GATE CSE 2008

## GATE CSE

You are given the post order traversal, P, of a binary search tree on the n element, 1,2,....,n. You have to determine t

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Consider the following functions:
F(n) = 2n
G(n) = n!
H(n) = nlogn
Which of the following statements about the asymptoti

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The minimum number of comparisons required to determine if an integer appears more than n/2 times in a sorted array of n

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The most efficient algorithm for finding the number of connected components in
an undirected graph on n vertices and m e

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Consider the following C functions:
int f1(int n){
if(n == 0 || n == 1){
return n;
}
return (2 * f1(n - 1) + 3 *

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The Breadth First Search algorithm has been implemented using the queue data
structure. One possible order of visiting t

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Consider the following C functions:
int f1(int n){
if(n == 0 || n == 1){
return n;
}
return (2 * f1(n - 1) + 3 *

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We have a binary heap on n elements and wish to insert n more elements (not
necessarily one after another) into this hea

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Consider the Quicksort algorithm. Suppose there is a procedure for finding a pivot element which splits the list into tw

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Dijkstra's single source shortest path algorithm when run from vertex a in the above graph, computes the correct shorte

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The subset-sum problem is defined as follows. Given a set of n positive integers, S = {a1 ,a2 ,a3 ,…,an} and positive in

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The subset-sum problem is defined as follows. Given a set of n positive integers, S = {a1 ,a2 ,a3 ,…,an} and positive in

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Consider the following C program that attempts to locate an element x in an array Y[] using binary search. The program i

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Consider the following C program that attempts to locate an element x in an array Y[] using binary search. The program i

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The subset-sum problem is defined as follows:
Given a set S of n positive
integers and a positive integer W, determine

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Which of the following are true?
I. A programming language which does not permit global variables of any kind and has n

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Which of the following describes a handle (as applicable to LR-parsing) appropriately?

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An LALR(1) parser for a grammar G can have shift-reduce (S-R) conflicts if and only if

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Some code optimizations are carried out on the intermediate code because

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If a class B network on the Internet has a subnet mask of 255.255.248.0, what is the maximum number of hosts per subnet?

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What is the maximum size of data that the application layer can pass on to the TCP layer below?

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Which of the following system calls results in the sending of SYN packets?

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In the slow start phase of the TCP congestion control algorithm, the size of the congestion window

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A client process P needs to make a TCP connection to a server process S. Consider the following situation: the server pr

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A computer on a 10 Mbps network is regulated by a token bucket. The token bucket is filled at a rate of 2 Mbps. It is in

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The total number of keys required for a set of n individuals to be able to communicate with each other using secret key

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In the $$IEEE$$ floating point representation the hexadecimal value $$0\, \times \,00000000$$ corresponds to

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For inclusion to hold between two cache levels $$L1$$ and $$L2$$ in a multilevel cache hierarchy, which of the following

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The following code is to run on a pipelined processor with one branch delay slot
$$\eqalign{
& {{\rm I}_1}:\,\,ADD

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In an instruction execution pipeline, the earliest that the data $$TLB$$ (Translation Look aside Buffer) can be accessed

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Which of the following are NOT true in a pipelined processor?
$$1.$$ Bypassing can handle all RAW hazards
$$2.$$ Registe

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The use of multiple register windows with overlap causes a reduction in the number of memory accesses for
$$1.\,\,\,\,$$

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Which of the following must be true for the $$RFE$$ (Return From Exception) instruction on a general purpose processor?

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Which of the following is/are true of the auto increment addressing mode?
$$1.$$ It is useful in creating self relocatin

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For all delayed conditional branch instructions, irrespective of whether the condition evaluate true or false,

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The following C function takes a single-linked list of integers as a parameter and rearranges the elements of the list.

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Which of the following is TRUE?

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The following three are known to be the preorder, inorder and postorder sequences of a binary tree. But it is not known

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A Binary Search Tree (BST) stores values in the range 37 to 573. Consider the following sequence of keys.
I. 81, 537,

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A Binary Search Tree (BST) stores values in the range 37 to 573. Consider the following sequence of keys.
I. 81, 537, 1

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How many distinct BSTs can be constructed with 3 distinct keys?

