Capella MAT2051 All Quizzes Latest 2020 February

MAT2051 Discrete Mathematics

Unit 2 Quiz 1

Question 1What is a set?

Answers:            

a. An unordered collection of objects.

b. An ordered collection of objects.

c. The study of reasoning.

d. A partition of numbers.

Answer Feedback:          .

Question 2What is the cardinality of the set X = {1, 5, 3, 8, 10}?

Answers:            

a. 5.

b. 1.

c. 10.

d. 27.

Question 3          What value replaces ?in the following truth table?

Answers:            

a. 0.

b. 1.

c. Cannot solve with the given information.

d. Can be either 0 or 1.

Question 4Let:

P: Jerry receives a scholarship.

Q: Jerry goes to college.

Assume the statement P  → Q is true.

If Jerry does not go to college, did he receive his scholarship?

Answers:            

a. Yes, because the converse of the statement is true.

b. No, because the contrapositive of the statement is true.

c. There is not enough information.

d. Can be either.

Question 5          What is deductive reasoning?

Answers:            

a. A hypothesis together with a conclusion.

b. Valid arguments of a hypothesis.

c. The process of drawing a conclusion from a sequence of propositions.

d. A simplification of the rules of inference.

 

MAT2051 Discrete Mathematics

Unit 4 Quiz2

Question 1          How many different eight-bit strings begin with 100?

Answers:            

a. 4.

b. 32.

c. 64.

d. 16.

Answer Feedback:          .

Question 2How many strings can be formed using the letters in the word router (that is, R-O-U-T-E-R)?

Answers:            

a. 6!/2!

b. C(6, 1).

c. (6 1)!

d. C(1, 6).

Question 3          There are 100 processors, 30 of which are defective. If you select 20 microprocessors from these 100 microprocessors, what is the probability that you select no defective processors?

Answers:            

a. C(100, 10)/C(30, 20).

b. C(100, 20).

c. C(100, 20)/C(70, 20).

d. C(70, 20)/C(100, 20).

Question 4          What is the probability of drawing a queen from a standard deck of cards?

a. 2/52.

b. 10%.

c. 8/52.

d. 4/52.

Answer Feedback:          .

Question 5          Assume the probability of having a boy or a girl is the same. If a family has five children, what is the probability that they are all boys?

Answers:            

a. 1/32.

b. 1/16.

c. 1/2 + 1/2 + 1/2 + 1/2 + 1/2.

d. 1/2.

 

 

 

MAT2051 Discrete Mathematics

Unit 6 Quiz 3

Question 1          How many times does the computer print the string “Hello”?

i = 2

while (i < 4) {

print (“Hello”)

i = i + 1}:

Answers:            

a. 1.

b. 2.

c. 3.

d. 4.

Question 2Which of the following is O(n)?

Answers:            

a. 3n + 1.

b. n * log(n).

c. n * n + n.

d. None of the above.

Question 3          If each of the following describes the run time of an algorithm, which of the following could have the longest run time?

Answers:            

a. O(nlog(n)).

b. O(n!).

c. O(n/2).

d. O(n * n).

Question 4What does the following algorithm return?

f(n){

if (n< 2)

return 1

else

return f(n – 1) * n:

Answers:            

a. n!

b. The maximum divisor of n.

c. (n – 1)!

d. n 2.

.Question 5         Given that S_n denotes the number of n-bit strings that do not contain the pattern 00, what are the initial conditions?

Answers:            

a. S_1 = 2, S_2 =3.

b. S_1 = 1, S_2 =2.

c. S_1 = 0, S_2 =2.

d. None of the above.

 

 

MAT2051 Discrete Mathematics

Unit 8 Quiz 4

Question 1          Is a graph a tree? Is a tree a graph?

a. Yes, Yes.

b. No, Yes.

c. Yes, No.

d. No, No.

Question 2Given a graph with n vertices, what is the minimum number of edges needed to make the graph connected?

Answers:            

a. n.

b. n – 1.

c. n * n.

d. n log n.

Question 3Given the graph below, what type of path is path (A, D, E, C, B)?

Graph A-E. [D]

 Answers:           

a. Simple Path.

b. Cycle.

c. Simple cycle.

d. None of the above.

Question 4          Given the graph below, which of the following is a Hamiltonian cycle?

Answers:            

a. (A, D, B).

b. (A, D, B, C, E, D, A).

c. (B, C, E, D, A, B).

d. (C, E, D, A, C).

Question 5          Given the graph below, what is the total weight of the shortest weighted path from A to E:

Answers:            

a. 8.

b. 5.

c. 4.

d. 3.

 

MAT2051 Discrete Mathematics

Unit 10 Quiz 5 

Question 1Given an unordered list of n numbers, what algorithm would you use to sort it, and what is the worst-case runtime of the algorithm?

Answers:            

a. Tournament sort, O(n log n).

b. Tournament sort, O(n).

c. Prim’s Algorithm, O(n log n).

d. Prim’s Algorithm, O(n * n).

Question 2Given a graph with n vertices, what is the minimum number of edges needed such that the graph is connected?

Answers:            

a. n.

b. n – 1.

c. n * n.

d. n log n.

Question 3Which is a minimal spanning tree of the following graph:

Graph A-E.[D]

Answers:            

a. A-B-D-E-C.

b. A-D-E-C-B.

c. A-B-D.

d. There is no minimal spanning tree.

Question 4How many six-bit strings begin with 100?

Answers:            

a. 4.

b. 8.

c. 32.

d. 16.

Question 5If you select 5 microprocessors from 100 microprocessors, where 30 of the 100 are defective, what is the probability that you select no defective processors?

Answers:            

a. C(100, 10)/C(30, 5).

b. C(70, 5)/C(100, 5).

c. C(100, 5).

d. C(100, 5)/C(70, 5).