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Discrete Mathematics | Total Solution and Generating Functions MCQs

Discrete Mathematics | Total Solution and Generating Functions MCQs: This section contains multiple-choice questions and answers on Total Solution and Generating Functions in Discrete Mathematics.
Submitted by Anushree Goswami, on July 23, 2022

1. Non-homogeneous linear difference equations with constant coefficients have a total or general solution which is the sum of ____ solutions?

1. Homogeneous
2. Particular
3. Both A and B
4. None of the above

Answer: C) Both A and B

Explanation:

Non-homogeneous linear difference equations with constant coefficients have a total or general solution which is the sum of homogeneous and particular solutions.

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2. You should obtain _____, if possible, and solve them in order to get the total solution if no initial conditions are given?

1. n linear equations
2. n unknowns
3. Both A and B
4. None of the above

Answer: C) Both A and B

Explanation:

You should obtain n linear equations with n unknowns, if possible, and solve them in order to get the total solution if no initial conditions are given.

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3. The total solution or general solution of the recurrence relation will be given by _____, if y_(h) denotes the homogeneous solution and y_(p) denotes the particular solution?

1. y =y_(h)/y_(p)
2. y =y_(h)+y_(p)
3. y =y_(h)-y_(p)
4. y =y_(h)*y_(p)

Answer: B) y =y_(h)+y_(p)

Explanation:

The total solution or general solution of the recurrence relation will be given by y =y_(h)+y_(p), if y_(h) denotes the homogeneous solution and y_(p) denotes the particular solution.

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4. Recurrence relations can be solved by ____?

1. Recurrence functions
2. Total functions
3. Generating functions
4. Partial functions

Answer: C) Generating functions

Explanation:

Recurrence relations can be solved by generating functions.

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5. The generating function of Z^r,(Z≠0 and Z is a constant and |Zt|<1)is given by -?

1. G (t) = 1
2. G (t) = 1/Zt
3. G (t) = 1/(Zt-1)
4. G (t) = 1/(1-Zt)

Answer: D) G (t) = 1/(1-Zt)

Explanation:

The generating function of Z^r,(Z≠0 and Z is a constant and |Zt|<1)is given by - G (t) = 1/(1-Zt).

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6. In which of the following condition(s) can generating function be used?

1. Recurrence relations can be solved using this method
2. Several combinatorial identities can be proved using this method
3. In order to find asymptotic formulas for sequence terms
4. All of the above

Answer: D) All of the above

Explanation:

In the following conditions can generating function be used -

1. Recurrence relations can be solved using this method
2. Several combinatorial identities can be proved using this method
3. In order to find asymptotic formulas for sequence terms

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