1

### GATE CSE 2016 Set 2

Let, ${x_1} \oplus {x_2} \oplus {x_3} \oplus {x_4} = 0$ where ${x_1},\,{x_2},\,{x_3},\,{x_4}$ are Boolean Variables, and $\oplus$ is the $XOR$ operator.

Which one of the following must always be TRUE?

A
${x_1}{x_2}{x_3}{x_4} = 0$
B
${x_1}{x_3} + {x_2} = 0$
C
${\overline x _1} \oplus {\overline x _3} = {\overline x _2} \oplus {\overline x _4}$
D
${x_1} + {x_2} + {x_3} + {x_4} = 0$
2
Numerical

### GATE CSE 2016 Set 2

Let $X$ be the number of distinct $16$-bit integers in $2’s$ complement representation. Let $Y$ be the number of distinct $16$-bit integers in sign magnitude representation.
Then $X −Y$ is ____________.

3
Numerical

### GATE CSE 2016 Set 2

Suppose that the eigen values of matrix $A$ are $1, 2, 4.$ The determinant of ${\left( {{A^{ - 1}}} \right)^T}$ is _______.

4

### GATE CSE 2016 Set 2

Consider the system, each consisting of m linear equations in $n$ variables.
$I.$ $\,\,\,$ If $m < n,$ then all such system have a solution
$II.$ $\,\,\,$ If $m > n,$ then none of these systems has a solution
$III.$ $\,\,\,$ If $m = n,$ then there exists a system which has a solution

Which one of the following is CORRECT?

A
$I$ , $II$ and $III$ are true
B
Only $II$ and $III$ are true
C
Only $III$ is true
D
None of them is true

### Paper Analysis of GATE CSE 2016 Set 2

Subject NameTotal Questions
Algorithms5
Compiler Design3
Computer Networks6
Computer Organization6
Data Structures5
Database Management System4
Digital Logic3
Discrete Mathematics11
Operating Systems3
Theory of Computation6
General Aptitude10