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Recent questions tagged gate1998
12
votes
4
answers
1
GATE CSE 1998 | Question: 10b
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 $R^m = R^n$.
Arjun
asked
in
Set Theory & Algebra
Aug 12, 2018
by
Arjun
3.1k
views
gate1998
descriptive
set-theory&algebra
relations
21
votes
2
answers
2
GATE CSE 1998 | Question: 6a
Solve the following recurrence relation $x_n = 2x_{n-1}-1, n>1$ $x_1=2$
Arjun
asked
in
Algorithms
May 4, 2016
by
Arjun
4.5k
views
gate1998
algorithms
recurrence-relation
descriptive
6
votes
5
answers
3
GATE CSE 1998 | Question: 25b
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 $(c_L, t_L, s_L)$, where ... the formula to calculate the disk address (i.e. cylinder, track and sector) of a logical record n assuming that $r_l=s_l$.
Arjun
asked
in
Operating System
Mar 6, 2016
by
Arjun
2.2k
views
gate1998
operating-system
disk
descriptive
41
votes
9
answers
4
GATE CSE 1998 | Question: 19b
Compute the post fix equivalent of the following expression $3^*\log(x+1)-\frac{a}{2}$
Arjun
asked
in
DS
Aug 29, 2015
by
Arjun
12.8k
views
gate1998
stack
infix-prefix
descriptive
44
votes
5
answers
5
GATE CSE 1998 | Question: 7-b
In a computer system where the best-fit' algorithm is used for allocating jobs' to memory partitions', the following situation was encountered:$\begin{array}{|l|l|} \hline \textbf{Partitions size in $KB$} & \textbf{$ ... $} \\\hline \end{array}$When will the $20K$ job complete?
Arjun
asked
in
Operating System
Jul 10, 2015
by
Arjun
9.8k
views
gate1998
operating-system
process-scheduling
normal
26
votes
5
answers
6
GATE CSE 1998 | Question: 3b
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)
Arjun
asked
in
Theory of Computation
Oct 17, 2014
by
Arjun
6.8k
views
gate1998
theory-of-computation
regular-expression
easy
descriptive
29
votes
10
answers
7
GATE CSE 1998 | Question: 27
Consider the following relational database schemes: COURSES (Cno, Name) PRE_REQ(Cno, Pre_Cno) COMPLETED (Student_no, Cno) COURSES gives the number and name of all the available courses. PRE_REQ gives the information about which courses are pre- ... relational algebra: List all the courses for which a student with Student_no 2310 has completed all the pre-requisites.
Kathleen
asked
in
Databases
Sep 26, 2014
by
Kathleen
6.0k
views
gate1998
databases
relational-algebra
normal
descriptive
53
votes
5
answers
8
GATE CSE 1998 | Question: 26
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 ... to {Name_of_Author, Book_title}, what will be the highest normal form satisfied by the relation?
Kathleen
asked
in
Databases
Sep 26, 2014
by
Kathleen
17.0k
views
gate1998
databases
database-normalization
normal
descriptive
25
votes
3
answers
9
GATE CSE 1998 | Question: 25-a
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.
Kathleen
asked
in
Operating System
Sep 26, 2014
by
Kathleen
4.1k
views
gate1998
operating-system
disk
descriptive
41
votes
4
answers
10
GATE CSE 1998 | Question: 24
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 $\text{par begin-par end}$ to represent the precedence graph shown below.
Kathleen
asked
in
Operating System
Sep 26, 2014
by
Kathleen
9.9k
views
gate1998
operating-system
process-scheduling
descriptive
17
votes
1
answer
11
GATE CSE 1998 | Question: 23
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 $S.val$.
Kathleen
asked
in
Compiler Design
Sep 26, 2014
by
Kathleen
9.5k
views
gate1998
compiler-design
syntax-directed-translation
normal
descriptive
22
votes
2
answers
12
GATE CSE 1998 | Question: 22
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 $LL(1)$ ... $X \rightarrow d \text{ semi } X \mid sY$ $Y \rightarrow \text{ semi } s Y \mid \epsilon$
Kathleen
asked
in
Compiler Design
Sep 26, 2014
by
Kathleen
3.0k
views
gate1998
compiler-design
parsing
descriptive
20
votes
1
answer
13
GATE CSE 1998 | Question: 21
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 $8$?
Kathleen
asked
in
DS
Sep 26, 2014
by
Kathleen
3.5k
views
gate1998
data-structures
tree
descriptive
numerical-answers
19
votes
1
answer
14
GATE CSE 1998 | Question: 20
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: $\text{a f c g e d b}$
Kathleen
asked
in
DS
Sep 26, 2014
by
Kathleen
3.6k
views
gate1998
data-structures
binary-tree
descriptive
22
votes
5
answers
15
GATE CSE 1998 | Question: 19a
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
Kathleen
asked
in
DS
Sep 26, 2014
by
Kathleen
6.3k
views
gate1998
data-structures
linked-list
normal
descriptive
31
votes
5
answers
16
GATE CSE 1998 | Question: 18
For a set-associative Cache organization, the parameters are as follows: ... $1 \leq m \leq l$. Give the value of the hit ratio for $l = 1$.