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You are given the postorder traversal, P, of a binary search tree on the n elements 1, 2,..........., n. You have to det

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Consider the following sequence of nodes for the undirected graph given below.
1.a b e f d g c
2.a b e f c g d
3.a d

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Consider a hash table of size 11 that uses open addressing with linear probing. Let h(k) = k mod 11 be the hash function

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Consider the following $$ER$$ diagram
The minimum number of table needed to represent $$M,$$ $$N,$$ $$P, R1, R2$$ is

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Consider the following $$ER$$ diagram
Which of the following is a correct attribute set for one of the tables for the

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Consider the following relational schemes for a library database. Book ( Title, Author, Catalog_ no, Publisher, Year, Pr

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Let $$R\left( {A,B,C,D} \right)$$ be a relational schema with the following functional dependencies:
$$A \to B,\,\,B \t

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Let $$R\left( {A,\,B,\,C,\,D,E,P,G} \right)$$ be a relational schema in which the following functional dependencies are

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Consider The Following Relational Scheme
Student (school-id, sch-roll-no, sname, saddress)
School (school-id, sch-name,

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Consider The Following Relational Scheme
Student (school-id, sch-roll-no, sname, saddress)
School (school-id, sch-name,

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Which of the following tuple relational calculus expression(s) is/are equivalent to $$\forall t \in r \left(P\left(t\rig

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Let R and S be two relations with the following schema
R (P, Q, R1, R2, R3)
S (P, Q, S1, S2)
Where {P, Q} is the key for

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Consider the following three schedules of transactions T1, T2 and T3. [ Notation: In the following NYO represents the ac

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A clustering index is defined on the fields which are of type

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Consider a file of 16384 records. Each record is 32 bytes long and its key field is of size 6 bytes. The file is ordered

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Given $${f_1},$$ $${f_3},$$ and $$f$$ in canonical sum of products form (in decimal) for the circuit.
$$${f_1} = \sum {m

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If $$P, Q, R$$ are Boolean variables, then $$\left( {P + \overline Q } \right)$$ $$\left( {P.\overline Q + P.R} \right)

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In the Karnaugh map shown below, $$X$$ denotes a don’t care term. What is the minimal form of the function represented b

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A set of Boolean connectives is functionally complete if all Boolean function can be synthesized using those, Which of t

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A sample space has two events A and B such that probabilities
$$P\,(A\, \cap \,B)\, = \,1/2,\,\,P(\overline A )\, = \,1

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Aishwarya studies either computer science or mathematics everyday. If she studies computer science on a day, then the pr

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Let X be a random variable following normal distribution with mean + 1 and variance 4. Let Y be another normal variable

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If $$P$$, $$Q$$, $$R$$ are Boolean variables, then $$(P + \bar{Q}) (P.\bar{Q} + P.R) (\bar{P}.\bar{R} + \bar{Q})$

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Let fsa and $$pda$$ be two predicates such that fsa$$(x)$$ means $$x$$ is a finite state automation, and pda$$(y)$$ mean

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Which of the following first order formulae is logically valid? Here $$\alpha \left( x \right)$$ is a first order formul

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$$P$$ and $$Q$$ are two propositions. Which of the following logical expressions are equivalent?
$${\rm I}.$$ $${\rm P}\

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Which of the following is the negation of
$$$\left[ {\forall x,\alpha \to \left( {\exists y,\beta \to \left( {\forall

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What is the probability that in a randomly choosen group of r people at least three people have the same birthday?

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If $$P, Q, R$$ are subsets of the universal set $$U$$, then
$$\left( {P \cap Q \cap R} \right) \cup \left( {{P^c} \cap

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The following system of equations
$${x_1}\, + \,{x_2}\, + 2{x_3}\, = 1$$
$${x_1}\, + \,2 {x_2}\, + 3{x_3}\, = 2$$
$${

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What is the size of the smallest MIS (Maximal Independent Set) of a chain of nine nodes?

