## GATE CSE 2016 Set 1

Exam Held on Thu Jan 01 1970 00:00:00 GMT+0000 (Coordinated Universal Time)
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## Algorithms

The worst case running times of Insertion sort, Merge sort and Quick sort, respe...
Let $$G$$ be a weighted connected undirected graph with distinct positive edge w...
Consider the weighted undirected graph with $$4$$ vertices, where the weight of ...
An operator $$delete(i)$$ for a binary heap data structure is to be designed to ...
$$G = (V,E)$$ is an undirected simple graph in which each edge has a distinct we...

## Compiler Design

Consider the following code segment. <pre><code>x = u - t; y = x * v; x = y + w;...
The attributes of three arithmetic operators in some programming language are gi...
Consider the following Syntax Directed Translation Scheme $$(SDTS),$$ with non-t...

## Computer Networks

A sender uses the Stop-and-Wait ARQ protocol for reliable transmission of frames...
An IP datagram of size 1000 bytes arrives at a router. The router has to forward...
For a host machine that uses the token bucket algorithm for congestion control, ...
Which one of the following protocols is <b>NOT</b> used to resolve one form of a...
Which of the following is/are example(s) of stateful application layer protocols...
Consider that B wants to send a message m that is digitally signed to A. Let the...

## Computer Organization

A processor can support a maximum memory of $$4$$ $$GB,$$ where the memory is wo...
The size of the data count register of a $$DMA$$ controller is $$16$$ bits. The ...
The stage delays in a $$4$$-stage pipeline are $$800, 500, 400$$ and $$300$$ pic...

## Data Structures

A queue is implemented using an array such that ENQUEUE and DEQUEUE operations a...
Consider the following directed graph: <img class="question-image" src="https:/...

## Database Management System

A database of research articles in a journal uses the following schema. <pre><co...
Which of the following is <b>NOT</b> a superkey in a relational schema with attr...
Which one of the following is <b>NOT</b> a part of the $$ACID$$ properties of da...
Consider the following two phase locking protocol. Suppose a transaction $$T$$ a...

## Digital Logic

We want to design a synchronous counter that counts the sequence $$0-1-0-2-0-3$$...
The $$16$$-bit $$2’s$$ complement representation of an integer is $$1111$$ $$111... Consider the Boolean operator$$ \ne $$with the following properties: <br>$$x ...
Consider the two cascaded $$2$$-to-$$1$$ multiplexers as shown in the figure. <i...
Consider a carry lookahead adder for adding two $$n$$-bit integers, built using ...

## Discrete Mathematics

Two eigenvalues of a $$3 \times 3$$ real matrix $$P$$ are $$\left( {2 + \sqrt { ...$$\mathop {\lim }\limits_{x \to 4} {{\sin \left( {x - 4} \right)} \over {x - 4}}...
Consider the following experiment. <br><b>Step1:</b> Flip a fair coin twice. <b...
A probability density function on the interval $$\left[ {a,1} \right]$$ is given...
Let $$p,q,r,s$$ represent the following propositions. <p>$$p:\,\,\,x \in \left\{... Let$${a_n}$$be the number of$$n$$-bit strings that do NOT contain two consecu... The coefficient of$${x^{12}}$$in$${\left( {{x^3} + {x^4} + {x^5} + {x^6} + .....
A function $$f:\,\,{N^ + } \to {N^ + },$$ defined on the set of positive integer...
Consider the recurrence relation $${a_1} = 8,\,{a_n} = 6{n^2} + 2n + {a_{n - 1}... ## General Aptitude Archimedes said, “Give me a lever long enough and a fulcrum on which to place it... Out of the following four sentences, select the most suitable sentence with resp... A rewording of something written or spoken is a ______________. If ‘relftaga’ means carefree, ‘otaga’ means careful and ‘fertaga’ means careless... A shaving set company sells$$4$$different types of razors, Elegance, Smooth, S... A cube is built using$$64$$cubic blocks of side one unit. After it is built, o... Indian currency notes show the denomination indicated in at least seventeen lang... Consider the following statements relating to the level of poker play of four pl... If$$f\left( x \right) = 2{x^7} + 3x - 5,$$which of the following is a factor o... In a process, the number of cycles to failure decreases exponentially with an in... ## Operating Systems Consider an arbitrary set of$$CPU$$-bound processes with unequal$$CPU$$burst ... Consider a disk queue with requests for$${\rm I}/O$$to blocks on cylinders$$4...
Consider a computer system with $$40$$-bit virtual addressing and page size of s...
Consider a computer system with ten physical page frames. The system is provided...

## Programming Languages

Consider the following C program <pre><code class='c'>void f(int, short); void m...
Consider the following C program. <pre><code class='c'>#include < stdio.h > ...

## Theory of Computation

Which of the following languages is generated by the given grammar? $$S \to aS|... Which one of the following regular expressions represents the language: the set ... Which of the following decision problems are undecidable? <p>$$\,\,\,\,\,\,\,\,...
Consider the following context-free grammars: <br>\eqalign{ & {G_1}:\,\,\,\... Consider the transition diagram of aPDA$$given below with input alphabet$$\...
Let $$X$$ be a recursive language and $$Y$$ be a recursively enumerable but not ...