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# Discrete Mathematics | Linear Recurrence Relations with Constant Coefficients MCQs

Discrete Mathematics | Linear Recurrence Relations with Constant Coefficients MCQs: This section contains multiple-choice questions and answers on Linear Recurrence Relations with Constant Coefficients in Discrete Mathematics.
Submitted by Anushree Goswami, on July 20, 2022

1. If the degree of a Recurrence Relation is ___, then it is called a linear Recurrence Relation?

1. One
2. Zero
3. Infinite
4. Two

Explanation:

If the degree of a Recurrence Relation is one, then it is called a linear Recurrence Relation.

2. Generally, linear recurrence relations with constant coefficients take the form of -?

1. C0 yn+r+C1 yn+r-1+C2 yn+r-2+⋯+Cy=R (n)
2. C0 yn+r+Cn yn+r-1+C2 yn+r-2+⋯+Cr yn=R (n)
3. Cn yn+r+C1 yn+r-1+C2 yn+r-2+⋯+Cr yn=R (n)
4. C0 yn+r+C1 yn+r-1+C2 yn+r-2+⋯+Cr yn=R (n)

Answer: D) C0 yn+r+C1 yn+r-1+C2 yn+r-2+⋯+Cr yn=R (n)

Explanation:

Generally, linear recurrence relations with constant coefficients take the form of - C0 yn+r+C1 yn+r-1+C2 yn+r-2+⋯+Cr yn=R (n).

3. In C0 yn+r+C1 yn+r-1+C2 yn+r-2+⋯+Cr yn=R (n),?

1. C0,C1,C2...Cn are same function of independent variable n. and R (n) is constant.
2. C0,C1,C2...Cn and R (n) is same function of independent variable n.
3. C0,C1,C2...Cn and R (n) is constant.
4. C0,C1,C2...Cn are constant and R (n) is same function of independent variable n.

Answer: D) C0,C1,C2...Cn are constant and R (n) is same function of independent variable n

Explanation:

In C0 yn+r+C1 yn+r-1+C2 yn+r-2+⋯+Cr yn=R (n), C0,C1,C2...Cn are constant and R (n) is same function of independent variable n.

4. If R (n) = _ and it is of order n, the equation is a linear homogeneous difference equation?

1. 0
2. 1
3. 2
4. Infinite

Explanation:

If R (n) = 0 and it is of order n, the equation is a linear homogeneous difference equation.

5. If R (n) ≠ 0, then the equation is a ____ difference equation?

1. Bilinear homogeneous
2. Linear homogeneous
3. Bilinear nonhomogeneous
4. Linear nonhomogeneous

Explanation:

If R (n) ≠ 0, then the equation is a linear nonhomogeneous difference equation.

6. Equation ar+3+6ar+2+12ar+1+8ar=0 is a ____ equation?

1. Linear homogeneous
2. Linear nonhomogeneous
3. Bilinear homogeneous
4. Bilinear nonhomogenenous

Explanation:

Equation ar+3+6ar+2+12ar+1+8ar=0 is a linear nonhomogeneous equation.

7. What is the order of the equation ar+3+6ar+2+12ar+1+8ar=0?

1. 0
2. 1
3. 2
4. 3

Explanation:

The order of the equation ar+3+6ar+2+12ar+1+8ar=0 is 3.

8. What is the order of the equation ar+2-8ar+1+5ar= 7r + 2r?

1. 0
2. 1
3. 2
4. 3

Explanation:

The order of the equation ar+2-8ar+1+5ar= 7r + 2r is 2.

9. The equation for a linear homogeneous difference equation with constant coefficients can be written as follows:?

1. C0 yn+C1 yn-1+C2 yn-2+⋯......+Cn yn-r=0
2. C0 yn+C1 yn-1+C2 yn-2+⋯......+Cr yn-r=1
3. C0 yn+C1 yn-1+C2 yn-2+⋯......+Cr yn-r=0
4. C0 yn+C1 yn-1+C2 yn-2+⋯......+Cn yn-r=1

Answer: C) C0 yn+C1 yn-1+C2 yn-2+⋯......+Cr yn-r=0

Explanation:

The equation for a linear homogeneous difference equation with constant coefficients can be written as follows: C0 yn+C1 yn-1+C2 yn-2+⋯......+Cr yn-r=0.

10. What is the characteristics equation of the linear homogeneous difference equation?

1. C01+C1r-1+C2r-2+⋯Cr=0
2. C00+C1r-1+C2r-2+⋯Cr=0
3. C02+C1r-1+C2r-2+⋯Cr=0
4. C0r+C1r-1+C2r-2+⋯Cr=0

Explanation:

The characteristics equation of the linear homogeneous difference equation is C0r+C1r-1+C2r-2+⋯Cr=0.

11. There are ____ cases to solve linear homogeneous difference equations?

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

Explanation:

There are four cases to solve linear homogeneous difference equations.

12. Which of the following is a/the case(s) while finding the solution of the linear homogeneous difference equation?

1. There are n distinct real roots ∝1, ∝2, ∝3,.......∝n in the characteristic equation.
2. There are repeated real roots in characteristic equation.
3. There is one imaginary root in characteristic equation.
4. All of the above

Answer: D) All of the above

Explanation:

The following are the cases while finding the solutions of the linear homogeneous difference equation -

1. There are n distinct real roots ∝1, ∝2, ∝3,.......∝n in the characteristic equation.
2. There are repeated real roots in characteristic equation.
3. There is one imaginary root in characteristic equation.