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Use the google search bar on side panel. It searches through all previous GATE/other questions. For hardcopy of previous year questions please see
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Recent questions tagged gate1998
+2
votes
2
answers
1
GATE199810b
Let $R$ be a binary relation on $A = \{a, b, c, d, e, f, g, h\}$ represented by the following two component digraph. Find the smallest integers $m$ and $n$ such that $m < n$ and $R^m = R^n$.
asked
Aug 12, 2018
in
Set Theory & Algebra
by
Arjun
Veteran
(
386k
points)

186
views
gate1998
descriptive
settheory&algebra
relations
+16
votes
3
answers
2
GATE19986a
Solve the following recurrence relation $x_n = 2x_{n1}1, n>1$ $x_1=2$
asked
May 4, 2016
in
Algorithms
by
Arjun
Veteran
(
386k
points)

1.2k
views
gate1998
algorithms
recurrence
descriptive
+3
votes
3
answers
3
GATE199825b
Consider a disk with $c$ cylinders, $t$ tracks per cylinder, $s$ sectors per track and a sector length $s_l$. A logical file $d_l$ with fixed record length $r_l$ is stored continuously on this disk starting at location $(c_L, t_L, s_L)$ ... . Derive the formula to calculate the disk address (i.e. cylinder, track and sector) of a logical record n assuming that $r_l=s_l$.
asked
Mar 6, 2016
in
Operating System
by
Arjun
Veteran
(
386k
points)

542
views
gate1998
operatingsystem
disks
descriptive
+20
votes
9
answers
4
GATE199819b
Compute the post fix equivalent of the following expression $3^*\log(x+1)\frac{a}{2}$
asked
Aug 29, 2015
in
DS
by
Arjun
Veteran
(
386k
points)

2.8k
views
gate1998
stack
infixpostfix
+30
votes
3
answers
5
GATE19987b
In a computer system where the ‘bestfit’ algorithm is used for allocating ‘jobs’ to ‘memory partitions’, the following situation was encountered: Partitions size in $KB$ $4K \ 8K \ 20K \ 2K$ Job sizes in $KB$ $2K \ 14K \ 3K \ 6K \ 6K \ 10K \ 20K \ 2K$ Time for execution $4 \ 10 \ 2 \ 1 \ 4 \ 1 \ 8 \ 6$ When will the $20K$ job complete?
asked
Jul 10, 2015
in
Operating System
by
Arjun
Veteran
(
386k
points)

2.7k
views
gate1998
operatingsystem
processschedule
normal
+11
votes
5
answers
6
GATE19983b
Give a regular expression for the set of binary strings where every $0$ is immediately followed by exactly $k$ $1$'s and preceded by at least $k$ $1$’s ($k$ is a fixed integer)
asked
Oct 17, 2014
in
Theory of Computation
by
Arjun
Veteran
(
386k
points)

1.4k
views
gate1998
theoryofcomputation
regularexpressions
easy
+20
votes
13
answers
7
GATE199827
Consider the following relational database schemes: COURSES (Cno.name) PREREQ(Cno, preCno) COMPLETED (student_no, Cno) COURSES gives the number and name of all the available courses. PREREQ gives the information about which courses are pre ... following using relational algebra: List all the courses for which a student with student_no 2310 has completed all the prerequisites.
asked
Sep 26, 2014
in
Databases
by
Kathleen
Veteran
(
59.9k
points)

1.9k
views
gate1998
databases
relationalalgebra
normal
+30
votes
4
answers
8
GATE199826
Consider the following database relations containing the attributes Book_id Subject_Category_of_book Name_of_Author Nationality_of_Author With Book_id as the primary key. What is the highest normal form satisfied by this relation? Suppose the attributes Book_title and ... changed to {Name_of_Author, Book_title}, what will be the highest normal form satisfied by the relation?
asked
Sep 26, 2014
in
Databases
by
Kathleen
Veteran
(
59.9k
points)

4.9k
views
gate1998
databases
databasenormalization
normal
+17
votes
2
answers
9
GATE199825a
Free disk space can be used to keep track of using a free list or a bit map. Disk addresses require $d$ bits. For a disk with $B$ blocks, $F$ of which are free, state the condition under which the free list uses less space than the bit map.
asked
Sep 26, 2014
in
Operating System
by
Kathleen
Veteran
(
59.9k
points)

1.3k
views
gate1998
operatingsystem
disks
descriptive
+24
votes
3
answers
10
GATE199824
Four jobs are waiting to be run. Their expected run times are $6, 3, 5$ and $x.$ In what order should they be run to minimize the average response time? Write a concurrent program using $\text{par beginpar end}$ to represent the precedence graph shown below.
asked
Sep 26, 2014
in
Operating System
by
Kathleen
Veteran
(
59.9k
points)

