GATE CSE 2016 Set 1

## GATE CSE

Let $$G$$ be a weighted connected undirected graph with distinct positive edge weights. If every edge weight is increase

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The worst case running times of Insertion sort, Merge sort and Quick sort, respectively, are:

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An operator $$delete(i)$$ for a binary heap data structure is to be designed to delete the item in the $$i$$-th node. As

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$$G = (V,E)$$ is an undirected simple graph in which each edge has a distinct weight, and e is a particular edge of G. W

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Consider the weighted undirected graph with $$4$$ vertices, where the weight of edge $$\left\{ {i,j} \right\}$$ is given

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Consider the following code segment.
x = u - t;
y = x * v;
x = y + w;
y = t - z;
y = x * y;
The minimum number of total

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The attributes of three arithmetic operators in some programming language are given below.
.tg {border-collapse:colla

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Consider the following Syntax Directed Translation Scheme $$(SDTS),$$ with non-terminals $$\left\{ {S,A} \right\}$$ and

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A sender uses the Stop-and-Wait ARQ protocol for reliable transmission of frames. Frames are of size 1000 bytes and the

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An IP datagram of size 1000 bytes arrives at a router. The router has to forward this packet on a link whose MTU (maximu

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For a host machine that uses the token bucket algorithm for congestion control, the token bucket has a capacity of 1 meg

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Which one of the following protocols is NOT used to resolve one form of address to another one?

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Which of the following is/are example(s) of stateful application layer protocols?
(i) HTTP
(ii) FTP
(iii) TCP
(iv) P

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Consider that B wants to send a message m that is digitally signed to A. Let the pair of private and public keys for A a

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A processor can support a maximum memory of $$4$$ $$GB,$$ where the memory is word-addressable (a word consists of two b

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The stage delays in a $$4$$-stage pipeline are $$800, 500, 400$$ and $$300$$ picoseconds. The first stage (with delay $$

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The size of the data count register of a $$DMA$$ controller is $$16$$ bits. The processor needs to transfer a file of $$

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A queue is implemented using an array such that ENQUEUE and DEQUEUE operations are performed efficiently. Which one of t

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Consider the following directed graph:
The number of different topological orderings of the vertices of the graph is

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A database of research articles in a journal uses the following schema.
(VOLUME, NUMBER, STARTPAGE, ENDPAGE, TITLE, YEAR

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Which of the following is NOT a superkey in a relational schema with attributes $$V, W, X, Y, Z$$ and primary key $$V Y?

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Which one of the following is NOT a part of the $$ACID$$ properties of database transactions?

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Consider the following two phase locking protocol. Suppose a transaction $$T$$ accesses (for read or write operations),

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The $$16$$-bit $$2’s$$ complement representation of an integer is $$1111$$ $$1111$$ $$1111$$ $$0101;$$ its decimal
repre

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We want to design a synchronous counter that counts the sequence $$0-1-0-2-0-3$$ and then repeats. The minimum number of

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Consider the Boolean operator $$ \ne $$ with the following properties:
$$x \ne 0 = x,\,\,x \ne 1 = \overline x ,\,\,x \

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Consider the two cascaded $$2$$-to-$$1$$ multiplexers as shown in the figure.
The minimal sum of products form of the

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Consider a carry lookahead adder for adding two $$n$$-bit integers, built using gates of fan-in at most two. The time to

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Two eigenvalues of a $$3 \times 3$$ real matrix $$P$$ are $$\left( {2 + \sqrt { - 1} } \right)$$ and $$3.$$ The determin

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$$\mathop {\lim }\limits_{x \to 4} {{\sin \left( {x - 4} \right)} \over {x - 4}} = \_\_\_\_\_\_\_.$$

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A probability density function on the interval $$\left[ {a,1} \right]$$ is given by $$1/{x^2}$$ and outside this interva

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Consider the following experiment.
Step1: Flip a fair coin twice.
Step2: If the outcomes are (TAILS, HEADS) then output

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Let $$p,q,r,s$$ represent the following propositions.
$$p:\,\,\,x \in \left\{ {8,9,10,11,12} \right\}$$
$$q:\,\,\,x$$ is

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Let $${a_n}$$ be the number of $$n$$-bit strings that do NOT contain two consecutive $$1s.$$ Which one of the following

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The coefficient of $${x^{12}}$$ in $${\left( {{x^3} + {x^4} + {x^5} + {x^6} + ...} \right)^3}\,\,\,\,\,\,$$ is _________

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A function $$f:\,\,{N^ + } \to {N^ + },$$ defined on the set of positive integers $${N^ + },$$ satisfies the following
p

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Consider the recurrence relation
$${a_1} = 8,\,{a_n} = 6{n^2} + 2n + {a_{n - 1}}.$$ Let $${a_{99}} = K \times {10^4}.$$

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Consider an arbitrary set of $$CPU$$-bound processes with unequal $$CPU$$ burst lengths submitted at the same time to a

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Consider a disk queue with requests for $${\rm I}/O$$ to blocks on cylinders $$47, 38, 121, 191,$$ $$87, 11, 92, 10.$$ T

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Consider a computer system with $$40$$-bit virtual addressing and page size of sixteen kilobytes. If the computer system

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Consider a computer system with ten physical page frames. The system is provided with an access sequence $$\left( {{a_1}

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Consider the following C program
void f(int, short);
void main()
{
int i = 100;
short s = 12;
short *p = &am

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Consider the following C program.
#include < stdio.h >
void mystery(int *ptra, int *ptrb) {
int *temp;

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Which of the following languages is generated by the given grammar?
$$$S \to aS|bS|\varepsilon $$$

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Which of the following decision problems are undecidable?
$$\,\,\,\,\,\,\,\,\,\,{\rm I}.\,\,\,\,\,\,\,\,\,\,$$ Given $$

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Which one of the following regular expressions represents the language: the set of all binary strings having two consecu

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Consider the transition diagram of a $$PDA$$ given below with input alphabet $$\sum {\, = \left\{ {a,b} \right\}} $$ and

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Consider the following context-free grammars:
$$\eqalign{
& {G_1}:\,\,\,\,\,S \to aS|B,\,\,B \to b|bB \cr
&am

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Let $$X$$ be a recursive language and $$Y$$ be a recursively enumerable but not recursive language. Let $$W$$ and $$Z$$

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## General Aptitude

Out of the following four sentences, select the most suitable sentence with respect to grammar and usage.

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A rewording of something written or spoken is a ______________.

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Archimedes said, “Give me a lever long enough and a fulcrum on which to place it, and I will move the world.”
The sente

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If ‘relftaga’ means carefree, ‘otaga’ means careful and ‘fertaga’ means careless, which of the following could mean ‘aft

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A shaving set company sells $$4$$ different types of razors, Elegance, Smooth, Soft and Executive. Elegance sells at Rs.

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A cube is built using $$64$$ cubic blocks of side one unit. After it is built, one cubic block is removed from every cor

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Consider the following statements relating to the level of poker play of four players $$P, Q, R$$ and $$S.$$
$$\,\,\,\,\

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Indian currency notes show the denomination indicated in at least seventeen languages. If this is not an indication of t

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If $$f\left( x \right) = 2{x^7} + 3x - 5,$$ which of the following is a factor of $$f(x)$$?

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In a process, the number of cycles to failure decreases exponentially with an increase in load. At a load of $$80$$ unit

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