Discrete Structures for Computer Science - MCQS

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Question 1:

Let R be relation defined as R ={ <x,y>/ x - y is divisible  by m,a positive integer}

Which of the following is true?

Select one:

a. R is only reflexive

b. R is neither reflexive nor symmetric

c. R is reflexive and symmetric

d. R is R is reflexive, symmetric and transitive

Correct Answer: D

Question 2:

Consider the recurrence relation : a(n) =2 a(n-1) + a(n- 3)

Then the order of the characteristic polynomial of this recurrence relation is

Select one:

a. We can not determine

b. 2

c. 1

d. 3

Correct Answer: D

Question 3:

A relation R: S to  S is called a  partial order relation  if it is

Select one:

a. Reflexive, Antisymmetric, Transitive 

b. Irreflexive,Transitive, Antisymmetric

c. Reflexive,Transitive,Symmetric

d. only Reflexive, Transitive

Correct Answer: A

Question 4:

Consider the following diagram. And choose the correct option from the given

Select one:

a. This is not a lattice       

b. represents a improper lattice  

c. Represent a proper lattice

d. Does not represent a poset 

Correct Answer: C

Question 5:

How many ways are there to distribute six indistinguishable balls into nine distinguishable bins?

Select one:

a. 3003

b. 3000

c. 3030

d. 3300

Correct Answer: A

Question 6:

Let F be the function such that F(n) is the sum of the first n positive integers. Give a recursive definition of F(n).

Select one:

a. f(0) = 1, f(n) = f(n − 1) - n for n ≥ 1

b. f(0) = 0, f(n) = f(n − 1) + n for n ≥ 1

c. f(0) = 0, f(n) = f(n + 1) + n for n ≥ 1

d. f(0) = 1, f(n) = f(n + 1) - n for n ≥ 1

Correct Answer: B

Question 7:

Which of the following represents the Hasse diagram of the the relation  ({1,2,3},less than or equal to ) 

Select one:

a.

b.

c. 

Correct Answer: C

Question 8:

What is the generating function for the finite sequence 2, 2, 2, 2, 2, 2

Select one:

a. f (x) = 2(x2−1)/(x6−1)

b. f (x) = 2(x2−1)/(x−1)

c. f (x) = 2(x2−1)/(x2−1)

d. f (x) = 2(x6−1)/(x−1)

Correct Answer: D

Question 9:

Which of the following is true?

Select one:

a. Composition of functions is  NOT associative

b. Composition of functions is NOT commutative

c. Composition of functions is  Associative

d. Composition of functions is commutative

Correct Answer: D

Question 10:

Which of the following is True?

Select one:

a. Then recurrence relation a(n) = a(n-1) + a(n-2) is neither linear nor homogeneous

b. Then recurrence relation a(n) = a(n-1) + a(n-2) is always linear and non homogeneous

c. Then recurrence relation a(n) = a(n-1) + a(n-2) is always  non linear and homogeneous

d. Then recurrence relation a(n) = a(n-1) + a(n-2) is always linear and homogeneous

Correct Answer: D