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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 gate1988
GATE 1988 Computer Science Questions
0
votes
0
answers
1
GATE198817iiiiii
The following table gives the cost of transporting one tonne of goods from the origins A, B, C to the destinations F, G, H. Also shown are the availabilities of the goods at the origins and the requirements at the destinations. The transportation problem ... i). For the solution of (ii) above, calculate the values of the duals and determine whether this is an optimal solution.
asked
Dec 20, 2016
in
Others
by
jothee
Veteran
(
96.1k
points)

128
views
gate1988
nongate
descriptive
linearprogramming
0
votes
0
answers
2
GATE198816iiiii
If $x \ \underline{x} \ \infty = 1< i^{max} < n \: \: max \: \: ( \mid x1 \mid ) $ for the vector $\underline{x} = (x1, x2 \dots x_n)$ ... using a known property of this norm. Although this norm is very easy to calculate for any matrix, explain why the condition number is difficult (i.e. expensive) to calculate.
asked
Dec 20, 2016
in
Linear Algebra
by
jothee
Veteran
(
96.1k
points)

138
views
gate1988
descriptive
matrices
outofsyllabusnow
+2
votes
2
answers
3
GATE198816i
Assume that the matrix $A$ given below, has factorization of the form $LU=PA$, where $L$ is lowertriangular with all diagonal elements equal to 1, $U$ is uppertriangular, and $P$ is a permutation matrix. For $A = \begin{bmatrix} 2 & 5 & 9 \\ 4 & 6 & 5 \\ 8 & 2 & 3 \end{bmatrix}$ Compute $L, U,$ and $P$ using Gaussian elimination with partial pivoting.
asked
Dec 20, 2016
in
Linear Algebra
by
jothee
Veteran
(
96.1k
points)

252
views
gate1988
normal
descriptive
linearalgebra
matrices
+3
votes
1
answer
4
GATE198815
Consider the DFA $M$ and NFA M2 as defined below. Let the language accepted by machine $M$ be $L$. What language machine M2 accepts, if $F2=A$ ? $F2=B$ ? $F2=C$ ? $F2=D$ ? $M=(Q, \Sigma, \delta, q_0, F)$ $M2=(Q2, \Sigma, \delta_2, q_{00}, F2)$ ... $D=\{\langle p, q, r \rangle \mid p \in Q; q \in F\}$
asked
Dec 20, 2016
in
Theory of Computation
by
jothee
Veteran
(
96.1k
points)

192
views
normal
gate1988
descriptive
theoryofcomputation
0
votes
0
answers
5
GATE198814ii
Consider the following wellformed formula: $\exists x \forall y [ \neg \exists z [ p (y, z) \wedge p (z, y) ] \equiv p(x,y)]$ Show using resolution principle that the wellformed formula, given above, cannot be satisfied for any interpretation.
asked
Dec 20, 2016
in
Mathematical Logic
by
jothee
Veteran
(
96.1k
points)

160
views
gate1988
descriptive
firstorderlogic
clausalform
nongate
0
votes
1
answer
6
GATE198814i
Consider the following wellformed formula: $\exists x \forall y [ \neg \: \exists z [ p (y, z) \wedge p (z, y) ] \equiv p(x,y)]$ Express the above wellformed formula in clausal form.
asked
Dec 20, 2016
in
Mathematical Logic
by
jothee
Veteran
(
96.1k
points)

144
views
gate1988
descriptive
firstorderlogic
clausalform
nongate
+5
votes
5
answers
7
GATE198813iv
Solve the recurrence equations: $T(n)= T( \frac{n}{2})+1$ $T(1)=1$
asked
Dec 20, 2016
in
Algorithms
by
jothee
Veteran
(
96.1k
points)

465
views
gate1988
descriptive
algorithms
recurrence
+2
votes
2
answers
8
GATE198813iii
Are the two digraphs shown in the above figure isomorphic? Justify your answer.
asked
Dec 20, 2016
in
Graph Theory
by
jothee
Veteran
(
96.1k
points)

332
views
normal
gate1988
descriptive
graphtheory
graphisomorphism
+11
votes
1
answer
9
GATE198813ii
If the set $S$ has a finite number of elements, prove that if $f$ maps $S$ onto $S$, then $f$ is onetoone.
asked
Dec 20, 2016
in
Set Theory & Algebra
by
jothee
Veteran
(
96.1k
points)

463
views
gate1988
descriptive
settheory&algebra
functions
0
votes
0
answers
10
GATE198813ic
Verify whether the following mapping is a homomorphism. If so, determine its kernel. $f(x)=x^3$, for all $x$ belonging to $G$.
asked
Dec 20, 2016
in
Set Theory & Algebra
by
jothee
Veteran
(
96.1k
points)

