GATE CSE 2007

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

Consider the following segment of C-code: <pre><code>int j, n; j=1; while(j <= n...
Consider the DAG with $$V = \{1,2,3,4,5,6\}$$, shown below. <img class="question...
Which of the following sorting algorithms has the lowest worst-case complexity?
What is the time complexity of the following recursive function? <pre><code>int ...
Consider the following C code segment: <pre><code class="c">int IsPrime(n){ int...
Consider the process of inserting an element into a Max Heap, where the Max Heap...
In the following C function, let n $$ \ge $$ m. <pre><code class='c'>int gcd(n,m...
An array of n numbers is given, where n is an even number. The maximum as well a...
Suppose the letters a, b, c, d, e, f have probabilities 1/2, 1/4, 1/8, 1/16, 1/3...
Let w be the minimum weight among all edge weights in an undirected connected gr...
Suppose the letters a, b, c, d, e, f have probabilities 1/2, 1/4, 1/8, 1/16, 1/3...
In an unweighted, undirected connected graph, the shortest path from a node S to...

Compiler Design

Which one of the following is a top-down parser?
Consider the following two statements: <p>P: Every regular grammar is LL(1) <br...
<p>Consider the grammar with non-terminals N = { S, C, S<sub>1</sub> }, terminal...
<p>Consider the CFG with { S, A, B } as the non-terminal alphabet, { a, b } as t...
<p>Consider the CFG with { S, A, B } as the non-terminal alphabet, { a, b } as t...

Computer Networks

In Ethernet when Manchester encoding is used, the bit rate is:
There are n stations in a slotted LAN. Each station attempts to transmit with a ...
The message 11001001 is to be transmitted using the CRC polynomial x<sup>3</sup>...
The distance between two stations M and N is L kilometers. All frames are K bits...
The address of a class B host is to be split into subnets with a 6-bit subnet nu...
Which one of the following uses UDP as the transport protocol?
Match the following: <p><b>List - I</b> </p> (P) SMTP <br/>(Q) BGP <br/>(R) TC...
Consider the following two statements: <p>i. A hash function (these are often u...
The minimum positive integer p such that <b>(3<sup>p</sup> modulo 17) = 1</b> is...
Exponentiation is a heavily used operation in public key cryptography. Which of ...

Computer Organization

In a look $$-$$ ahead carry generator, the carry generate function $${G_i}$$ and...
Consider a $$4$$-way set associative cache consisting of $$128$$ lines with a li...
Consider a machine with a byte addressable main memory of $${2^{16}}$$ bytes. As...
Consider a machine with a byte addressable main memory of $${2^{16}}$$ bytes. As...
Consider a pipelined processor with the following four stages <br>$$\,\,\,\,\,$$...

Data Structures

Suppose you are given an implementation of a queue of integers. The operations t...
The following postfix expression with single digit operands is evaluated using a...
Consider the following C program: <pre><code class="c">#include #define EOF -1...
The maximum number of binary trees that can be formed with three unlabeled nodes...
The height of a binary tree is the maximum number of edges in any root to leaf p...
The inorder and preorder traversal of a binary tree are d b e a f c g and a b d ...
When searching for the key value 60 in a binary search tree, nodes containing th...
Consider the following C program segment where CellNode represents a node in a b...
A complete n-ary tree is a tree in which each node has n children or no children...
What is the largest integer m such that every simple connected graph with n vert...
Consider the following two statements: <br/> i. A hash function (these are often...
Consider a hash table of size seven, with starting index zero, and a hash functi...
Consider a hash function that distributes keys uniformly. The hash table size is...