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$$\mathop {\lim }\limits_{x \to \infty } {{x - \sin x} \over {x + \cos \,x}}\,\,Equals$$

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If $$\,\,\,\,f\,\,\,\,\left( x \right)$$ is defined as follows, what is the minimum value of $$f\,\left( x \right)$$ for

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A point on a curve is said to be an extremum if it is a local minimum or a local maximum. The number of distinct extrema

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What is the chromatic number of the following graph?

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Let $${x_n}$$ denote the number of binary strings of length $$n$$ that contain no consecutive $$0s$$.
The value of $${x_

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Let $${x_n}$$ denote the number of binary strings of length $$n$$ that contains no consecutive $$0s$$.
Which of the foll

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The exponent of $$11$$ in the prime factorization of $$300!$$ is

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In how many ways can $$b$$ blue balls and $$r$$ red balls be distributed in $$n$$ distinct boxes?

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When $$n = {2^{2k}}$$ for some $$k \ge 0$$, the recurrence relation
$$$T\left( n \right) = \sqrt 2 T\left( {n/2} \right

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Which of the following statements is true for every planar graph on $$n$$ vertices?

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$$G$$ is a simple undirected graph. Some vertices of $$G$$ are of odd degree. Add a node $$v$$ to $$G$$ and make it adja

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$$G$$ is a graph on $$n$$ vertices and $$2n-2$$ edges. The edges of $$G$$ can be partitioned into two edge-disjoint span

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A binary tree with $$n>1$$ nodes has $${n_1}$$, $${n_2}$$ and $${n_3}$$ nodes of degree one, two and three respective

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A binary tree with $$n>1$$ nodes has $${n_1}$$, $${n_2}$$ and $${n_3}$$ nodes of degree one, two and three respective

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How many of the following matrices have an eigen value $$1$$?
$$\left[ {\matrix{
1 & 0 \cr
0 & 0 \cr

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If $$M$$ is a square matrix with a zero determinant, which of the following assertion(s) is (are) correct?
$$S1$$ : Eac

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The value of $$\int\limits_0^3 {\int\limits_0^x {\left( {6 - x - y} \right)dxdy\,\,\,} } $$ is _____.

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A process executes the following code
for (i = 0; i < n; i + +) fork ( );
The total number of child processes create

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Which of the following is/are true of the auto-increment addressing mode?
$${\rm I}.\,\,\,$$ It is useful in creating se

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The P and V operations on counting semaphores, where s is a counting semaphore, are defined as follows:
P(s): s = s-1;

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A processor uses 36 bit physical addresses and 32 bit virtual addresses, with a page frame size of 4 Kbytes. Each page t

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The data blocks of a very large file in the Unix file system are allocated using

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For a magnetic disk with concentric circular tracks, the seek latency is not linearly proportional to the seek distance

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Which of the following is NOT true of deadlock prevention and deadlock avoidance schemes?

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Which of the following are true?
I. A programming language which does not permit global variables of any kind
and has no

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Choose the correct option to fill ? 1 and ? 2 so that the program below prints an
input string in reverse order. Assume

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What is printed by the following C program?
#include < stdio.h >
int f(int x, int *py, int **ppz)
{
int y, z;

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Given below are two finite state automata ($$ \to $$ indicates the start state and $$F$$ indicates a final state)
W

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Match the following $$NFAs$$ with the regular expressions they correspond to

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Which of the following are regular sets?

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Which of the following statement is false?

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Which of the following statements are true?
$$1.$$ Every left-recursive grammar can be converted to a right-recursive g

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Match the following List-$${\rm I}$$ with List - $${\rm II}$$
List-$${\rm I}$$
$$E)$$ Checking that identifiers are decl

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Which of the following is true for the language $$\left\{ {{a^p}} \right.\left| P \right.$$ prime $$\left. \, \right\}$

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If $$L$$ and $$\overline L $$ are recursively enumerable then $$L$$ is

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Which of the following are decidable?
$$1.$$ Whether the intersection of two regular languages is infinite
$$2.$$ Whethe

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