GATE CSE 2006
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GATE CSE

Consider the following C-program fragment in which i, j and n are integer variables. for (i = n, j = 0; i > 0; i /= 2
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In a binary max heap containing n numbers, the smallest element can be found in time
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Which one of the following in place sorting algorithms needs the minimum number of swaps?
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An element in an array X is called a leader if it is greater than all elements to the right of it in X. The best algorit
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A 3-ary max heap is like a binary max heap, but instead of 2 children, nodes have 3 children. A 3-ary heap can be repres
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Given two arrays of numbers a1,......,an and b1,......, bn where each number is 0 or 1, the fastest algorithm to find th
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A 3-ary max heap is like a binary max heap, but instead of 2 children, nodes have 3 children. A 3-ary heap can be repres
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Consider the following recurrence: $$T\left( n \right){\rm{ }} = {\rm{ 2T(}}\left\lceil {\sqrt n } \right\rceil {\rm{) +
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The median of n elements can be found in O(n) time. Which one of the following is correct about the complexity of quick
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Consider a weighted complete graph G on the vertex set {v1, v2, ..vn} such that the weight of the edge (vi, vj) is $$2|i
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To implement Dijkstra’s shortest path algorithm on unweighted graphs so that it runs in linear time, the data structure
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Consider the following graph: Which one of the following cannot be the sequence of edges added, in that order, to a min
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Let S be an NP-complete problem and Q and R be two other problems not known to be in NP. Q is polynomial time reducible
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Let SHAM3 be the problem of finding a Hamiltonian cycle in a graph G = (V, E) with |V| divisible by 3 and DHAM3 be th
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Consider the following grammar. $$\eqalign{ & S \to S*E \cr & S \to E \cr & E \to F + E \cr &a
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Which one of the following grammars generates the following language? $$L = \left( {{a^i}{b^j}|i \ne j} \right)$$
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In the correct grammar of the previous question, what is the length of the derivation (number of steps starring from S)
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Consider the following grammar: $$\eqalign{ & S \to FR \cr & R \to *S\,|\,\varepsilon \cr & F \to
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Consider the following translation scheme. $$\eqalign{ & S \to ER \cr & R \to *E\left\{ {pr{\mathop{\rm in
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Consider the following C code segment. for (i = 0; i < n; i++) { for (j=0; j < n; j++) {
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Consider the diagram shown below where a number of LANs are connected by (transparent) bridges. In order to avoid packet
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Consider the diagram shown below where a number of LANs are connected by (transparent) bridges. In order to avoid packet
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Station A uses 32 byte packets to transmit messages to Station B using a sliding window protocol. The round trip delay b
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Station A needs to send a message consisting of 9 packets to Station B using a sliding window (window size 3) and go-bac
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For which one of the following reasons does Internet Protocol (IP) use the time-to-live (TTL) field in the IP datagram h
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Two computers C1 and C2 are configured as follows. C1 has IP address 203.197.2.53 and netmask 255.255.128.0. C2 has IP a
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Given two three bit number $${a_2}{a_1}{a_0}$$ and $${b_2}{b_1}{b_0}$$ and $$c,$$ the carry in the function that repres
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A $$CPU$$ has a cache with block size $$64$$ bytes. The main memory has $$k$$ banks, each bank being $$c$$ bytes wide. C
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Consider two cache organization: The first one is $$32$$ $$KB$$ $$2$$-way set associate with $$32$$-byte block size. The
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Consider two cache organization: The first one is $$32$$ $$KB$$ $$2$$-way set associate with $$32$$-byte block size. The
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A CPU has five stages pipeline and runs at $$1$$ $$GHz$$ frequency. Instruction fetch happens in the first stage of the
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A $$CPU$$ has $$24$$-bit instructions. A program starts at address $$300$$ (in decimal). Which one of the following is a
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Consider the following program segment. Here R1, R2 and R3 are the general purpose registers. Assume that the content
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Consider the following program segment. Here R1, R2 and R3 are the general purpose registers. Assume that the content
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Consider the following program segment. Here R1, R2 and R3 are the general purpose registers. Assume that the content
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An implementation of a queue Q, using two stacks S1 and S2, is given below: void insert(Q, X){ push(S1, X); } void de
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The following function computes the value of mCn correctly for all legal values m and n (m≥1,n≥0 and m>n) int func(
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A scheme for storing binary trees in an array X is as follows. Indexing of X starts at 1 instead of 0. the root is store
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In a binary tree, the number of internal nodes of degree 1 is 5, and the number of internal nodes of degree 2 is 10. The
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Suppose that we have numbers between 1 and 100 in a binary search tree and want to search for the number 55. Which of th
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Which of the following sequences of array elements forms a heap?