124
views
gate1988
normal
descriptive
groups
grouphomomorphism
nongate
0
votes
0
answers
11
GATE198813ib
Verify whether the following mapping is a homomorphism. If so, determine its kernel. $\bar{G}=G$
asked
Dec 20, 2016
in
Graph Theory
by
jothee
Veteran
(
96.1k
points)

77
views
gate1988
normal
descriptive
groups
grouphomomorphism
nongate
0
votes
0
answers
12
GATE198813ia
Verify whether the following mapping is a homomorphism. If so, determine its kernel. $G$ is the group of non zero real numbers under multiplication.
asked
Dec 20, 2016
in
Set Theory & Algebra
by
jothee
Veteran
(
96.1k
points)

104
views
gate1988
normal
descriptive
groups
grouphomomorphism
nongate
0
votes
2
answers
13
GATE198812iv
Select SNAME from S Where SNOin (select SNO from SP where PNOin (select PNO from P Where COLOUR='BLUE')) What relations are being used in the above SQL query? Given at least two attributes of each of these relations.
asked
Dec 20, 2016
in
Databases
by
jothee
Veteran
(
96.1k
points)

167
views
gate1988
normal
descriptive
databases
0
votes
1
answer
14
GATE198812iii
Describe the relational algebraic expression giving the relation returned by the following SQL query. Select SNAME from S Where SNOin (select SNO from SP where PNOin (select PNO from P Where COLOUR='BLUE'))
asked
Dec 20, 2016
in
Databases
by
jothee
Veteran
(
96.1k
points)

126
views
gate1988
normal
descriptive
databases
0
votes
1
answer
15
GATE198812iic
Using Armstrong’s axioms of functional dependency derive the following rules: $\{ x \rightarrow y, \: z \subset y \} \mid= x \rightarrow z$ (Note: $x \rightarrow y$ denotes $y$ is functionally dependent on $x$, $z \subseteq y$ denotes $z$ is subset of $y$, and $\mid =$ means derives).
asked
Dec 20, 2016
in
Databases
by
jothee
Veteran
(
96.1k
points)

114
views
gate1988
normal
descriptive
databases
functionaldependencies
0
votes
1
answer
16
GATE198812iib
Using Armstrong’s axioms of functional dependency derive the following rules: $\{ x \rightarrow y, \: wy \rightarrow z \} \mid= xw \rightarrow z$ (Note: $x \rightarrow y$ denotes $y$ is functionally dependent on $x$, $z \subseteq y$ denotes $z$ is subset of $y$, and $\mid =$ means derives).
asked
Dec 20, 2016
in
Databases
by
jothee
Veteran
(
96.1k
points)

104
views
gate1988
normal
descriptive
databases
functionaldependencies
0
votes
1
answer
17
GATE198812iia
Using Armstrong’s axioms of functional dependency derive the following rules: $\{ x \rightarrow y, \: x \rightarrow z \} \mid= x \rightarrow yz$ (Note: $x \rightarrow y$ denotes $y$ is functionally dependent on $x$, $z \subseteq y$ denotes $z$ is subset of $y$, and $\mid =$ means derives).
asked
Dec 19, 2016
in
Databases
by
jothee
Veteran
(
96.1k
points)

106
views
gate1988
easy
descriptive
databases
functionaldependencies
+1
vote
1
answer
18
GATE198812i
What are the three axioms of functional dependency for the relational databases given by Armstrong.
asked
Dec 19, 2016
in
Databases
by
jothee
Veteran
(
96.1k
points)

134
views
gate1988
normal
descriptive
databases
+2
votes
3
answers
19
GATE198811
A number of processes could be in a deadlock state if none of them they execute due to nonavailability of sufficient resources. Let $P_i, 0 \leq i \leq 4$ represent five processes and let there be four resources types $r_j, 0 \leq j \leq 3$. Suppose the following data ... 6 5 6 $\textbf{Available}$ r0 r1 r2 r3 1 5 2 0 Is the system currently in a safe state? If yes, explain why.
asked
Dec 19, 2016
in
Operating System
by
jothee
Veteran
(
96.1k
points)

537
views
gate1988
normal
descriptive
operatingsystem
resourceallocation
0
votes
1
answer
20
GATE198810iib
Given below is solution for the critical section problem of two processes $P_0$ and $P_1$ sharing the following variables: var flag :array [0..1] of boolean; (initially false) turn: 0 .. 1; The program below is for process Pi (i=0 or 1) ... :=false; until false Determine of the above solution is correct. If it is incorrect, demonstrate with an example how it violates the conditions.
asked
Dec 19, 2016
in
Operating System
by
jothee
Veteran
(
96.1k
points)

