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.

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 10 of 12

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Q91.

In a blindfolded game, a boy can hit the target 8 times out of 12. If he fired 8 shots, find out the probability of more than 4 hits?

2.530

0.1369

0.5938

3.998

Discuss

Answer: (c).0.5938

Q92.

A fair coin is tossed 15 times. Determine the probability in which no heads turned up.

2.549 * 10⁻³

0.976

3.051 * 10⁻⁵

5.471

Discuss

Answer: (c).3.051 * 10⁻⁵

Q93.

When a programmer compiles her code there is a 95% chance of finding a bug every time. It takes three hours to rewrite her code when she finds out a bug. Determine the probability such that she will finish her coding by the end of her workday. (Assume, a workday is 7 hours)

0.065

0.344

0.2

3.13

Discuss

Answer: (c).0.2

Q94.

Determine the probability when a die is thrown 2 times such that there are no fours and no fives occur?

4/9

56/89

13/46

3/97

Discuss

Answer: (a).4/9

Q95.

In earlier days, there was a chance to make a telephone call would be of 0.6. Determine the probability when it could make 11 successes in 20 attempts of phone call.

0.2783

0.2013

0.1597

3.8561

Discuss

Answer: (c).0.1597

Q96.

By the expression \(\left(\frac{x}{3} + \frac{1}{x}\right)^5\), evaluate the middle term in the expression.

10*(x⁵)

\(\frac{1}{5}*(\frac{x}{4})\)

10*(\(\frac{x}{3}\))

6*(x³)

Discuss

Answer: (c).10*(\(\frac{x}{3}\))

Q97.

Evaluate the expression (y+1)⁴ – (y-1)⁴.

3y² + 2y⁵

7(y⁴ + y² + y)

8(y³ + y¹)

y + y² + y³

Discuss

Answer: (c).8(y³ + y¹)

Q98.

Find the coefficient of x⁷ in (x+4)⁹.

523001

428700

327640

129024

Discuss

Answer: (d).129024

Q99.

Determine the 7th term in the expansion of (x-2y)¹².

6128y⁷

59136y⁶

52632x⁶

39861y⁵

Discuss

Answer: (b).59136y⁶

Q100.

What is the middle term in the expansion of (x/2 + 6y)⁸?

45360x⁴

34210x³

1207x⁴

3250x⁵

Discuss

Answer: (a).45360x⁴

Page 10 of 12

Welcome to the Counting Theory MCQs Page

Counting Theory MCQs | Page 10 of 12

Explore more Topics under Discrete Mathematics

Logics and Proofs

Sets and Functions

Sequences,Sums and Matrices

Algorithms

Number Theory and Cryptography

Induction and Recursion

Discrete Probability

Relations

Graphs and Graphs Properties

Tree Properties

Boolean Algebra and Modeling Computations

Group Theory

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