discrete mathematics

The number of edges in a complete graph

with ‘n’ vertices is equal to:

• n(n-1)

• n(n-1)/2

• n^2

• 2n-1

A relation R is from set A to B and a relation S from set B to C. Then is from_____

• Set C to A

• Set A to C

• Does not exist

• None of these

What is the identity element In the group G = {2, 4, 6, 8) under multiplication modulo 10?

• 5

• 6

• 9

• 12

The function  $f:R^+→R^+$  ,   $f(x)=x^3,g:R^+→R^+,g(x)=x^{1/3}\ then\ (fog)(x)=$  

•  $x^3$  

•  $1/x$  

•  $∛x$  

• x

Which two of the following are equivalent for an undirected graph G?

(i) G is a tree

(ii) There is at least one path between any two distinct vertices of G

(iii) G contains no cycles and has (n-1) edges

(iv) G has n edges

• (i) and (ii)

• (i) and (iii)

• (i) and (iv)

• (ii) and (iii)

The number of binary operation on set {1,2} is____

• 8

• 16

• 2

• 4

Which sentence is true?

• Set of all matrices forms a group under multiplication

• Set of all rational negative numbers forms a group under multiplication

• Set of all non-singular matrices forms a group under multiplication

• Both (b) and (c)

 $The\ function\ f:R→R,\ f(x)=5x+7\ then\$  function f is

• One one and onto

• One one but  not onto

• Onto but not one one

• Neither one one nor onto

The complete graph with four vertices has k edges where k is:

• 3

• 4

• 5

• 6

The number of onto function from set $\left\{1,2,3,4\right\}to\left\{3,4,7\right\}$    is

• 18

• 36

• 64

• none