GATE CSE 2003
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## GATE CSE

Consider an array multiplier for multiplying two n bit numbers. If each gate in the circuit has a unit delay, the total
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Consider the following three claims I. (n + k)m = $$\Theta \,({n^m})$$ where k and m are constants II. 2n+1 = O(2n) II
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In a heap with n elements with the smallest element at the root, the 7th smallest element can be found in time
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The cube root of a natural number n is defined as the largest natural number m such that $${m^3} \le n$$. The complexity
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The usual $$\Theta ({n^2})$$ implementation of Insertion Sort to sort an array uses linear search to identify the positi
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Let G=(V,E) be an undirected graph with a subgraph G1=(V1,E1). Weights are assigned to edges of G as follows. $$w(e) = View Question Let G = (V, E) be a directed graph with n vertices. A path from vi to vj in G is sequence of vertices (vi, vi+1, ……., vj View Question Ram and Shyam have been asked to show that a certain problem Π is NP-complete. Ram shows a polynomial time reduction fro View Question What is the weight of a minimum spanning tree of the following graph? View Question Assume that the SLR parser for a grammar G has n1 states and the LALR parser for G has n2 states. The relationship betwe View Question In a bottom-up evaluation of a syntax directed definition, inherited attributes can View Question Which of the following suffices to convert an arbitrary CFG to an LL(1) grammar? View Question Consider the grammar shown below$$\eqalign{ &amp; S \to iEtSS'\,|\,\,a \cr &amp; S' \to eS\,|\,\,\varepsilon \c
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Consider the translation scheme shown below \eqalign{ &amp; S \to TR \cr &amp; R \to + T\left\{ {pr{\mathop{\rm View Question Consider the grammar shown below.\eqalign{ &amp; S \to CC \cr &amp; C \to cC\,|\,d \cr} $$This grammar is View Question Which of the following statements is FALSE? View Question Which of the following is NOT an advantage of using shared, dynamically linked libraries as opposed to using statically View Question Consider the syntax directed definition shown below. Here, gen is a function that generates the output code, and newtem View Question A 2 km long broadcast LAN has 107 bps bandwidth and uses CSMA/CD. The signal travels along the wire at 2 × 108 m/s. What View Question Host A is sending data to host B over a full duplex link. A and B are using the sliding window protocol for flow control View Question Which of the following assertions is FALSE about the Internet Protocol (IP)? View Question The subnet mask for a particular network is 255.255.31.0. Which of the following pairs of IP addresses could belong to t View Question Which of the following functionalities must be implemented by a transport protocol over and above the network protocol? View Question The following is a scheme for floating point number representation using$$16$$bits. Let$$s, e,$$and$$m$$be the n View Question For a pipelined$$CPU$$with a single$$ALU$$, consider the following situations$$1.\,\,\,\,\,$$The$$j+1$$instructio View Question Let S be a stack of size n &gt;= 1. Starting with the empty stack, suppose we push the first n natural numbers in sequen View Question Consider the function f defined below. struct item { int data; struct item * next; }; int f(struct ite View Question Consider the following graph among the following sequences I. a b e g h f II. a b f e h g III. a b f h g e IV. a f g View Question Suppose the numbers 7, 5, 1, 8, 3, 6, 0, 9, 4, 2 are inserted in that order into an initially empty binary search tree. View Question Consider the following functional dependencies in a database.$$\eqalign{ &amp; \,\,\,\,Date\,\,of\,\,Birth\,\, \to \,
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Consider the set of relations shown below and the SQL query that follows. Students: (Roll_number, Name, Date_of_birth) C
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Consider the following SQL query: Select distinct a1, a2, ..., an From r1, r2, ..., rm Where P; For an arbitrary p
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Which of the following scenarios may lead to an irrecoverable error in a database system?
