GATE CSE 2003

## GATE CSE

Consider an array multiplier for multiplying two n bit numbers. If each gate in the circuit has a unit delay, the total

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Consider the following three claims
I. (n + k)m = $$\Theta \,({n^m})$$ where k and m are constants
II. 2n+1 = O(2n)
II

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In a heap with n elements with the smallest element at the root, the 7th smallest
element can be found in time

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The cube root of a natural number n is defined as the largest natural number m such that $${m^3} \le n$$. The complexity

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The usual $$\Theta ({n^2})$$ implementation of Insertion Sort to sort an array uses linear search to identify the positi

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Let G=(V,E) be an undirected graph with a subgraph G1=(V1,E1). Weights are assigned to edges of G as follows.
$$$w(e) =

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Let G = (V, E) be a directed graph with n vertices. A path from vi to vj in G is sequence of vertices (vi, vi+1, ……., vj

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Ram and Shyam have been asked to show that a certain problem Π is NP-complete. Ram shows a polynomial time reduction fro

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What is the weight of a minimum spanning tree of the following graph?

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Which of the following suffices to convert an arbitrary CFG to an LL(1) grammar?

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In a bottom-up evaluation of a syntax directed definition, inherited attributes can

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Assume that the SLR parser for a grammar G has n1 states and the LALR parser for G has n2 states. The relationship betwe

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Consider the grammar shown below
$$\eqalign{
& S \to iEtSS'\,|\,\,a \cr
& S' \to eS\,|\,\,\varepsilon \c

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Consider the translation scheme shown below
$$\eqalign{
& S \to TR \cr
& R \to + T\left\{ {pr{\mathop{\rm

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Consider the grammar shown below.
$$\eqalign{
& S \to CC \cr
& C \to cC\,|\,d \cr} $$
This grammar is

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Which of the following statements is FALSE?

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Consider the syntax directed definition shown below.
Here, gen is a function that generates the output code, and newtem

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Which of the following is NOT an advantage of using shared, dynamically linked libraries as opposed to using statically

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A 2 km long broadcast LAN has 107 bps bandwidth and uses CSMA/CD. The signal travels along the wire at 2 × 108 m/s. What

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Host A is sending data to host B over a full duplex link. A and B are using the sliding window protocol for flow control

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Which of the following assertions is FALSE about the Internet Protocol (IP)?

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The subnet mask for a particular network is 255.255.31.0. Which of the following pairs of IP addresses could belong to t

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Which of the following functionalities must be implemented by a transport protocol over and above the network protocol?

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The following is a scheme for floating point number representation using $$16$$ bits.
Let $$s, e,$$ and $$m$$ be the n

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For a pipelined $$CPU$$ with a single $$ALU$$, consider the following situations
$$1.\,\,\,\,\,$$ The $$j+1$$ instructio

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Let S be a stack of size n >= 1. Starting with the empty stack, suppose we push the first n natural numbers in sequen

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Consider the function f defined below.
struct item {
int data;
struct item * next;
};
int f(struct ite

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Consider the following graph among the following sequences
I. a b e g h f
II. a b f e h g
III. a b f h g e
IV. a f g

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Suppose the numbers 7, 5, 1, 8, 3, 6, 0, 9, 4, 2 are inserted in that order into an
initially empty binary search tree.

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Consider the following functional dependencies in a database.
$$\eqalign{
& \,\,\,\,Date\,\,of\,\,Birth\,\, \to \,

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Consider the set of relations shown below and the SQL query that follows.
Students: (Roll_number, Name, Date_of_birth)
C

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Consider the following SQL query:
Select distinct a1, a2, ..., an
From r1, r2, ..., rm
Where P;
For an arbitrary p

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Which of the following scenarios may lead to an irrecoverable error in a database system?

