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 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 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 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 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




There are 5 questions to complete.

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