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Consider three data items D1, D2, and D3, and the following execution schedule of transactions T1, T2, and T3. In the di
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Assuming all numbers are in $$2's$$ complement representation, which of the following numbers is divisible by $$11111011 View Question The literal count of a Boolean expression is the sum of the number of times each literal appears in the expression. For View Question Consider the following circuit composed of$$XOR$$gates are non-inverting buffers. The non-inverting buffers have del View Question A 1- input, 2- output synchronous sequential circuit behaves as follows. Let$${z_k},\,{n_k}$$denote the number of$$0’
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Consider the $$ALU$$ shown below If the operands are in $$2's$$ complement representation, which of the following oper
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The following resolution rule is used in logic programming. Derive clause $$\left( {P \vee Q} \right)$$ from clauses $$\ View Question Let P(E) denote the probability of the event E. Given P(A) = 1, P(B) =$${\raise0.5ex\hbox{$\scriptstyle 1$} \kern-0.1em
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Let $$A$$ be a sequence of $$8$$ distinct integers sorted in ascending order. How many distinct pairs of sequence, $$B$$
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$$n$$ couples are invited to a party with the condition that every husband should be accompanied by his wife. However,
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$$m$$ identical balls are to be placed in $$n$$ distinct bags. You are given that $$m \ge kn$$, where $$k$$ is a natural
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Let $$G$$ be an arbitrary graph with $$n$$ nodes and $$k$$ components. If a vertex is removed from $$G$$, the number of
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Consider the following system of linear equations $$\left[ {\matrix{ 2 &amp; 1 &amp; { - 4} \cr 4 &amp; 3 &amp View Question$$A$$graph$$G=(V, E)$$satisfies$$\left| E \right| \le \,3\left| V \right| - 6.$$The min-degree of$$G$$View Question How many perfect matchings are there in a complete graph of 6 vertices? View Question$$A$$system of equations represented by$$AX=0$$where$$X$$is a column vector of unknown and$$A$$is a square matrix View Question$$\mathop {Lim}\limits_{x \to 0} \,{{Si{n^2}x} \over x} = \_\_\_\_.$$View Question A uni-processor computer system only has two processes, both of which alternate$$10msCPU$$bursts with$$90$$View Question Suppose we want to synchronize two concurrent processes P and Q using binary semaphores S and T. The code for the proces View Question Suppose we want to synchronize two concurrent processes P and Q using binary semaphores S and T. The code for the proces View Question In a system with$$32$$bit virtual addresses and$$1KB$$page size, use of one-level page tables for virtual to ph View Question Which of the following is NOT an advantage of using shared, dynamically linked libraries as opposed to using statically View Question A processor uses$$2$$-level page tables for virtual to physical address translation. Page tables for both levels are st View Question A processor uses$$2$$-level page tables for virtual to physical address translation. Page tables for both levels are st View Question Using a larger block size in a fixed block size file system leads to View Question Which of the following statements is FALSE? View Question The following program fragment is written in a programming language that allows global variables and does not allow nest View Question The following program fragment is written in a programming language that allows global variables and does not allow nest View Question Consider the following C function. float f,(float x, int y) { float p, s; int i; for (s=1,p=1,i=1; i &lt; y; i++ View Question Consider the following class definitions in a hypothetical Object Oriented language that supports inheritance and uses d View Question Assume the following C variable declaration int * A[10], B[10][10]; Of the following expressions I. A[2] II. A[2] [3] II View Question Consider the C program shown below. #include &lt; stdio.h &gt; #define print(x) printf("%d ", x) int x; void Q(int z) { View Question The regular expression$${0^ * }\left( {{{10}^ * }} \right){}^ * $$denotes the same set as View Question Consider the set$$\sum {^ * } $$of all strings over the alphabet$$\,\sum { = \,\,\,\left\{ {0,\,\,\,1} \right\}.\sum
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Consider the $$NFA$$ $$M$$ shown below. Let the language accepted by $$M$$ be $$L.$$ Let $${L_1}$$ be the language acc
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Consider the following deterministic finite state automation $$M.$$ Let $$S$$ denote the set of seven bit binary stri
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Nobody knows yet if $$P=NP$$. Consider the language $$L$$ defined as follows $$L = \left\{ {\matrix{ {{{\left( {0 + 1 View Question If the strings of a language$$L$$can be effectively enumerated in lexicographic (i.e., alphabetic$$(c)$$order, which View Question A single tape Turing Machine$$M$$has two states$${q_0}$$and$${q_1}$$, of which$${q_0}$$is the starting state. The View Question Define Languages$${L_0}$$and$${L_1}$$as follows$${L_0} = \left\{ { &lt; M,\,w,\,0 &gt; \left| {M\,\,} \right.} \rig
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