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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.


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.


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)


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.


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. ar=yk
  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 ar=yk highest and lowest subscripts to determine the order of the recurrence relation or difference equation.


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

  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 ar=yk.





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