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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
- Zr
- Ar
- 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 -?
- A
- Zr
- Ar
- 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?
- A0 rn+A1 r1+⋯..An
- A0 r+A1 rn-1+⋯..An
- A1 rn+A1 rn-1+⋯..An
- 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 ____?
- 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. Zn, 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 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. Zn, where A and Z are constants
- When R (n) be a polynomial of degree m is n.