Kathleen
asked
in
CO and Architecture
Sep 26, 2014
by
Kathleen
6.5k
views
gate1998
co-and-architecture
cache-memory
descriptive
3
votes
2
answers
17
GATE CSE 1998 | Question: 17
Calculate the total time required to read 35 sectors on a 2-sided floppy disk. Assume that each track has 8 sectors and the track-to-track step time is 8 milliseconds. The first sector to be read is sector 3 on track 10. Assume that the diskette ... sectored and the controller has a 1-sector buffer. The diskette spins at 300 RPM and initially, the head is on track 10.
Kathleen
asked
in
Operating System
Sep 26, 2014
by
Kathleen
2.4k
views
gate1998
operating-system
disk
normal
numerical-answers
out-of-syllabus-now
23
votes
3
answers
18
GATE CSE 1998 | Question: 16
Design a synchronous counter to go through the following states:$1, 4, 2, 3, 1, 4, 2, 3, 1, 4 \dots $
Kathleen
asked
in
Digital Logic
Sep 26, 2014
by
Kathleen
3.5k
views
gate1998
digital-logic
normal
descriptive
synchronous-asynchronous-circuits
0
votes
0
answers
19
GATE CSE 1998 | Question: 15
Kathleen
asked
in
CO and Architecture
Sep 26, 2014
by
Kathleen
391
views
gate1998
co-and-architecture
8085-microprocessor
descriptive
out-of-syllabus-now
12
votes
4
answers
20
GATE CSE 1998 | Question: 14
Let $G_1 = (N, T, P, S_1)$ be a CFG where, $N=\{S_1, A, B\},T=\{a, b\}$ and $P$ ... $5$ production rules. Is $L_2$ inherently ambiguous?
Kathleen
asked
in
Compiler Design
Sep 26, 2014
by
Kathleen
3.4k
views
gate1998
compiler-design
grammar
descriptive
29
votes
1
answer
21
GATE CSE 1998 | Question: 13
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 $\delta(q_0, 1, z_0) = \{(q_0, Xz_0)\}$ $\delta(q_0, \epsilon, z_0) = \{(q_0, \epsilon)\}$ ... $\delta(q_0, 0, z_0) = \{(q_0, z_0)\}$ What is the language accepted by this PDA by empty stack? Describe informally the working of the PDA
Kathleen
asked
in
Theory of Computation
Sep 26, 2014
by
Kathleen
4.8k
views
gate1998
theory-of-computation
pushdown-automata
descriptive
24
votes
3
answers
22
GATE CSE 1998 | Question: 12
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 $A$, $a*b*c=a*c$
Kathleen
asked
in
Set Theory & Algebra
Sep 26, 2014
by
Kathleen
5.6k
views
gate1998
set-theory&algebra
group-theory
descriptive
29
votes
4
answers
23
GATE CSE 1998 | Question: 11
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 ... $\left\langle\left\{\Pi_1, \Pi_2, \Pi_3, \Pi_4\right\}, \text{ refines } \right\rangle$.
Kathleen
asked
in
Set Theory & Algebra
Sep 26, 2014
by
Kathleen
9.5k
views
gate1998
set-theory&algebra
normal
partial-order
descriptive
19
votes
6
answers
24
GATE CSE 1998 | Question: 10a
Prove by induction that the expression for the number of diagonals in a polygon of $n$ sides is $\frac{n(n-3)}{2}$
Kathleen
asked
in
Set Theory & Algebra
Sep 26, 2014
by
Kathleen
3.0k
views
gate1998
set-theory&algebra
descriptive
relations
4
votes
1
answer
25
GATE CSE 1998 | Question: 9
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.
Kathleen
asked
in
Linear Algebra
Sep 26, 2014
by
Kathleen
2.2k
views
gate1998
linear-algebra
system-of-equations
descriptive
11
votes
1
answer
26
GATE CSE 1998 | Question: 8
Find the points of local maxima and minima, if any, of the following function defined in $0\leq x\leq 6$. $x^3-6x^2+9x+15$ Integrate $\int_{-\pi}^{\pi} x \cos x dx$
Kathleen
asked
in
Calculus
Sep 26, 2014
by
Kathleen
2.8k
views
gate1998
calculus
maxima-minima
integration
normal
descriptive
23
votes
4
answers
27
GATE CSE 1998 | Question: 7-a
Suppose we have a database consisting of the following three relations. $\text{FREQUENTS (student, parlor)}$ giving the parlors each student visits. $\text{SERVES (parlor, ice-cream)}$ ... the following in SQL: Print the students that frequent at least one parlor that serves some ice-cream that they like.
Kathleen
asked
in
Databases
Sep 26, 2014
by
Kathleen
5.0k
views
gate1998
databases
sql
descriptive
26
votes
2
answers
28
GATE CSE 1998 | Question: 6b
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.
Kathleen
asked
in
Compiler Design
Sep 26, 2014
by
Kathleen
6.0k
views
gate1998
compiler-design
grammar
descriptive
22
votes
2
answers
29
GATE CSE 1998 | Question: 5
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.
Kathleen
asked
in
Digital Logic
Sep 26, 2014
by
Kathleen
2.8k
views
gate1998
digital-logic
functional-completeness
descriptive
33
votes
2
answers
30
GATE CSE 1998 | Question: 4
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 $\}.$
Kathleen
asked
in
Theory of Computation
Sep 26, 2014
by
Kathleen
9.9k
views
gate1998
theory-of-computation
finite-automata
normal
minimal-state-automata
descriptive
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