2.5k
views
gate1998
operatingsystem
processschedule
descriptive
+11
votes
1
answer
11
GATE199823
Let the attribute ‘$val$’ give the value of a binary number generated by $S$ in the following grammar: $S \rightarrow L.L \mid L$ $L \rightarrow LB \mid B$ $B \rightarrow 0 \mid 1$ For example, an input $101.101$ gives $S.val = 5.625$ Construct a syntax directed translation scheme using only synthesized attributes, to determine $S.val$.
asked
Sep 26, 2014
in
Compiler Design
by
Kathleen
Veteran
(
59.9k
points)

1.8k
views
gate1998
compilerdesign
syntaxdirectedtranslation
normal
+14
votes
2
answers
12
GATE199822
An identifier in a programming language consists of up to six letters and digits of which the first character must be a letter. Derive a regular expression for the identifier. Build an $LL(1)$ parsing table for the language defined by the $LL(1)$ ... $X \rightarrow d \text{ semi } X \mid sY$ $Y \rightarrow \text{ semi } s Y \mid \epsilon$
asked
Sep 26, 2014
in
Compiler Design
by
Kathleen
Veteran
(
59.9k
points)

909
views
gate1998
compilerdesign
parsing
descriptive
+13
votes
1
answer
13
GATE199821
Derive a recurrence relation for the size of the smallest AVL tree with height $h$. What is the size of the smallest AVL tree with height $8$?
asked
Sep 26, 2014
in
DS
by
Kathleen
Veteran
(
59.9k
points)

1.1k
views
gate1998
datastructure
trees
descriptive
numericalanswers
+13
votes
1
answer
14
GATE199820
Draw the binary tree with node labels $\text{a, b, c, d, e, f and g}$ for which the inorder and postorder traversals result in the following sequences: Inorder: $\text{a f b c d g e}$ Postorder: $\text{a f c g e d b}$
asked
Sep 26, 2014
in
DS
by
Kathleen
Veteran
(
59.9k
points)

576
views
gate1998
datastructure
binarytree
descriptive
+14
votes
4
answers
15
GATE199819a
Let $p$ be a pointer as shown in the figure in a single linked list. What do the following assignment statements achieve? q: = p > next p > next:= q > next q > next:=(q > next) > next (p > next) > next:= q
asked
Sep 26, 2014
in
DS
by
Kathleen
Veteran
(
59.9k
points)

1.3k
views
gate1998
datastructure
linkedlists
normal
+15
votes
2
answers
16
GATE199818
For a setassociative Cache organization, the parameters are as follows: $t_c$ Cache access time $t_m$ Main memory access time $l$ number of sets $b$ block size $k\times b$ set size Calculate the hit ratio for a loop executed 100 times where the size of the loop is $n\times b$, and $n = k\times m$ is a nonzero integer and $1 < m \leq l$. Give the value of the hit ratio for $l = 1$.
asked
Sep 26, 2014
in
CO & Architecture
by
Kathleen
Veteran
(
59.9k
points)

1.7k
views
gate1998
coandarchitecture
cachememory
descriptive
0
votes
2
answers
17
GATE199817
Calculate the total time required to read 35 sectors on a 2sided floppy disk. Assume that each track has 8 sectors and the tracktotrack step time is 8 milliseconds. The first sector to be read is sector 3 on track 10. Assume that the diskette is soft sectored and the controller has a 1sector buffer. The diskette spins at 300 RPM and initially, the head is on track 10.
asked
Sep 26, 2014
in
Operating System
by
Kathleen
Veteran
(
59.9k
points)

832
views
gate1998
operatingsystem
disks
normal
numericalanswers
+14
votes
2
answers
18
GATE199816
Design a synchronous counter to go through the following states: $1, 4, 2, 3, 1, 4, 2, 3, 1, 4 \dots $
asked
Sep 26, 2014
in
Digital Logic
by
Kathleen
Veteran
(
59.9k
points)

908
views
gate1998
digitallogic
normal
descriptive
synchronousasynchronouscircuits
0
votes
0
answers
19
GATE199815
asked
Sep 26, 2014
in
CO & Architecture
by
Kathleen
Veteran
(
59.9k
points)

206
views
gate1998
coandarchitecture
8085
descriptive
outofsyllabusnow
+5
votes
3
answers
20
GATE199814
Let $G_1 = (N, T, P, S_1)$ be a CFG where, $N=\{S_1, A, B\},T=\{a, b\}$ and $P$ is given by $S_1 \rightarrow a S_1 b$ $S_1 \rightarrow a B b$ $S_1 \rightarrow a A b$ $B \rightarrow Bb$ $A \rightarrow a A$ $B \rightarrow b$ $A \rightarrow a$ ... $5$ production rules. Is $L_2$ inherently ambiguous?
asked
Sep 26, 2014
in
Compiler Design
by
Kathleen
Veteran
(
59.9k
points)

