# 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 $E_{2}\equiv \{(u,v)|(u,v)\in E\}$ 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:
 Question 6
Let the function
$f(\theta)=\begin{vmatrix} sin\theta & cos\theta & tan\theta \\ sin(\frac{\pi}{6}) & cos(\frac{\pi}{6}) & tan(\frac{\pi}{6})\\ sin(\frac{\pi}{3})& cos(\frac{\pi}{3}) & tan(\frac{\pi}{3}) \end{vmatrix}$
where $\theta \in [\frac{\pi}{6},\frac{\pi}{3}]$ and $f'(\theta )$ denote the derivative of f with respect to $\theta$ . Which of the following statements is/are TRUE?
(I) There existrs $\theta \in (\frac{\pi}{6},\frac{\pi}{3})$ such that $f'(\theta )=0$
(I) There existrs $\theta \in (\frac{\pi}{6},\frac{\pi}{3})$ such that $f'(\theta )\neq 0$
 A I only B II only C Both I and II D Neither I nor II
Engineering Mathematics   Calculus
Question 6 Explanation:
 Question 7
Consider the following Boolean Algebra for F:
$F(P,Q,R,S)=PQ+\bar{P}QR+\bar{P}Q\bar{R}S$
The minimal sum-of products form of F is
 A PQ+QR+QS B P+Q+R+S C $\bar{P}+\bar{Q}+\bar{R}+\bar{S}$ D $\bar{P}R+\bar{PRS}+P$
Digital Logic   Boolean Algebra
Question 7 Explanation:
 Question 8
The base (or radix) of the number system such that the following equation holds is_______.
$\frac{312}{20}=13.1$
 A 4 B 5 C 6 D 7
Digital Logic   Number System
Question 8 Explanation:
 Question 9
A machine has a 32-bit architecture, with 1-word long instructions. It has 64 registers, each of which is 32 bits long. It needs to support 45 instructions, which have an immediate operand in addition to two register operands. Assuming that the immediate operand is an unsigned integer, the maximum value of the immediate operand is ____________.
 A 16383 B 8191 C 32767 D 4097
Computer Organization   Machine Instruction
Question 9 Explanation:
 Question 10
Consider the following program in C language:
# include < stdio.h >
main()
{
int i;
int * pi = &i;
scanf( "%d", pi) ;
printf ("%d \ n", i+5) ;
}
Which one of the following statements is TRUE?
 A Compilation fails. B Execution results in a run-time error. C On execution, the value printed is 5 more than the address of variable i. D On execution, the value printed is 5 more than the integer value entered
C Programming   Array and Pointer
Question 10 Explanation:
There are 10 questions to complete.