GATE CSE 2000

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Algorithms

Consider the following functions<br/> $$f(n) = 3{n^{\sqrt n }}$$<br/> $$g(n) = {...
Let s be a sorted array of n integers. Let t(n) denote the time taken for the mo...
Let G be an undirected connected graph with distinct edge weight. Let emax be th...

Compiler Design

The number of tokens in the following C statement is: <pre><code class="c">print...

Computer Organization

Comparing the time $$T1$$ taken for a single instruction on a pipelined $$CPU$$ ...
The most appropriate matching for the following pairs <br>$$X:$$ Indirect addres...
An instruction pipeline has five stages where each stage takes $$2$$ nanoseconds...
A graphics card has on board memory of $$1$$ $$MB.$$ Which of the following mode...

Data Structures

An n $$\times$$ n array v is defined as follows V [i, j] = i - j for all i, j, $...
Suppose you are given an array s[1..n] and a procedure reverse (s, i, j) which r...
Consider the following nested representation of binary trees: (X Y Z) indicates ...
Let LASTPOST, LASTIN and LASTPRE denote the last vertex visited in a postorder, ...
Let G be an undirected graph. Consider a depth-first traversal of G, and let T b...

Database Management System

Given the following relation instance <br>$$\eqalign{ & X\,\,\,\,\,Y\,\,\,\,\,...
Given relations r( w, x ) and s( y, z ), the result of <pre><code class="sql"> s...
In SQL, relations can contain null values, and comparisons with null values are ...
<p>Given the relations </p> <p><b>employee (name, salary, deptno)</b>, and <br/>...
B<sup>+</sup>-trees are preferred to binary trees in databases because

Digital Logic

The number $$43$$ in $$2's$$ complement representation is
The simultaneous equations on the Boolean variables $$x, y, z$$ and $$w,$$ $$$x...
Which function does NOT implement the Karnaugh map given below? <img class="ques...
The following arrangement of master-slave flip-flop <img class="question-image" ...

Discrete Mathematics

Let $$a, b, c, d$$ be propositions. Assume that the equivalences $$a \leftrighta...
A relation R is defined on the set of integers as zRy if f (x + y) is even. Whic...
Let P(S) denote the power set of a set S. Which of the following is always true?...
$${{E_1}}$$ and $${{E_2}}$$ are events in a probability space satisfying the fol...
The minimum number of cards to be dealt from an arbitrarily shuffled deck of 52 ...
The solution to the recurrence equation <br>$$T\left( {{2^k}} \right)$$ $$ = 3T...
The determinant of the matrix $$$\left[ {\matrix{ 2 & 0 & 0 & 0 \cr 8 & ...
An $$n\,\, \times \,\,n$$ array v is defined as follows v[i, j] = i - j for all ...
A multiset is an unordered collection of elements where elements may repeat ay n...
Let $$S = \left\{ {0,1,2,3,4,5,6,7} \right\}$$ and $$ \otimes $$ denote multipli...

Operating Systems

Let m[0] ..m[4] be mutexes (binary semaphores) and P[0] ...P[4] be processes. Su...
Suppose the time to service a page fault is on the average $$10$$ milliseconds, ...
Which of the following is NOT a valid deadlock prevention scheme?

Programming Languages

The value of j at the end of the execution of the following C program <pre><code...
The following C declarations <pre><code class="c">struct node{ int i: float ...
The following C declarations <pre><code class="c">struct node{ int i: float ...
The following C declarations <pre><code class="c">struct node{ int i: float ...
The following C declarations <pre><code class="c">struct node{ int i: float ...
The most appropriate matching for the following pairs <br/><br/>X: m=malloc(5); ...
Consider the following C declaration <pre><code class="c">struct { short s...

Theory of Computation

Let $$S$$ and $$T$$ be languages over $$\sum { = \left\{ {a,b} \right\}} $$ repr...
Let $$L$$ denote the language generated by the grammar $$S \to 0S\left. 0 \right...
What can be said about a regular language $$L$$ over $$\left\{ a \right\}$$ who...
Consider the following decision problems: <br>$${P_1}$$ Does a given finite stat...

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