718
views
gate1998
compilerdesign
grammar
descriptive
+15
votes
1
answer
21
GATE199813
Let $M=(\{q_0, q_1\}, \{0, 1\}, \{z_0, X\}, \delta, q_0, z_0, \phi)$ be a Pushdown automation where $\delta$ is given by $\delta(q_0, 1, z_0) = \{(q_0, xz_0)\}$ $\delta(q_0, \epsilon, z_0) = \{(q_0, \epsilon)\}$ ... $\delta(q_0, 0, z_0) = \{(q_0, z_0)\}$z What is the language accepted by this PDA by empty stack? Describe informally the working of the PDA
asked
Sep 26, 2014
in
Theory of Computation
by
Kathleen
Veteran
(
59.9k
points)

921
views
gate1998
theoryofcomputation
pushdownautomata
descriptive
+12
votes
2
answers
22
GATE199812
Let $(A, *)$ be a semigroup, Furthermore, for every $a$ and $b$ in $A$, if $a \neq b$, then $a*b \neq b*a$. Show that for every $a$ in $A$, $a*a=a$ Show that for every $a$, $b$ in $A$, $a*b*a=a$ Show that for every $a,b,c$ in $A$, $a*b*c=a*c$
asked
Sep 26, 2014
in
Set Theory & Algebra
by
Kathleen
Veteran
(
59.9k
points)

1.1k
views
gate1998
settheory&algebra
groups
descriptive
+16
votes
2
answers
23
GATE199811
Suppose $A = \{a, b, c, d\}$ and $\Pi_1$ is the following partition of A $\Pi_1 = \left\{\left\{a, b, c\right\}\left\{d\right\}\right\}$ List the ordered pairs of the equivalence relations induced by $\Pi_1$. Draw the graph of the above equivalence relation ... $\left\langle\left\{\Pi_1, \Pi_2, \Pi_3, \Pi_4\right\}, \text{ refines } \right\rangle$.
asked
Sep 26, 2014
in
Engineering Mathematics
by
Kathleen
Veteran
(
59.9k
points)

1.3k
views
gate1998
settheory&algebra
normal
partialorder
descriptive
+16
votes
4
answers
24
GATE199810a
Prove by induction that the expression for the number of diagonals in a polygon of $n$ sides is $\frac{n(n3)}{2}$
asked
Sep 26, 2014
in
Set Theory & Algebra
by
Kathleen
Veteran
(
59.9k
points)

1.1k
views
gate1998
settheory&algebra
descriptive
relations
+1
vote
0
answers
25
GATE19989
Derive the expressions for the number of operations required to solve a system of linear equations in $n$ unknowns using the Gaussian Elimination Method. Assume that one operation refers to a multiplication followed by an addition.
asked
Sep 26, 2014
in
Linear Algebra
by
Kathleen
Veteran
(
59.9k
points)

216
views
gate1998
linearalgebra
systemofequations
descriptive
+7
votes
1
answer
26
GATE19988
(a) Find the points of local maxima and minima, if any, of the following function defined in $0\leq x\leq 6$. $x^36x^2+9x+15$ (b) Integrate $\int_{\pi}^{\pi} x \cos x dx$
asked
Sep 26, 2014
in
Calculus
by
Kathleen
Veteran
(
59.9k
points)

781
views
gate1998
calculus
maximaminima
integration
normal
descriptive
+16
votes
2
answers
27
GATE19987a
Suppose we have a database consisting of the following three relations. $\text{FREQUENTS (student, parlor)}$ giving the parlors each student visits. $\text{SERVES (parlor, icecream)}$ ... ) Express the following in SQL: Print the students that frequent at least one parlor that serves some icecream that they like.
asked
Sep 26, 2014
in
Databases
by
Kathleen
Veteran
(
59.9k
points)

1.3k
views
gate1998
databases
sql
descriptive
+15
votes
2
answers
28
GATE19986b
Consider the grammar S $\rightarrow Aa \mid b$ A $\rightarrow Ac \mid Sd \mid \epsilon$ Construct an equivalent grammar with no left recursion and with minimum number of production rules.
asked
Sep 26, 2014
in
Compiler Design
by
Kathleen
Veteran
(
59.9k
points)

1.7k
views
gate1998
compilerdesign
grammar
descriptive
+11
votes
2
answers
29
GATE19985
The implication gate, shown below has two inputs ($x \text{ and }y)$; the output is 1 except when $x =1 \text{ and } y=0\text{, realize }f=\bar{x}y+x\bar{y}$ using only four implication gates. Show that the implication gate is functionally complete.
asked
Sep 26, 2014
in
Digital Logic
by
Kathleen
Veteran
(
59.9k
points)

831
views
gate1998
digitallogic
functionalcompleteness
descriptive
+19
votes
2
answers
30
GATE19984
Design a deterministic finite state automaton (using minimum number of states) that recognizes the following language: $L=\{w \in \{0, 1\}^* \mid w$ interpreted as binary number (ignoring the leading zeros) is divisible by five $\}.$
asked
Sep 26, 2014
in
Theory of Computation
by
Kathleen
Veteran
(
59.9k
points)

1.8k
views
gate1998
theoryofcomputation
finiteautomata
normal
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