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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 12 of 12

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Q111.
Determine the solution of the recurrence relation Fₙ=20Fₙ₋₁ − 25Fₙ₋₂ where F₀=4 and F₁=14.

a.

aₙ = 14*5ⁿ⁻¹

b.

aₙ = 7/2*2ⁿ−1/2*6ⁿ

c.

aₙ = 7/2*2ⁿ−3/4*6ⁿ⁺¹

d.

aₙ = 3*2ⁿ−1/2*3ⁿ

Discuss
Answer: (b).aₙ = 7/2*2ⁿ−1/2*6ⁿ
Q112.
What is the recurrence relation for 1, 7, 31, 127, 499?

a.

bₙ₊₁=5bₙ₊₁+3

b.

bₙ=4bₙ+7!

c.

bₙ=4bₙ₋₁+3

d.

bₙ=bₙ₋₁+1

Discuss
Answer: (c).bₙ=4bₙ₋₁+3
Q113.
If Sₙ=4Sₙ₋₁+12n, where S₀=6 and S₁=7, find the solution for the recurrence relation.

a.

aₙ=7(2ⁿ)−29/6n6ⁿ

b.

aₙ=6(6ⁿ)+6/7n6ⁿ

c.

aₙ=6(3ⁿ⁺¹)−5n

d.

aₙ=nn−2/6n6ⁿ

Discuss
Answer: (b).aₙ=6(6ⁿ)+6/7n6ⁿ
Q114.
Find the value of a₄ for the recurrence relation aₙ=2aₙ₋₁+3, with a₀=6.

a.

320

b.

221

c.

141

d.

65

Discuss
Answer: (c).141
Q115.
The solution to the recurrence relation aₙ=aₙ₋₁+2n, with initial term a₀=2 are _________

a.

4n+7

b.

2(1+n)

c.

3n²

d.

5*(n+1)/2

Discuss
Answer: (b).2(1+n)
Q116.
Determine the solution for the recurrence relation bₙ=8bₙ₋₁−12bₙ₋₂ with b₀=3 and b₁=4.

a.

7/2*2ⁿ−1/2*6ⁿ

b.

2/3*7ⁿ-5*4ⁿ

c.

4!*6ⁿ

d.

2/8ⁿ

Discuss
Answer: (a).7/2*2ⁿ−1/2*6ⁿ
Q117.
What is the solution to the recurrence relation aₙ=5aₙ₋₁+6aₙ₋₂?

a.

2n²

b.

6n

c.

(3/2)n

d.

n!*3

Discuss
Answer: (b).6n
Q118.
Determine the value of a₂ for the recurrence relation aₙ = 17aₙ₋₁ + 30n with a₀=3.

a.

4387

b.

5484

c.

238

d.

1437

Discuss
Answer: (d).1437
Q119.
Determine the solution for the recurrence relation aₙ = 6aₙ₋₁−8aₙ₋₂ provided initial conditions a₀=3 and a₁=5.

a.

aₙ = 4 * 2ⁿ – 3ⁿ

b.

aₙ = 3 * 7ⁿ – 5*3ⁿ

c.

aₙ = 5 * 7ⁿ

d.

aₙ = 3! * 5ⁿ

Discuss
Answer: (b).aₙ = 3 * 7ⁿ – 5*3ⁿ
Page 12 of 12

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