# GATE CSE 2014 SET-2

 Question 1
The security system at an IT office is composed of 10 computers of which exactly four are working. To check whether the system is functional, the officials inspect four of the computers picked at random (without replacement). The system is deemed functional if at least three of the four computers inspected are working. Let the probability that the system is deemed functional be denoted by p. Then 100p= _____________.
 A 9.2 B 11.9 C 15.6 D 19.2
Discrete Mathematics   Probability Theory
Question 1 Explanation:
 Question 2
Each of the nine words in the sentence "The quick brown fox jumps over the lazy og" is written on a separate piece of paper. These nine pieces of paper are kept in a box. One of the pieces is drawn at random from the box. The expected length of the word drawn is _____________. (The answer should be rounded to one decimal place)
 A 2.5 B 2.9 C 3.8 D 4.6
Discrete Mathematics   Probability Theory
Question 2 Explanation:
 Question 3
The maximum number of edges in a bipartite graph on 12 vertices is _____.
 A 24 B 36 C 48 D 60
Discrete Mathematics   Graph Theory
Question 3 Explanation:
 Question 4
If the matrix A is such that
$\begin{bmatrix} 2\\ -4\\ 7 \end{bmatrix}\begin{bmatrix} 1 &9 &5 \end{bmatrix}$
Then the determinant of A is equal to ________.
 A 0 B 1 C 2 D 3
Engineering Mathematics   Linear Algebra
Question 4 Explanation:
 Question 5
A non-zero polynomial f(x) of degree 3 has roots at x = 1,x = 2 and x = 3. Which one of the following must be TRUE?
 A $f(0)f(4) \lt 0$ B $f(0)f(4) \gt 0$ C $f(0)+f(4) \gt 0$ D $f(0)+f(4) \lt 0$
Engineering Mathematics   Linear Algebra
Question 5 Explanation:
 Question 6
The dual of a Boolean function $F(x_{1},x_{2},...,x_{n}, +, \cdot , ' )$ , written as $F^{D}$, is the same expression as that of F with + and $\cdot$ swapped. F is said to be self-dual if $F=F^{D}$. The number of self-dual functions with n Boolean variables is
 A $2^{n}$ B $2^{n-1}$ C $2^{2^{n}}$ D $2^{2^{n-1}}$
Digital Logic   Boolean Algebra
Question 6 Explanation:
 Question 7
Let $k = 2^{n}$ . A circuit is built by giving the output of an n-bit binary counter as input to an n-to-$2^{n}$ bit decoder. This circuit is equivalent to a
 A k-bit binary up counter B k-bit binary down counter. C k-bit ring counter. D k-bit Johnson counter
Digital Logic   Sequential Circuit
Question 7 Explanation:
 Question 8
Consider the equation $(123)_{5}=(x8)_{y}$ with x and y as unknown. The number of possible solutions is _____ .
 A 2 B 3 C 4 D 5
Digital Logic   Number System
Question 8 Explanation:
 Question 9
A 4-way set-associative cache memory unit with a capacity of 16 KB is built using a block size of 8 words. The word length is 32 bits. The size of the physical address space is 4 GB. The number of bits for the TAG field is _____
 A 18 B 19 C 20 D 21
Computer Organization   Cache Memory
Question 9 Explanation:
 Question 10
Consider the function func shown below:
 int func(int num) {
int count = 0;
while (num) {
count++;
num$\gt \gt$= 1;
}
return (count);
} 
The value returned by func(435)is __________.
 A 8 B 9 C 10 D 11
C Programming   Function
Question 10 Explanation:
There are 10 questions to complete.