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Welcome to the Counting Theory MCQs Page

Dive deep into the fascinating world of Counting Theory with our comprehensive set of Multiple-Choice Questions (MCQs). This page is dedicated to exploring the fundamental concepts and intricacies of Counting Theory, a crucial aspect of Discrete Mathematics. In this section, you will encounter a diverse range of MCQs that cover various aspects of Counting Theory, from the basic principles to advanced topics. Each question is thoughtfully crafted to challenge your knowledge and deepen your understanding of this critical subcategory within Discrete Mathematics.

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Check out the MCQs below to embark on an enriching journey through Counting Theory. Test your knowledge, expand your horizons, and solidify your grasp on this vital area of Discrete Mathematics.

Note: Each MCQ comes with multiple answer choices. Select the most appropriate option and test your understanding of Counting Theory. You can click on an option to test your knowledge before viewing the solution for a MCQ. Happy learning!

Counting Theory MCQs | Page 8 of 12

Explore more Topics under Discrete Mathematics

Q71.
The linear system Cx = d is known as _________ if d! = 0.

a.

homogeneous

b.

heterogeneous

c.

nonhomogeneous

d.

augmented system

Discuss
Answer: (c).nonhomogeneous
Q72.
Every linear equation determines a _______ in n-dimensional space for n variables.

a.

shipshape

b.

hyperplane

c.

cone

d.

pyramid

Discuss
Answer: (b).hyperplane
Q73.
Determine all possibilities for the number of solutions of the system of 7 equations in 5 unknowns and it has x₁ = 0, x₂ = −6, and x₃ = 4 as a solution.

a.

unique or infinitely many

b.

unique

c.

finitely many

d.

zero

Discuss
Answer: (a).unique or infinitely many
Q74.
Determine all possibilities for the solution set of the homogeneous system that has y₁ = 6, y₂ = −4, y₃ = 0 as a solution.

a.

zero

b.

infinitely many

c.

finitely many

d.

only one

Discuss
Answer: (b).infinitely many
Q75.
Determine all possibilities for the solution set of the homogeneous system of 5 equations in 3 unknowns and the rank of the system is 3.

a.

more than two

b.

only one

c.

zero

d.

infinite

Discuss
Answer: (c).zero
Q76.
Determine all possibilities for the solution set of a homogeneous system that has y₁ = 5, y₂ = −3, y₃ = 2 as a solution.

a.

one

b.

finitely many

c.

infinitely many

d.

either one or infinitely many

Discuss
Answer: (c).infinitely many
Q77.
Determine all possibilities for the solution set of the system of 2 equations in 3 unknowns that has x₁ = 4, x₂ = −7, x₃ = 0 as a solution.

a.

one or finitely many

b.

infinite

c.

finite

d.

zero

Discuss
Answer: (b).infinite
Q78.
Determine all possibilities for the solution set of a homogeneous system of 4 equations in 4 unknowns.

a.

only one

b.

finitely many or zero

c.

zero

d.

one or infinitely many

Discuss
Answer: (b).finitely many or zero
Q79.
Determine all possibilities for the solution set of a homogeneous system of 6 equations in 5 unknowns.

a.

only one

b.

zero

c.

one or infinitely many

d.

finitely many

Discuss
Answer: (c).one or infinitely many
Q80.
Determine all possibilities for the solution set of a homogeneous system of 5 equations in 4 unknowns and the rank of the system is 3.

a.

finite

b.

zero or finitely many

c.

only one

d.

infinite

Discuss
Answer: (d).infinite
Page 8 of 12

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