GATE CSE 2003

Exam Held on Thu Jan 01 1970 00:00:00 GMT+0000 (Coordinated Universal Time)
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Algorithms

Consider an array multiplier for multiplying two n bit numbers. If each gate in ...
Consider the following three claims <br/> I. (n + k)<sup>m</sup> = $$\Theta \,({...
In a heap with n elements with the smallest element at the root, the 7<sup>th</s...
The cube root of a natural number n is defined as the largest natural number m s...
The usual $$\Theta ({n^2})$$ implementation of Insertion Sort to sort an array u...
Let G=(V,E) be an undirected graph with a subgraph G<sub>1</sub>=(V<sub>1</sub>,...
Let G = (V, E) be a directed graph with n vertices. A path from v<sub>i</sub> to...
Ram and Shyam have been asked to show that a certain problem Π is NP-complete. R...
What is the weight of a minimum spanning tree of the following graph? <img class...

Compiler Design

Which of the following suffices to convert an arbitrary CFG to an LL(1) grammar?...
Assume that the SLR parser for a grammar G has n<sub>1</sub> states and the LALR...
In a bottom-up evaluation of a syntax directed definition, inherited attributes ...
<p>Consider the grammar shown below</p> $$\eqalign{ & S \to iEtSS'\,|\,\,a \c...
<p>Consider the translation scheme shown below</p> $$\eqalign{ & S \to TR \cr...
<p>Consider the grammar shown below.</p> $$\eqalign{ & S \to CC \cr & C \t...
Which of the following statements is <b>FALSE</b>?
<p>Consider the syntax directed definition shown below.</p> <img class="question...
Which of the following is NOT an advantage of using shared, dynamically linked l...

Computer Networks

A 2 km long broadcast LAN has 10<sup>7</sup> bps bandwidth and uses CSMA/CD. The...
Host A is sending data to host B over a full duplex link. A and B are using the ...
Which of the following assertions is FALSE about the Internet Protocol (IP)?
The subnet mask for a particular network is 255.255.31.0. Which of the following...
Which of the following functionalities must be implemented by a transport protoc...

Computer Organization

The following is a scheme for floating point number representation using $$16$$ ...
For a pipelined $$CPU$$ with a single $$ALU$$, consider the following situations...

Data Structures

Let S be a stack of size n >= 1. Starting with the empty stack, suppose we push ...
Consider the function f defined below. <pre><code>struct item { int data...
Consider the following graph among the following sequences <br/> I. a b e g h f ...
Suppose the numbers 7, 5, 1, 8, 3, 6, 0, 9, 4, 2 are inserted in that order into...

Database Management System

Consider the following functional dependencies in a database. <br>$$\eqalign{ ...
Consider the set of relations shown below and the SQL query that follows. <p>Stu...
Consider the following SQL query: <pre><code class='sql'>Select distinct a<sub>...
Which of the following scenarios may lead to an irrecoverable error in a databas...
Consider three data items D1, D2, and D3, and the following execution schedule o...

Digital Logic

Assuming all numbers are in $$2's$$ complement representation, which of the foll...
The literal count of a Boolean expression is the sum of the number of times each...
Consider the following circuit composed of $$XOR$$ gates are non-inverting buffe...
A 1- input, 2- output synchronous sequential circuit behaves as follows. <p>Let ...
Consider the $$ALU$$ shown below <img class="question-image" src="https://imagex...

Discrete Mathematics

The following resolution rule is used in logic programming. Derive clause $$\lef...
Let P(E) denote the probability of the event E. Given P(A) = 1, P(B) = $${\raise...
Let $$A$$ be a sequence of $$8$$ distinct integers sorted in ascending order. Ho...
$$n$$ couples are invited to a party with the condition that every husband shou...
$$m$$ identical balls are to be placed in $$n$$ distinct bags. You are given tha...
Let $$G$$ be an arbitrary graph with $$n$$ nodes and $$k$$ components. If a vert...
Consider the following system of linear equations $$$\left[ {\matrix{ 2 & 1 ...
$$A$$ graph $$G$$ $$=$$ $$(V, E)$$ satisfies $$\left| E \right| \le \,3\left| V...
How many perfect matchings are there in a complete graph of 6 vertices?
$$A$$ system of equations represented by $$AX=0$$ where $$X$$ is a column vector...
$$\mathop {Lim}\limits_{x \to 0} \,{{Si{n^2}x} \over x} = \_\_\_\_.$$

Operating Systems

A uni-processor computer system only has two processes, both of which alternate ...
Suppose we want to synchronize two concurrent processes P and Q using binary sem...
Suppose we want to synchronize two concurrent processes P and Q using binary sem...
In a system with $$32$$ bit virtual addresses and $$1$$ $$KB$$ page size, use of...
A processor uses $$2$$-level page tables for virtual to physical address transla...
Which of the following is NOT an advantage of using shared, dynamically linked l...
A processor uses $$2$$-level page tables for virtual to physical address transla...
Using a larger block size in a fixed block size file system leads to

Programming Languages

Which of the following statements is FALSE?
The following program fragment is written in a programming language that allows ...
The following program fragment is written in a programming language that allows ...
Consider the following C function. <pre><code class="c">float f,(float x, int y)...
Consider the following class definitions in a hypothetical Object Oriented langu...
Assume the following C variable declaration <p>int * A[10], B[10][10];</p> Of th...
Consider the C program shown below. <pre><code>#include < stdio.h > #define prin...

Theory of Computation

The regular expression $${0^ * }\left( {{{10}^ * }} \right){}^ * $$denotes the s...
Consider the set $$\sum {^ * } $$ of all strings over the alphabet $$\,\sum { = ...
Consider the $$NFA$$ $$M$$ shown below. <img class="question-image" src="https:/...
Consider the following deterministic finite state automation $$M.$$ <img class=...
Nobody knows yet if $$P=NP$$. Consider the language $$L$$ defined as follows <br...
If the strings of a language $$L$$ can be effectively enumerated in lexicographi...
A single tape Turing Machine $$M$$ has two states $${q_0}$$ and $${q_1}$$, of wh...
Define Languages $${L_0}$$ and $${L_1}$$ as follows <br>$${L_0} = \left\{ { < M,...

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