Discrete Mathematics | Particular Solution MCQs

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

1. By putting the ____ conditions into the homogeneous solutions, we can find the particular solution of the difference equation?

  1. Initial
  2. Middle
  3. Final
  4. Transition

Answer: A) Initial

Explanation:

By putting the initial conditions into the homogeneous solutions, we can find the particular solution of the difference equation.


2. Non-homogeneous linear difference equations can be solved using ___ methods?

  1. Two
  2. Three
  3. Four
  4. Five

Answer: A) Two

Explanation:

Non-homogeneous linear difference equations can be solved using two methods.


3. What is/are the correct method(s) used to solve nonhomogeneous linear difference equations?

  1. Undetermined coefficients method
  2. E and ∆ operator method.
  3. Both A and B
  4. None of the above

Answer: C) Both A and B

Explanation:

The correct methods used to solve nonhomogeneous linear difference equations are Undetermined coefficients method and E and ∆ operator method.


4. A non-homogeneous linear difference equation whose ____ consists of terms of special forms can be solved using the Undetermined Coefficients Method?

  1. R.H.S R (n)
  2. L.H.S L (n)
  3. Both A and B
  4. None of the above

Answer: A) R.H.S R (n)

Explanation:

A non-homogeneous linear difference equation whose R.H.S term R (n) consists of terms of special forms can be solved using the Undetermined Coefficients Method.


5. What is TRUE about Undermined Coefficients Method -?

  1. Our first assumption is that the particular solutions are based on the type of R (n), with some unknown constant coefficients.
  2. We will then determine the exact solution based on the difference equation.
  3. Both A and B
  4. None of the above

Answer: C) Both A and B

Explanation:

In Undetermined Coefficients Method -

  1. Our first assumption is that the particular solutions are based on the type of R (n), with some unknown constant coefficients.
  2. We will then determine the exact solution based on the difference equation.

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6. What is the general form to be assumed for Z, where z is constant -?

  1. A
  2. Zr
  3. Ar
  4. Z

Answer: A) A

Explanation:

The general form to be assumed for Z, where z is constant is A.


7. What is the general form to be assumed for Zr, here z is constant -?

  1. A
  2. Zr
  3. Ar
  4. Z

Answer: B) Zr

Explanation:

The general form to be assumed for Zr, where z is constant is Zr.


8. What is the general form to be assumed for P (r), a polynomial of degree n?

  1. A0 rn+A1 r1+⋯..An
  2. A0 r+A1 rn-1+⋯..An
  3. A1 rn+A1 rn-1+⋯..An
  4. A0 rn+A1 rn-1+⋯..An

Answer: D) A0 rn+A1 rn-1+⋯..An

Explanation:

The general form to be assumed for P (r), a polynomial of degree n is A0 rn+A1 rn-1+⋯..An.


9. If E is applied to f(x), then the value of x is ____?

  1. Incremented
  2. Decremented
  3. Divided
  4. Multiplied

Answer: A) Incremented

Explanation:

If E is applied to f(x), then the value of x is incremented.


10. In Ef(x) = f(x+h), h is -?

  1. Decrement quantity
  2. Increment quantity
  3. Increment quality
  4. Decrement quality

Answer: B) Increment quantity

Explanation:

In Ef(x) = f(x+h), h is Increment quality.


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11. Symbol E is known as -?

  1. End Operator
  2. Slow operator
  3. Polynomial operator
  4. Shift operator

Answer: D) Shift operator

Explanation:

Symbol E is known as Shift Operator.


12. There are ___ steps in Operation ∆?

  1. Two
  2. Three
  3. Four
  4. Five

Answer: A) Two

Explanation:

There are two steps in Operation ∆.


13. Which of the following is TRUE?

  1. f(x)=f(x+h)-f(x)
  2. ∆f(x)=f(x+h)-f(x-h)
  3. ∆f(x)=f(x-h)-f(x)
  4. ∆f(x)=f(x+h)-f(x)

Answer: D) ∆f(x)=f(x+h)-f(x)

Explanation:

∆f(x)=f(x+h)-f(x) is TRUE.


14. For the different forms of R (n), in order to find the solution of yn= R (n) / P (E), there are ___ cases?

  1. Two
  2. Three
  3. Four
  4. Five

Answer: C) Four

Explanation:

For the different forms of R (n), in order to find the solution of yn= R (n) / P (E), there are four cases.


15. Which of the following is/are a/the case(s) to find the solution of yn= R (n) / P (E), for the different forms of R (n)?

  1. When R (n) is some constant A
  2. When R (n) is of the form A. Zn, where A and Z are constants
  3. When R (n) be a polynomial of degree m is n.
  4. All of the above

Answer: D) All of the above

Explanation:

The following are the cases to find the solution of yn= R (n) / P (E), for the different forms of R (n) -

  1. When R (n) is some constant A
  2. When R (n) is of the form A. Zn, where A and Z are constants
  3. When R (n) be a polynomial of degree m is n.


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