GATE CSE 2015 Set 3
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## GATE CSE

Consider the equality $$\sum\limits_{i = 0}^n {{i^3}} = X$$ and the following choices for $$X$$ \eqalign{ &amp; \, View Question Consider the following array of elements.\,\,\,\,\,\,\,\,〈89, 19, 50, 17, 12, 15, 2, 5, 7, 11, 6, 9, 100〉$$The m View Question Assume that a mergesort algorithm in the worst case takes$$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{ &amp; \,\,\,\,\,\,\,S \to \,\,\,\,\,\,\,F|H \cr &amp; \,\,\,\,\,
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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 × 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 $$𝑇$$ with $$25$$ slots that stores $$2000$$ elements, the load factor $$\alpha$$ for $$𝑇$$ 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{ 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'$$where$$𝑋$$and$$𝑌$$are Boolean variables. Consi View Question Given the function$$F = P′ + 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 &amp; { - 1} &amp; 2 \cr 0 &amp; 1 &amp; 0 \cr 1 &amp; 2 &amp; 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
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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 $$𝑈$$ 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(
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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. $$\,\,\,\,\,\,\, View Question For the processes listed in the following table, which of the following scheduling schemes will give the lowest average View Question Consider the following C program segment. #include &lt; stdio.h &gt; int main() { char s1 = "1234", *p; p = s View Question Consider a software project with the following information domain characteristics for calculation of function point metr View Question Consider a software program that is artificially seeded with$$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\
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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{ &amp; {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
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