1

### GATE CSE 2015 Set 2

Which one of the following well formed formulae is a tautology?
A
$\forall x\,\exists y\,R\left( {x,y} \right) \leftrightarrow \exists y\forall x\,R\left( {x,y} \right)$
B
$\left( {\forall x\left[ {\exists y\,R\left( {x,y} \right) \to S\left( {x,y} \right)} \right]} \right) \to \forall x\exists y\,S\left( {x,y} \right)$
C
$\left[ {\forall x\,\exists y\,\left( {P\left( {x,y} \right)} \right. \to R\left( {x,y} \right)} \right] \leftrightarrow \left[ {\forall x\,\exists y\,\left( {\neg P\left( {x,y} \right)V\,R\left( {x,y} \right)} \right.} \right]$
D
$\forall x\,\forall y\,P\left( {x,y} \right) \to \forall x\forall y\,P\left( {y,x} \right)$
2

### GATE CSE 2015 Set 2

A system has 6 identical resources and N processes competing for them. Each process can request atmost 2 resources. Which one of the following values of N could lead to a deadlock?
A
1
B
2
C
3
D
6
3
Numerical

### GATE CSE 2015 Set 2

A computer system implements a $40$-bit virtual address, page size of $8$ kilobytes, and a $128$-entry translation look-aside buffer $(TLB)$ organized into $32$ sets each having four ways. Assume that the $TLB$ tag does not store any process id. The minimum length of the $TLB$ tag in bits is ________________.

4
Numerical

### GATE CSE 2015 Set 2

A computer system implements $8$ kilobyte pages and a $32$-bit physical address space. Each page table entry contains a valid bit, a dirty bit, three permission bits, and the translation. If the maximum size of the page table of a process is $24$ megabytes, the length of the virtual address supported by the system is _______________ bits.

### 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