GATE CSE 2014 SET-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?

Suppose you break a stick of unit length at a point chosen uniformly at random. Then the expected length of the shorter stick is

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 ?

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

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

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

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

The base (or radix) of the number system such that the following equation holds is_______.
\frac{312}{20}=13.1

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 ____________.

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?