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# 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?**

- Initial
- Middle
- Final
- 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?**

- Two
- Three
- Four
- 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?**

- Undetermined coefficients method
- E and ∆ operator method.
- Both A and B
- 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?**

- R.H.S R (n)
- L.H.S L (n)
- Both A and B
- 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 -?**

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

**Answer:** C) Both A and B

**Explanation:**

In Undetermined Coefficients Method -

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

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

- A
- Z
^{r} - A
^{r} - 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 Z ^{r}, here z is constant -?**

- A
- Z
^{r} - A
^{r} - Z

**Answer:** B) Z^{r}

**Explanation:**

The general form to be assumed for Z^{r}, where z is constant is Z^{r}.

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

- A
_{0}r^{n}+A_{1}r^{1}+⋯..A_{n} - A
_{0}r+A_{1}r^{n-1}+⋯..A_{n} - A
_{1}r^{n}+A_{1}r^{n-1}+⋯..A_{n} - A
_{0}r^{n}+A_{1}r^{n-1}+⋯..A_{n}

**Answer:** D) A_{0} r^{n}+A_{1} r^{n-1}+⋯..A_{n}

**Explanation:**

The general form to be assumed for P (r), a polynomial of degree n is A_{0} r^{n}+A_{1} r^{n-1}+⋯..A_{n}.

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

- Incremented
- Decremented
- Divided
- 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 -?**

- Decrement quantity
- Increment quantity
- Increment quality
- Decrement quality

**Answer:** B) Increment quantity

**Explanation:**

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

**11. Symbol E is known as -?**

- End Operator
- Slow operator
- Polynomial operator
- Shift operator

**Answer:** D) Shift operator

**Explanation:**

Symbol E is known as Shift Operator.

**12. There are ___ steps in Operation ∆?**

- Two
- Three
- Four
- Five

**Answer:** A) Two

**Explanation:**

There are two steps in Operation ∆.

**13. Which of the following is TRUE?**

- f(x)=f(x+h)-f(x)
- ∆f(x)=f(x+h)-f(x-h)
- ∆f(x)=f(x-h)-f(x)
- ∆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?**

- Two
- Three
- Four
- 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)?**

- When R (n) is some constant A
- When R (n) is of the form A. Z
^{n}, where A and Z are constants - When R (n) be a polynomial of degree m is n.
- All of the above

**Answer:** D) All of the above

**Explanation:**

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

- When R (n) is some constant A
- When R (n) is of the form A. Z
^{n}, where A and Z are constants - When R (n) be a polynomial of degree m is n.

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