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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?

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.

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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.

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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.

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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.

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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. Z^r
3. A^r
4. Z

Answer: A) A

Explanation:

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

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

1. A
2. Z^r
3. A^r
4. Z

Answer: B) Z^r

Explanation:

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

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

1. A₀ rⁿ+A₁ r¹+⋯..A_n
2. A₀ r+A₁ r^n-1+⋯..A_n
3. A₁ rⁿ+A₁ r^n-1+⋯..A_n
4. A₀ rⁿ+A₁ r^n-1+⋯..A_n

Answer: D) A₀ rⁿ+A₁ r^n-1+⋯..A_n

Explanation:

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

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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.

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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.

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12. There are ___ steps in Operation ∆?

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

Answer: A) Two

Explanation:

There are two steps in Operation ∆.

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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.

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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.

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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 y_n= 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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