1

### 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}$
2
Numerical

### GATE CSE 2015 Set 2

The cardinally of the power set of $\left\{ {0,1,2,\,\,....,\,\,10} \right.\left. \, \right\}$ is _____________.

3

### GATE CSE 2015 Set 2

Consider the following two statements.

$S1:$ If a candidate is known to be corrupt, then he will not be elected
$S2:$ If a candidate is kind, he will be elected

Which one of the following statements follows from $S1$ and $S2$ as per sound inference rules of logic?

A
If a person is known to be corrupt, he is kind
B
If a person is not known to be corrupt, he is not kind
C
If a person is kind, he is not known to be corrupt
D
If a person is not kind, he is not known to be corrupt
4

### GATE CSE 2015 Set 2

Let $𝑅$ be the relation on the set of positive integers such that $aRb$ if and only if $𝑎$ and $𝑏$ are distinct and have a common divisor other than $1.$ Which one of the following statements about $𝑅$ is true?
A
$𝑅$ is symmetric and reflexive but not transitive
B
$𝑅$ is reflexive but not symmetric and not transitive
C
$𝑅$ is transitive but not reflexive and not symmetric
D
$𝑅$ is symmetric but not reflexive and not transitive

### 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