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{
& \,

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

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

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

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

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

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

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

View Question 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

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

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

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

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

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

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

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

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

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

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

View Question 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

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

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

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

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

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

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

View Question 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)}

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

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

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

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

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

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

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

View Question 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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

View Question