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Consider three data items D1, D2, and D3, and the following execution schedule of transactions T1, T2, and T3. In the di

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Assuming all numbers are in $$2's$$ complement representation, which of the following numbers is divisible by $$11111011

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The literal count of a Boolean expression is the sum of the number of times each literal appears in the expression. For

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Consider the following circuit composed of $$XOR$$ gates are non-inverting buffers.
The non-inverting buffers have del

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A 1- input, 2- output synchronous sequential circuit behaves as follows.
Let $${z_k},\,{n_k}$$ denote the number of $$0’

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Consider the $$ALU$$ shown below
If the operands are in $$2's$$ complement representation, which of the following oper

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The following resolution rule is used in logic programming. Derive clause $$\left( {P \vee Q} \right)$$ from clauses $$\

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Let P(E) denote the probability of the event E. Given P(A) = 1, P(B) = $${\raise0.5ex\hbox{$\scriptstyle 1$}
\kern-0.1em

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Let $$A$$ be a sequence of $$8$$ distinct integers sorted in ascending order. How many distinct pairs of sequence, $$B$$

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$$n$$ couples are invited to a party with the condition that every husband should be accompanied by his wife. However,

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$$m$$ identical balls are to be placed in $$n$$ distinct bags. You are given that $$m \ge kn$$, where $$k$$ is a natural

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Let $$G$$ be an arbitrary graph with $$n$$ nodes and $$k$$ components. If a vertex is removed from $$G$$, the number of

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Consider the following system of linear equations
$$$\left[ {\matrix{
2 & 1 & { - 4} \cr
4 & 3 &

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$$A$$ graph $$G$$ $$=$$ $$(V, E)$$ satisfies $$\left| E \right| \le \,3\left| V \right| - 6.$$ The min-degree of $$G$$

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How many perfect matchings are there in a complete graph of 6 vertices?

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$$A$$ system of equations represented by $$AX=0$$ where $$X$$ is a column vector of unknown and $$A$$ is a square matrix

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$$\mathop {Lim}\limits_{x \to 0} \,{{Si{n^2}x} \over x} = \_\_\_\_.$$

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A uni-processor computer system only has two processes, both of which alternate $$10$$ $$ms$$ $$CPU$$ bursts with $$90$$

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Suppose we want to synchronize two concurrent processes P and Q using binary semaphores S and T. The code for the proces

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Suppose we want to synchronize two concurrent processes P and Q using binary semaphores S and T. The code for the proces

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In a system with $$32$$ bit virtual addresses and $$1$$ $$KB$$ page size, use of one-level page tables for virtual to ph

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Which of the following is NOT an advantage of using shared, dynamically linked libraries as opposed to using statically

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A processor uses $$2$$-level page tables for virtual to physical address translation. Page tables for both levels are st

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A processor uses $$2$$-level page tables for virtual to physical address translation. Page tables for both levels are st

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Using a larger block size in a fixed block size file system leads to

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Which of the following statements is FALSE?

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The following program fragment is written in a programming language that allows global
variables and does not allow nest

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The following program fragment is written in a programming language that allows global
variables and does not allow nest

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Consider the following C function.
float f,(float x, int y) {
float p, s; int i;
for (s=1,p=1,i=1; i < y; i++

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Consider the following class definitions in a hypothetical Object Oriented
language that supports inheritance and uses d

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Assume the following C variable declaration
int * A[10], B[10][10];
Of the following expressions
I. A[2] II. A[2] [3] II

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Consider the C program shown below.
#include < stdio.h >
#define print(x) printf("%d ", x)
int x;
void Q(int z) {

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The regular expression $${0^ * }\left( {{{10}^ * }} \right){}^ * $$denotes the same set as

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Consider the set $$\sum {^ * } $$ of all strings over the alphabet $$\,\sum { = \,\,\,\left\{ {0,\,\,\,1} \right\}.\sum

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Consider the $$NFA$$ $$M$$ shown below.
Let the language accepted by $$M$$ be $$L.$$ Let $${L_1}$$ be the language acc

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Consider the following deterministic finite state automation $$M.$$
Let $$S$$ denote the set of seven bit binary stri

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Nobody knows yet if $$P=NP$$. Consider the language $$L$$ defined as follows
$$L = \left\{ {\matrix{
{{{\left( {0 + 1

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If the strings of a language $$L$$ can be effectively enumerated in lexicographic (i.e., alphabetic$$(c)$$ order, which

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A single tape Turing Machine $$M$$ has two states $${q_0}$$ and $${q_1}$$, of which $${q_0}$$ is the starting state. The

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Define Languages $${L_0}$$ and $${L_1}$$ as follows
$${L_0} = \left\{ { < M,\,w,\,0 > \left| {M\,\,} \right.} \rig

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