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## GATE CSE 2003

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

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> = $$\Theta \,({n... In a heap with n elements with the smallest element at the root, the 7<sup>th</s... The cube root of a natural number n is defined as the largest natural number m s... The usual$$\Theta ({n^2})$$implementation of Insertion Sort to sort an array u... Let G=(V,E) be an undirected graph with a subgraph G<sub>1</sub>=(V<sub>1</sub>,... Let G = (V, E) be a directed graph with n vertices. A path from v<sub>i</sub> to... Ram and Shyam have been asked to show that a certain problem Π is NP-complete. R... What is the weight of a minimum spanning tree of the following graph? <img class... Which of the following suffices to convert an arbitrary CFG to an LL(1) grammar?... In a bottom-up evaluation of a syntax directed definition, inherited attributes ... Assume that the SLR parser for a grammar G has n<sub>1</sub> states and the LALR... <p>Consider the grammar shown below</p>$$\eqalign{ &amp; S \to iEtSS'\,|\,\,a...
<p>Consider the translation scheme shown below</p> \eqalign{ &amp; S \to TR ... <p>Consider the grammar shown below.</p>\eqalign{ &amp; S \to CC \cr &a...
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...
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...
The following is a scheme for floating point number representation using $$16$$ ...
For a pipelined $$CPU$$ with a single $$ALU$$, consider the following situations...
Let S be a stack of size n &gt;= 1. Starting with the empty stack, suppose we pu...
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...
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... Assuming all numbers are in2'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$$shown below <img class="question-image" src="https://imagex... The following resolution rule is used in logic programming. Derive clause$$\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 &amp... $$A$$ 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} = \_\_\_\_.$$A uni-processor computer system only has two processes, both of which alternate ... Suppose we want to synchronize two concurrent processes P and Q using binary sem... Suppose we want to synchronize two concurrent processes P and Q using binary sem... In a system with$$32$$bit virtual addresses and$$1KB$$page size, use of... Which of the following is NOT an advantage of using shared, dynamically linked l... A processor uses$$2$$-level page tables for virtual to physical address transla... A processor uses$$2$$-level page tables for virtual to physical address transla... Using a larger block size in a fixed block size file system leads to Which of the following statements is FALSE? The following program fragment is written in a programming language that allows ... The following program fragment is written in a programming language that allows ... Consider the following C function. <pre><code class="c">float f,(float x, int y)... Consider the following class definitions in a hypothetical Object Oriented langu... Assume the following C variable declaration <p>int * A[10], B[10][10];</p> Of th... Consider the C program shown below. <pre><code>#include &lt; stdio.h &gt; #defin... The regular expression$${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\{ { &lt;...

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