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...
In the following C function, let n $$ \ge $$ m. <pre><code class='c'>int gcd(n,m...
Consider the process of inserting an element into a Max Heap, where the Max Heap...
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 ...
Consider the following C program segment where CellNode represents a node in a b...
When searching for the key value 60 in a binary search tree, nodes containing th...
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 ...
Consider a selection of the form σ<sub>A</sub> ≤ 100(r), where r is a relation w...
<p>Information about a collection of students is given by the relation <b>studIn...
<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 ...
The order of a leaf node in a B<sup>+</sup>- tree is the maximum number of (valu...
Consider the B<sup>+</sup> tree in the adjoining figure, where each node has at ...

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?
Let $$S$$ be a set6 of $$n$$ elements. The number of ordered pairs in the larges...
What is the maximum number of different Boolean functions involving $$n$$ Boolea...
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$$ be the non-planar graph with minimum possible number of edges. Then $$...
Consider a weighted undirected graph with positive edge weights and let $$uv$$ b...
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 the following two statements about the function $$$f\left( x \right) =...
Suppose that a robot is placed on the Cartesian plane. At each step it is allowe...
Suppose that a robot is placed on the Cartesian plane. At each step it is allowe...
Which of the following graphs has an Eulerian circuit?
Let Graph$$(x)$$ be a predicate which denotes that $$x$$ is a graph. Let Connect...
Let $$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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