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An array X of n distinct integers is interpreted as a complete binary tree. The index of the first element of the array
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An array X of n distinct integers is interpreted as a complete binary tree. The index of the first element of the array
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An array X of n distinct integers is interpreted as a complete binary tree. The index of the first element of the array
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Consider the depth-first-search of an undirected graph with 3 vertices P, Q, and R. Let discovery time d(u) represent th
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Let T be a depth first search tree in an undirected graph G. Vertices u and v are leaves of this tree T. The degrees of
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Let T be a depth-first search tree in an undirected graph G. Vertices u and v are leaves of this tree T. The degrees of
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Consider the relation enrolled (student, course) in which (student, course ) is the primary key, and the relation Paid (
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The following functional dependencies are given : $$\eqalign{ & AB \to CD,\,AF \to D,\,\,DE \to F, \cr & C
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Consider the relation account (customer, balance) where customer is a primary key and there are no null values. We would
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Consider the relation "enrolled (student, course)" in which (student, course) is the primary key, and the relation "paid
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Consider a database with three relation instances shown below. The primary keys for the Drivers and Cars relation are Di
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Consider a database with three relation instances shown below. The primary keys for the Drivers and Cars relation are Di
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Consider the relations r1(P, Q, R) and r2(R, S, T) with primary keys P and R respectively. The relation r1 contains 2000
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Which of the following relational query languages have the same expressive power? I) Relational algebra II) Tuple relati
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Consider a Boolean function $$f(w, x, y, z).$$ Suppose that exactly one of its inputs is allowed to change at a time. If
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Consider the circuit above. Which one of the following options correctly represents $$f(x,y,z)?$$
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You are given a free running clock with a duty cycle of $$50$$% and a digital waveform $$f$$ which changes only at the n
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Consider the circuit in the diagram. The $$ \oplus $$ operator represents $$EX$$-$$OR.$$ The $$D$$ flip-flops are initia
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Which one of the first order predicate calculus statements given below correctly expresses the following English stateme
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Consider the following propositional statements: $${\rm P}1:\,\,\left( {\left( {A \wedge B} \right) \to C} \right) \equ
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In a certain town, the probability that it will rain in the afternoon is known to be 0.6. Moreover, meteorological data
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A logical binary relation $$ \odot $$, is defined as follows: Let ~ be the unary negation (NOT) operator, with higher
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When a coin is tossed, the probability of getting a Head is p, 0 < p < 1. Let N be the random variable denoting th
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Consider the following first order logic formula in which $$R$$ is a binary relation symbol. $$\forall x\forall y\left(
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Let $$P, Q$$, and $$R$$ be sets. Let $$\Delta $$ denote the symmetric difference operator defined as $$P\Delta Q = \left
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Let E, F and G be finite sets. Let $$X = \,\left( {E\, \cap \,F\,} \right)\, - \,\left( {F\, \cap \,G\,} \right)$$ and
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A relation $$R$$ is defined on ordered pairs of integers as follows: $$\left( {x,y} \right)R\left( {u,v} \right)\,if\,x
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Let $$X,. Y, Z$$ be sets of sizes $$x, y$$ and $$z$$ respectively. Let $$W = X x Y$$ and $$E$$ be the set of all
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The set $$\left\{ {1,\,\,2,\,\,3,\,\,5,\,\,7,\,\,8,\,\,9} \right\}$$ under multiplication modulo 10 is not a group. Give
