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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

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

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

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

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

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

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

6.0k views

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

17.0k views

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

4.1k views

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

9.9k views

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

9.5k views

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

3.0k views

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

3.5k views

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

3.6k views

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

6.3k views

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

6.5k views

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

2.4k views

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

3.5k views

0 votes

0 answers

19

GATE CSE 1998 | Question: 15

Kathleen asked in CO and Architecture Sep 26, 2014

391 views

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

3.4k views

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

4.8k views

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

5.6k views

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

9.5k views

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

3.0k views

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

2.2k views

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

2.8k views

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

5.0k views

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

6.0k views

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

2.8k views

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

9.9k views

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Recent questions tagged gate1998