1
Numerical

### GATE CSE 2015 Set 2

A half adder is implemented with $XOR$ and $AND$ gates. A full adder is implemented with two half adders and one $OR$ gate. The propagation delay of an $XOR$ gate is twice that of an $AND/OR$ gate. The propagation delay of an $AND/OR$ gate is $1.2$ microseconds. A $4$-bit ripple-carry binary adder is implemented by using four full adders. The total propagation time of this $4$-bit binary adder in microseconds is____________ .

2
Numerical

### GATE CSE 2015 Set 2

The larger of the two eigenvalues of the matrix $\left[ {\matrix{ 4 & 5 \cr 2 & 1 \cr } } \right]$ is ______.

3
Numerical

### GATE CSE 2015 Set 2

Perform the following operations on the matrix $\left[ {\matrix{ 3 & 4 & {45} \cr 7 & 9 & {105} \cr {13} & 2 & {195} \cr } } \right]$
(i) Add the third row to the second row
(ii) Subtract the third column from the first column.

The determinant of the resultant matrix is _________.

4

### GATE CSE 2015 Set 2

Let $\,\,f\left( x \right) = {x^{ - \left( {1/3} \right)}}\,\,$ and ${\rm A}$ denote the area of the region bounded by $f(x)$ and the $X-$axis, when $x$ varies from $-1$ to $1.$ Which of the following statements is/are TRUE?
${\rm I}.$ $f$ is continuous in $\left[ { - 1,1} \right]$
${\rm I}{\rm I}.$ $f$ is not bounded in $\left[ { - 1,1} \right]$
${\rm I}{\rm I}{\rm I}.$ ${\rm A}$ is nonzero and finite
A
${\rm I}$${\rm I} only B {\rm I}$${\rm I}$${\rm I} only C {\rm I}$${\rm I}$ and ${\rm I}$${\rm I}$${\rm I}$ only
D
${\rm I}$, ${\rm I}$${\rm I}, and {\rm I}$${\rm I}$${\rm I}$

### Paper Analysis of GATE CSE 2015 Set 2

Subject NameTotal Questions
Algorithms5
Compiler Design3
Computer Networks6
Computer Organization4
Data Structures3
Database Management System4
Digital Logic3
Discrete Mathematics12
Operating Systems4
Programming Languages3
Software Engineering3
Theory of Computation4
Web Technologies1