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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

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 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

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

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

Answer: B) Linear nonhomogeneous

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

Answer: D) 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

Answer: C) 2

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

Answer: D) 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

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.




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