# GATE CSE 2014 SET-1

 Question 1
Consider the statement
"Not all that glitters is gold"
Predicate glitters(x) is true if x glitters and predicate gold(x) is true if x is gold. Which one of the following logical formulae represents the above statement?
 A $\forall x:glitters(x)\Rightarrow \neg gold(x)$ B $\forall x:gold(x)\Rightarrow glitters(x)$ C $\exists x:gold(x)\wedge \neg glitters(x)$ D $\exists x:glitters(x)\wedge \neg gold(x)$
Discrete Mathematics   Propositional Logic
Question 1 Explanation:
 Question 2
Suppose you break a stick of unit length at a point chosen uniformly at random. Then the expected length of the shorter stick is
 A 0.25 B 0.5 C 0.75 D 1
Discrete Mathematics   Probability Theory
Question 2 Explanation:

 Question 3
Let G=(V,E) be a directed graph where V is the set of vertices and E the set of edges. Then which one of the following graphs has the same strongly connected components as G ?
 A $G_{1}=(V,E_{1})$ where $E_{1}\equiv \{(u,v)|(u,v)\notin E\}$ B $G_{2}=(V,E_{2})$ where $E_{2}\equiv \{(u,v)|(v,u)\in E\}$ C $G_{3}=(V,E_{3})$ where $E_{3}\equiv \{(u,v)|$ there is a path of lenth $\leq$ 2 from u to v in E} D $G_{4}=(V_{4},E)$ where $V_{4}$ is the set of vertices in G which are not isolated
Discrete Mathematics   Graph Theory
Question 3 Explanation:
 Question 4
Consider the following system of equations:
3x + 2y = 1
4x + 7z = 1
x + y + z = 3
x - 2y + 7z = 0
The number of solutions for this system is
 A 0 B 1 C 2 D 3
Engineering Mathematics   Linear Algebra
Question 4 Explanation:
 Question 5
The value of the dot product of the eigenvectors corresponding to any pair of different eigenvalues of a 4-by-4 symmetric positive definite matrix is
 A 0 B 1 C 2 D 3
Engineering Mathematics   Linear Algebra
Question 5 Explanation:

There are 5 questions to complete.