GATE CSE 2009

 Question 1
Which one of the following in NOT necessarily a property of a Group?
 A Commutativity B Associativity C Existence of inverse for every element D Existence of identity
Discrete Mathematics   Group Theory
Question 1 Explanation:
 Question 2
What is the chromatic number of an n-vertex simple connected graph which does not contain any odd length cycle? Assume n$\geq$2.
 A 2 B 3 C n-1 D n
Discrete Mathematics   Graph Theory
Question 2 Explanation:

 Question 3
Which one of the following is TRUE for any simple connected undirected graph with more than 2 vertices?
 A No two vertices have the same degree. B At least two vertices have the same degree. C At least three vertices have the same degree. D All vertices have the same degree.
Discrete Mathematics   Graph Theory
Question 3 Explanation:
 Question 4
Consider the binary relation R = {(x,y), (x,z), (z,x), (z,y)} on the set {x,y,z}. Which one of the following is TRUE?
 A R is symmetric but NOT antisymmetric B R is NOT symmetric but antisymmetric C R is both symmetric and antisymmetric D R is neither symmetric nor antisymmetric
Discrete Mathematics   Relation
Question 4 Explanation:
 Question 5
$(1217)_{8}$ is equivalent to
 A $(1217)_{16}$ B $(028F)_{16}$ C $(2297)_{10}$ D $(0B17)_{16}$
Digital Logic   Number System
Question 5 Explanation:

There are 5 questions to complete.