Database Management System

Which one of the following statements if <b>FALSE?</b>
Consider the table <b>employee(empId, name, department, salary)</b> and the two ...
<p>Information about a collection of students is given by the relation <b>studIn...
Consider a selection of the form σ<sub>A</sub> ≤ 100(r), where r is a relation w...
<p>Consider the relation <b>employee(name, sex, supervisorName)</b> with name as...
Consider the following relation schemas : <p>b-Schema = (b-name, b-city, assets)...
Consider the following schedules involving two transactions. Which one of the fo...
Consider the following two transactions: T<sub>1</sub> and T<sub>2</sub>. <pre><...
Consider the B<sup>+</sup> tree in the adjoining figure, where each node has at ...
Consider the B<sup>+</sup> tree in the adjoining figure, where each node has at ...
The order of a leaf node in a B<sup>+</sup>- tree is the maximum number of (valu...

Digital Logic

Consider the following Boolean function with four variables <br>$$F\left( {w,\,...
Let $$f\left( {w,x,y,z} \right) = \sum {\left( {0,4,5,7,8,9,13,15} \right).} $$ ...
How many $$3$$ to $$8$$ decodes with an enable input are needed to construct to ...
Suppose only one multiplexer and one inverter are allowed to be used to implemen...
The control signal functions of a $$4$$-bit binary counter are given below $$($$...

Discrete Mathematics

Suppose there are two coins. The first coin gives heads with probability 5/8 whe...
Suppose we uniformly and randomly select a permutation from the 20! permutations...
Which one of these first-order logic formulae is valid?
How many different non-isomorphic Abelian groups of order 4 are there?
What is the maximum number of different Boolean functions involving $$n$$ Boolea...
Let $$S$$ be a set6 of $$n$$ elements. The number of ordered pairs in the larges...
Consider the following Hasse diagrams. <br> <img class="question-image" src="htt...
A partial order P is defined on the set of natural numbers as following. Herw x/...
Consider the set of (column) vectors defined by $$X = \,\{ \,x\, \in \,{R^3}\,\l...
Let $$G$$ be the non-planar graph with minimum possible number of edges. Then $$...
The height of a binary tree is the maximum number of edges in any root to leaf p...
The maximum number of binary trees that can be formed with three unlabeled nodes...
Consider a weighted undirected graph with positive edge weights and let $$uv$$ b...
Consider the following two statements about the function $$$f\left( x \right) =...
Suppose that a robot is placed on the Cartesian plane. At each step it is allowe...
Suppose that a robot is placed on the Cartesian plane. At each step it is allowe...
Let Graph$$(x)$$ be a predicate which denotes that $$x$$ is a graph. Let Connect...
Which of the following graphs has an Eulerian circuit?
Let $$A$$ be $$a$$ $$4$$ $$x$$ $$4$$ matrix with eigen values $$-5$$, $$-2, 1, 4...
Let $$A$$ be the matrix $$\left[ {\matrix{ 3 & 1 \cr 1 & 2 \cr } } ...

Operating Systems

<b>Group-1</b> contains some $$CPU$$ scheduling algorithms and <b>Group-2</b> co...
Consider the following statements about user level threads and kernel level thre...
An operating system uses Shortest Remaining Time first $$(SRT)$$ process schedul...
Two processes, P1 and P2, need to access a critical section of code. Consider th...
A virtual memory system uses First In First Out (FIFO) page replacement policy a...
A process has been allocated $$3$$ page frames. Assume that none of the pages of...
A process has been allocated $$3$$ page frames. Assume that none of the pages of...
Consider a disk pack with 16 surfaces, 128 tracks per surface and 256 sectors pe...
A single processor system has three resource types X, Y and Z, which are shared ...

Programming Languages

Consider the following C function: <pre><code>int f(int n) { static int r = 0...

Theory of Computation

A minimum state deterministic finite automation accepting the language $$L = \le...
Which of the following languages is regular?
Consider the following finite state automation <img class="question-image" src="...
Consider the following finite state automation <img class="question-image" src="...
The language $$L = \left\{ {{0^i}{{21}^i}\,|\,i \ge 0} \right\}$$ over the alpha...
Consider the $$CFG$$ with $$\left\{ {S,A,B} \right\}$$ as the non-terminal alpha...
Consider the $$CFG$$ with $$\left\{ {S,A,B} \right\}$$ as the non-terminal alpha...

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