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For the set $$N$$ of natural numbers and a binary operation $$f:N \times N \to N$$, an element $$z \in N$$ is called an
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Given a set of elements N = {1, 2, ....., n} and two arbitrary subsets $$A\, \subseteq \,N\,$$ and $$B\, \subseteq \,N\,
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Let S = {1, 2, 3,....., m} , m > 3. Let $${X_1},\,....,\,{X_n}$$ be subsets of S each of size 3. Define a function f
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Consider the set S = {a, b, c, d}. Consider the following 4 partitions $$\,{\pi _1},\,{\pi _2},\,{\pi _3},\,{\pi _4}$$ o
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If all the edge weights of an undirected graph are positive, then any subject of edges that connects all the vertices an
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Consider a weighted complete graph $$G$$ on the vertex set $$\left\{ {{v_1},\,\,\,{v_2},....,\,\,\,{v_n}} \right\}$$ suc
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Consider the polynomial $$P\left( x \right) = {a_0} + {a_1}x + {a_2}{x^2} + {a_3}{x^3},$$ where $${a_i} \ne 0,\forall i
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For each elements in a set of size $$2n$$, an unbiased coin in tossed. The $$2n$$ coin tosses are independent. An elemen
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What is the cardinality of the set of integers $$X$$ defined below? $$X = $$ {$$n\left| {1 \le n \le 123,\,\,\,\,\,n} \r
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The $${2^n}$$ vertices of a graph $$G$$ correspond to all subsets of a set of size $$n$$, for $$n \ge 6$$. Two vertices
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The $${2^n}$$ vertices of a graph $$G$$ correspond to all subsets of a set of size $$n$$, for $$n \ge 6$$. Two vertices
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Consider the undirected graph $$G$$ defined as follows. The vertices of $$G$$ are bit strings of length $$n$$. We have a
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$$F$$ is an $$n$$ $$x$$ $$n$$ real matrix. $$b$$ is an $$n$$ $$x$$ $$1$$ real vector. Suppose there are two $$n$$ $$x$$
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What are the eigen values of the matrix $$P$$ given below? $$$P = \left( {\matrix{ a & 1 & 0 \cr 1 &
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Consider three $$CPU$$-intensive process, which require $$10,20$$ and $$30$$ time units and arrive at times $$0,2$$ and
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Consider three processes (process id $$0,1,2,$$ respectively) with compute time bursts $$2, 4,$$ and $$8$$ time units. A
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Consider three processes, all arriving at time zero, with total execution time of $$10,20,$$ and $$30$$ units, respectiv
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The atomic fetch-and-set x, y instruction unconditionally sets the memory location x to 1 and fetches the old value of x
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Barrier is a synchronization construct where a set of processes synchronizes globally i.e. each process in the set arriv
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Barrier is a synchronization construct where a set of processes synchronizes globally i.e. each process in the set arriv
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A Computer system supports $$32$$-bit virtual addresses as well as $$32$$-bit physical addresses. Since the virtual addr
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Consider the following snapshot of a system running n processes. Process i is holding xi instances of a resource R, for
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Consider this C code to swap two integers and these five statements: void swap(int *px, int *py) { *px = *px - *py
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If $$s$$ is a string over $${\left( {0 + 1} \right)^ * }$$ then let $${n_0}\left( s \right)$$ denote the number of $$0'$
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Consider the regular language $$L = {\left( {111 + 11111} \right)^ * }.$$ The minimum number of states in any $$DFA$$ ac
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Let $${L_1} = \left\{ {{0^{n + m}}{1^n}{0^m}\left| {n,m \ge 0} \right.} \right\},$$ $$\,\,\,{L_2} = \left\{ {{0^{n + m}
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Consider the following statements about the context-free grammar $$G = \left\{ {S \to SS,\,S \to ab,\,S \to ba,\,S \to \
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For $$s \in {\left( {0 + 1} \right)^ * },$$ let $$d(s)$$ denote the decimal value of $$s(e. g.d(101)=5)$$ Let $$L = \lef
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Let $${L_1}$$ be a regular language, $${L_2}$$ be a deterministic context-free language and $${L_3}$$ a recursively enum
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