adplus-dvertising

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.

frame-decoration

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

Suggested Topics

Are you eager to expand your knowledge beyond Discrete Mathematics? We've curated a selection of related categories that you might find intriguing.

Click on the categories below to discover a wealth of MCQs and enrich your understanding of Computer Science. Happy exploring!

Operating System

Dive deep into the core of computers with our Operating System MCQs. Learn about...

Cryptography and Network Security

Secure your knowledge of information security with our Cryptography and Network...

DBMS

Get a firm grasp on database systems with our DBMS MCQs. Explore relational...

CompTIA PenTest+ Certification Exam PT0 002

Prepare for the CompTIA PenTest+ PT0-002 exam with our targeted MCQs. Covering...

PHP

Venture into server-side scripting with our PHP MCQs. Cover everything from syntax...

MySQL Database

Enhance your knowledge of relational databases with our MySQL MCQs. Understand...

Web Technologies

Master the building blocks of the web with our Web Technologies MCQs. From HTML and...

Systems Analysis and Design Methods

Get familiar with the process of designing and improving business systems with our...

R Programming

Unleash the power of statistical computing with our R Programming MCQs. Topics cover...