286
views
gate1988
descriptive
operatingsystem
processsynchronization
0
votes
1
answer
21
GATE198810iia
Translate the executable statements of the following Pascal Program into quadruples. Assume that integer and real values require four words each. repeat flag[i]:=true; while turn !=i do begin while flag[j] do skip turn:=i; end critical section flag[i]:=false; until false Program Test; var i:integer ... [1...10] of real; begin i:=0; While i:<=10 do begin a[i]:=0; i:=i+1 end; end.
asked
Dec 19, 2016
in
Compiler Design
by
jothee
Veteran
(
96.1k
points)

262
views
gate1988
descriptive
compilerdesign
intermediatecode
pascal
outofsyllabusnow
0
votes
2
answers
22
GATE198810ib
Consider the following grammar: $S \rightarrow S$ $S \rightarrow SS \mid a \mid \epsilon$ Indicate the shiftreduce and reducereduce conflict (if any) in the various states of the LR(0) parser.
asked
Dec 19, 2016
in
Compiler Design
by
jothee
Veteran
(
96.1k
points)

286
views
gate1988
descriptive
grammar
parsing
+2
votes
0
answers
23
GATE198810ia
Consider the following grammar: $S \rightarrow S$ $S \rightarrow SS \mid a \mid \epsilon$ Construct the collection of sets of LR (0) items for this grammar and draw its goto graph.
asked
Dec 19, 2016
in
Compiler Design
by
jothee
Veteran
(
96.1k
points)

237
views
gate1988
descriptive
grammar
parsing
0
votes
0
answers
24
GATE19889iii
In the program scheme given below indicate the instructions containing any operand needing relocation for position independent behaviour. Justify your answer. Y=10. MOV X (OR), R1 MOV X, RO MOV 2(RO), R1 MOV Y (RO), R5 . . . X: WORD 0, 0, 0
asked
Dec 19, 2016
in
CO & Architecture
by
jothee
Veteran
(
96.1k
points)

97
views
gate1988
normal
descriptive
coandarchitecture
0
votes
0
answers
25
GATE19889ii
The code for the implementation of a subroutine to convert positive numeric data from binary to appropriate character string in a PDP11 like machine has been given below Notethat SP is the stack pointer and $R_i$ represents ith register respectively. BTOD: MOV (SP)+, RO : ... R3, (R1) : autodecrement will decrease R1 MOV R2, R3 BNE BTOD 1 MOV RO(SP) : restore PC RTS PC : return
asked
Dec 19, 2016
in
CO & Architecture
by
jothee
Veteran
(
96.1k
points)

82
views
gate1988
normal
descriptive
coandarchitecture
0
votes
2
answers
26
GATE19889i
The following program fragment was written in an assembly language for a single address computer with one accumulator register: LOAD B MULT C STORE T$_1$ ADD A STORE T$_2$ MULT T$_2$ ADD T$_1$ STORE Z Give the arithmetic expression implemented by the fragment.
asked
Dec 19, 2016
in
CO & Architecture
by
jothee
Veteran
(
96.1k
points)

97
views
gate1988
normal
descriptive
coandarchitecture
0
votes
0
answers
27
GATE19888iv
Consider the following Ada program: Procedure P is BADFORMAT: exception Procedure Q is begin ... if S/='b' then raise BADFORMAT end if; ... end Q; Procedure R is begin Q; exception when BADFormat => ... handler body 1 end R; begin R; Q; exception when BADFORMAT => ... handler body 2 end P; Under what conditions are the two handler bodies 1 and 2 executed?
asked
Dec 19, 2016
in
Programming
by
jothee
Veteran
(
96.1k
points)

101
views
gate1988
normal
descriptive
programming
ada
outofsyllabusnow
0
votes
0
answers
28
GATE19888iii
Write a LISP function to compute the product of all the numbers in a list. Assume that the list contains only number.
asked
Dec 19, 2016
in
Programming
by
jothee
Veteran
(
96.1k
points)

86
views
gate1988
descriptive
programming
lisp
outofsyllabusnow
+2
votes
1
answer
29
GATE19888ii
Consider the two program segments below: for i:=1 to f(x) by 1 do S end i:=1; While i<=f(x) do S i:=i+1 end Under what conditions are these two programs equivalent? Treat $S$ as any sequence of statement and f as a function.
asked
Dec 19, 2016
in
Programming
by
jothee
Veteran
(
96.1k
points)

287
views
gate1988
programming
descriptive
+1
vote
0
answers
30
GATE19888i
Consider the procedure declaration: Procedure P (k: integer) where the parameter passing mechanism is callbyvalueresult. Is it correct if the call, P (A[i]), where A is an array and i an integer, is implemented as below. create a new local variable, say z; ... body of P using z for k; set A [i] to z; Explain your answer. If this is incorrect implementation, suggest a correct one.
asked
Dec 19, 2016
in
Compiler Design
by
jothee
Veteran
(
96.1k
points)

292
views
gate1988
descriptive
compilerdesign
runtimeenvironments
parameterpassing
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