GATE CSE 2015 Set 3

## GATE CSE

Consider the equality $$\sum\limits_{i = 0}^n {{i^3}} = X$$ and the following choices for $$X$$
$$\eqalign{
& \,

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Consider the following array of elements.
$$\,\,\,\,\,\,\,\,$$$$ā©89, 19, 50, 17, 12, 15, 2, 5, 7, 11, 6, 9, 100āŖ$$
The m

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Assume that a mergesort algorithm in the worst case takes $$30$$ seconds for an input of size $$64.$$ Which of the follo

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Let $$f\left( n \right) = n$$ and $$g\left( n \right) = {n^{\left( {1 + \sin \,\,n} \right)}},$$ where $$n$$ is a positi

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Among simple $$LR (SLR) ,$$ canonical $$LR,$$ and look-ahead $$LR$$ $$(LALR),$$ which of the following pairs identify th

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Consider the following grammar $$G$$
$$\eqalign{
& \,\,\,\,\,\,\,S \to \,\,\,\,\,\,\,F|H \cr
& \,\,\,\,\,

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Consider a CSMA/CD network that transmits data at a rate of 100 Mbps (108 bits second) over a 1 km(kilometer) cable with

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Consider a network connected two systems located 8000 kilometers apart. The bandwidth of the network is 500 Ć 106 bits p

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In the network 200.20.11.144/27, the fourth octet (in decimal) of the last IP address of the network which can be assign

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Consider the following statements.
I. TCP connections are full duplex
II. TCP has no option for selective acknowledgme

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Two hosts are connected via a packet switch with $${10^7}$$ bits per second links. Each link has a propagation delay of

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Consider a machine with a byte addressable main memory of $${2^{20}}$$ bytes, block size of $$16$$ bytes and a direct ma

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Consider the following reservation table for a pipeline having three stages $${S_1},{S_2}$$ and $${S_3}.$$
The minimum

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Consider the following code sequence having five instructions $${I_1}$$ to $${I_5}$$. Each of these instructions has the

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Consider a binary tree $$T$$ that has $$200$$ leaf nodes. Then, the number of nodes in $$T$$ that have exactly two child

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Given a hash table $$š$$ with $$25$$ slots that stores $$2000$$ elements, the load factor $$\alpha $$ for $$š$$ is ___

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While inserting the elements $$71, 65, 84, 69, 67, 83$$ in an empty binary search tree $$(BST)$$ in the sequence shown,

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The result evaluating the postfix expression $$10\,\,5\, + 60$$ $$\,\,6/\, * \,8\, - $$ is

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Let $$G$$ be a connected undirected graph of $$100$$ vertices and $$300$$ edges. The weight of a minimum spanning tree o

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Consider a B+ tree in which the search key is 12 bytes long, block size is 1024 bytes, record pointer is 10 bytes long a

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Consider the relation $$X\left( {P,Q,R,S,T,U} \right)$$ with the following set of functional dependencies
$$\eqalign{

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Consider the following relation
$$\,\,\,\,\,\,\,\,$$ Cinema(theater, address, capacity)
Which of the following options w

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Consider the following partial Schedule S involving two transactions $$T1$$ and $$T2.$$ Only the read and the write oper

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Let $$ \ne $$ be a binary operator defined as $$X \ne Y = X' + Y'$$ where $$š$$ and $$š$$ are Boolean variables. Consi

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Given the function $$F = Pā² + QR,$$ where $$F$$ is a function in three Boolean variables $$P,Q$$ and $$R$$ and $$P'=!P,$

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Consider the equation $${\left( {43} \right)_x} = {\left( {y3} \right)_8}$$ where $$x$$ and $$y$$ are unknown. The numbe

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The total number of prime implicants of the function
$$f\left( {w,x,y,z} \right) = \sum {\left( {0,2,4,5,6,10} \right)}

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In the given matrix $$\left[ {\matrix{
1 & { - 1} & 2 \cr
0 & 1 & 0 \cr
1 & 2 & 1

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If the following system has non - trivial solution
$$$px+qy+rz=0$$$
$$$qx+ry+pz=0$$$
$$$rx+py+qz=0$$$
Then which one of

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A function $$f(x)$$ is linear and has a value of $$29$$ at $$x=-2$$ and $$39$$ at $$x=3.$$ Find its value at $$x=5.$$

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If for non-zero $$x,$$ $$af\left( x \right) + bf\left( {{1 \over x}} \right) = {1 \over x} - 25$$
where $$a \ne b$$ th

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The value of $$\mathop {\lim }\limits_{x \to \alpha } {\left( {1 + {x^2}} \right)^{{e^{ - x}}}}\,\,$$ is

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Choose the most appropriate equation for the function drawn as a thick line, in the plot below.

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Suppose $${X_i}$$ for $$i=1,2,3$$ are independent and identically distributed random variables whose probability mass fu

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Suppose $$š$$ is the power set of the set $$S = \left\{ {1,2,3,4,5,6,} \right\}$$. For any $$T \in U,$$ let $$\left| T

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The number of $$4$$ digit numbers having their digits in non-decreasing order (from left to right) constructed by using

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In a room there are only two types of people, namely Type $$1$$ and Type $$2.$$ Type $$1$$ people always tell the truth

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Let $$R$$ be a relation on the set of ordered pairs of positive integers such that $$\left( {\left( {p,q} \right),\left(

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The maximum number of processes that can be in $$Ready$$ state for a computer system with $$n$$ $$CPUs$$ is

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Consider the following policies for preventing deadlock in a system with mutually exclusive resources.
$$\,\,\,\,\,\,\,

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For the processes listed in the following table, which of the following scheduling schemes will give the lowest average

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Consider the following C program segment.
#include < stdio.h >
int main()
{
char s1[7] = "1234", *p;
p = s

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Consider a software project with the following information domain characteristics for calculation of function point metr

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Consider a software program that is artificially seeded with $$100$$ faults. While testing this program, $$159$$ faults

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Consider three software items: Program-$$X,$$ Control Flow Diagram of Program-$$Y$$ and Control Flow Diagram of Program-

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Let $$L$$ be the language represented by the regular expression $$\sum {^ * 0011\sum {^ * } } $$ where $$\sum { = \left\

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Language $${L_1}$$ is polynomial time reducible to language $${L_2}$$ . Language $${L_3}$$ is polynomial time reducible

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Which of the following languages are context-free?
$$$\eqalign{
& {L_1} = \left\{ {{a^m}{b^n}{a^n}{b^m}|m,n \ge 1

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In a web server, ten WebPages are stored with the URLs of the form
http://www.yourname.com/$$var$$.html; where, $$var$$

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