Home » MCQs » Discrete Mathematics MCQs

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

Answer: A) One

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 y_n+r+C₁ y_n+r-1+C₂ y_n+r-2+⋯+Cy=R (n)
2. C₀ y_n+r+C_n y_n+r-1+C₂ y_n+r-2+⋯+C_r y_n=R (n)
3. C_n y_n+r+C₁ y_n+r-1+C₂ y_n+r-2+⋯+C_r y_n=R (n)
4. C₀ y_n+r+C₁ y_n+r-1+C₂ y_n+r-2+⋯+C_r y_n=R (n)

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

Explanation:

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

---

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

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

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

Explanation:

In C₀ y_n+r+C₁ y_n+r-1+C₂ y_n+r-2+⋯+C_r y_n=R (n), C₀,C₁,C₂...C_n 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

Answer: A) 0

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

Answer: D) Linear nonhomogeneous

Explanation:

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

---

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

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

Answer: B) Linear nonhomogeneous

Explanation:

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

---

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

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

Answer: D) 3

Explanation:

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

---

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

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

Answer: C) 2

Explanation:

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

---

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

1. C₀ y_n+C₁ y_n-1+C₂ y_n-2+⋯......+C_n y_n-r=0
2. C₀ y_n+C₁ y_n-1+C₂ y_n-2+⋯......+C_r y_n-r=1
3. C₀ y_n+C₁ y_n-1+C₂ y_n-2+⋯......+C_r y_n-r=0
4. C₀ y_n+C₁ y_n-1+C₂ y_n-2+⋯......+C_n y_n-r=1

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

Explanation:

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

---

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

1. C₀ ∝¹+C₁ ∝^r-1+C₂ ∝^r-2+⋯C_r=0
2. C₀ ∝⁰+C₁ ∝^r-1+C₂ ∝^r-2+⋯C_r=0
3. C₀ ∝²+C₁ ∝^r-1+C₂ ∝^r-2+⋯C_r=0
4. C₀ ∝^r+C₁ ∝^r-1+C₂ ∝^r-2+⋯C_r=0

Answer: D) C₀ ∝^r+C₁ ∝^r-1+C₂ ∝^r-2+⋯C_r=0

Explanation:

The characteristics equation of the linear homogeneous difference equation is C₀ ∝^r+C₁ ∝^r-1+C₂ ∝^r-2+⋯C_r=0.

---

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

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

Answer: B) Four

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.

---

---