  

• 2620
  

• 2296
  

• 2240
  

Question 12

For a set A, the power set of A is denoted by 2^A. If A = {5, {6}, {7}}, which of the following options are True.

• I and III only
• II and III only
• I, II and III only
• I, II and IV only

Question 13

The number of 4 digit numbers having their digits in non-decreasing order (from left to right) constructed by using the digits belonging to the set {1, 2, 3} is ____.

• 12

• 13

• 14

• 15

Question 14

The number of binary strings of n zeros and k ones such that no two ones are adjacent is:

• a
• b
• c
• d

Question 15

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

• A
• B
• C
• D

Question 16

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 17

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 18

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

• 32
• 128
• 160
• 192

Question 19

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 20

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