## August 26, 2019

Note: We have tried to upload as much as we can, all the question and answers might be shuffled - Please find the answer below each question, some answers might be wrong please review on the last date(some answers might be changed) if you find any wrong answer please comment down below.

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

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

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

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

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

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

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.

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)

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

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