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Discrete Mathematics | Pigeonhole Principle and Recurrence Relations MCQs

Discrete Mathematics | Pigeonhole Principle and Recurrence Relations MCQs: This section contains multiple-choice questions and answers on Pigeonhole Principle and Recurrence Relations in Discrete Mathematics.
Submitted by Anushree Goswami, on July 20, 2022

1. A pigeonhole is occupied by more than one pigeon if n pigeonholes are occupied by ___ or more pigeons?

1. n
2. n+1
3. n-1
4. None of the above

Answer: B) n+1

Explanation:

A pigeonhole is occupied by more than one pigeon if n pigeonholes are occupied by n+1 or more pigeons.

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2. There must be at least one pigeonhole occupied by k+1 or more pigeons if n pigeonholes are occupied by ___ or more pigeons, where k is a positive integer?

1. k+1
2. n+1
3. kn+1
4. kn-1

Answer: C) kn+1

Explanation:

There must be at least one pigeonhole occupied by k+1 or more pigeons if n pigeonholes are occupied by kn+1 or more pigeons, where k is a positive integer.

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3. There are various orders of differences of f (x) in a ____ relationship between the independent variable x and the dependent variable f(x)?

1. Occurrence
2. Recurrence
3. Deviant
4. Variable

Answer: B) Recurrence

Explanation:

There are various orders of differences of f (x) in a recurrence relationship between the independent variable x and the dependent variable f(x)

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4. Recurrence relation can be used interchangeably with a ____ to refer to a recurrence relation?

1. Dividend Equation
2. Divisional Equation
3. Difference Equation
4. Data Equation

Answer: C) Difference Equation

Explanation:

Recurrence relation can be used interchangeably with a difference equation to refer to a recurrence relation.

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5. It is defined as the difference between ____ highest and lowest subscripts to determine the order of the recurrence relation or difference equation?

1. f(x)
2. a_r=y_k
3. Both A and B
4. None of the above

Answer: C) Both A and B

Explanation:

It is defined as the difference between f(x) or a_r=y_k highest and lowest subscripts to determine the order of the recurrence relation or difference equation.

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6. Defining degree of a difference equation as the ____ power of f (x) or a_r=y_k?

1. Highest
2. Lowest
3. Average
4. Middle

Answer: A) Highest

Explanation:

Defining degree of a difference equation as the highest power of f (x) or a_r=y_k.

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