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GATE 1988 Computer Science Questions
Recent questions tagged gate1988
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GATE CSE 1988 | Question: 17i-ii-iii
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 ... . For the solution of (ii) above, calculate the values of the duals and determine whether this is an optimal solution.
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...
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583
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Dec 20, 2016
Others
gate1988
linear-programming
descriptive
out-of-gate-syllabus
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–
0
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0
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2
GATE CSE 1988 | Question: 16ii-iii
If $x \| \underline{x} \| \infty = 1< i^{max} < n \: \: max \: \: ( \mid x1 \mid ) $ for the vector $\underline{x} = (x1, x2 \dots x_n)$ ... 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.
If $x \| \underline{x} \| \infty = 1< i^{max} < n \: \: max \: \: ( \mid x1 \mid ) $ for the vector $\underline{x} = (x1, x2 \dots x_n)$ and $\| A \| \infty = x^{Sup} \fr...
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736
views
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Dec 20, 2016
Linear Algebra
gate1988
descriptive
matrix
out-of-gate-syllabus
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8
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3
answers
3
GATE CSE 1988 | Question: 16i
Assume that the matrix $A$ given below, has factorization of the form $LU=PA$, where $L$ is lower-triangular with all diagonal elements equal to $1, U$ is upper-triangular, and $P$ ... $L, U,$ and $P$ using Gaussian elimination with partial pivoting.
Assume that the matrix $A$ given below, has factorization of the form $LU=PA$, where $L$ is lower-triangular with all diagonal elements equal to $1, U$ is upper-triangula...
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3.3k
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Dec 20, 2016
Linear Algebra
gate1988
normal
descriptive
linear-algebra
matrix
+
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10
votes
2
answers
4
GATE CSE 1988 | Question: 15
Consider the DFA $M$ and NFA $M_{2}$ as defined below. Let the language accepted by machine $M$ be $L$. What language machine $M_{2}$ accepts, if $F2=A?$ $F2=B?$ $F2=C?$ $F2=D?$ $M=(Q, \Sigma, \delta, q_0, F)$ $M_{2}=(Q2, \Sigma, \delta_2, q_{00}, F2)$ ... $D=\{\langle p, q, r \rangle \mid p,q \in Q; r \in F\}$
Consider the DFA $M$ and NFA $M_{2}$ as defined below. Let the language accepted by machine $M$ be $L$. What language machine $M_{2}$ accepts, if$F2=A?$$F2=B?$$F2=C?$$...
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2.8k
views
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Dec 20, 2016
Theory of Computation
gate1988
descriptive
theory-of-computation
finite-automata
difficult
+
–
1
votes
1
answer
5
GATE CSE 1988 | Question: 14ii
Consider the following well-formed formula: $\exists x \forall y [ \neg \exists z [ p (y, z) \wedge p (z, y) ] \equiv p(x,y)]$ Show using resolution principle that the well-formed formula, given above, cannot be satisfied for any interpretation.
Consider the following well-formed formula:$\exists x \forall y [ \neg \exists z [ p (y, z) \wedge p (z, y) ] \equiv p(x,y)]$Show using resolution principle that the well...
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663
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Dec 20, 2016
Mathematical Logic
gate1988
descriptive
first-order-logic
clausal-form
out-of-gate-syllabus
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–
1
votes
1
answer
6
GATE CSE 1988 | Question: 14i
Consider the following well-formed formula: $\exists x \forall y [ \neg \: \exists z [ p (y, z) \wedge p (z, y) ] \equiv p(x,y)]$ Express the above well-formed formula in clausal form.
Consider the following well-formed formula:$\exists x \forall y [ \neg \: \exists z [ p (y, z) \wedge p (z, y) ] \equiv p(x,y)]$Express the above well-formed formula in c...
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646
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Dec 20, 2016
Mathematical Logic
gate1988
descriptive
first-order-logic
clausal-form
out-of-gate-syllabus
+
–
13
votes
5
answers
7
GATE CSE 1988 | Question: 13iv
Solve the recurrence equations: $T(n)= T( \frac{n}{2})+1$ $T(1)=1$
Solve the recurrence equations:$T(n)= T( \frac{n}{2})+1$$T(1)=1$
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3.2k
views
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Dec 20, 2016
Algorithms
gate1988
descriptive
algorithms
recurrence-relation
+
–
7
votes
3
answers
8
GATE CSE 1988 | Question: 13iii
Are the two digraphs shown in the above figure isomorphic? Justify your answer.
Are the two digraphs shown in the above figure isomorphic? Justify your answer.
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1.2k
views
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Dec 20, 2016
Graph Theory
normal
gate1988
descriptive
graph-theory
graph-isomorphism
out-of-gate-syllabus
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25
votes
2
answers
9
GATE CSE 1988 | Question: 13ii
If the set $S$ has a finite number of elements, prove that if $f$ maps $S$ onto $S$, then $f$ is one-to-one.
If the set $S$ has a finite number of elements, prove that if $f$ maps $S$ onto $S$, then $f$ is one-to-one.
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2.6k
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Dec 20, 2016
Set Theory & Algebra
gate1988
descriptive
set-theory&algebra
functions
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–
1
votes
1
answer
10
GATE CSE 1988 | Question: 13ic
Verify whether the following mapping is a homomorphism. If so, determine its kernel. $f(x)=x^3$, for all $x$ belonging to $G$.
Verify whether the following mapping is a homomorphism. If so, determine its kernel.$f(x)=x^3$, for all $x$ belonging to $G$.
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537
views
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asked
Dec 20, 2016
Set Theory & Algebra
gate1988
normal
descriptive
group-theory
group-homomorphism
out-of-gate-syllabus
+
–
1
votes
0
answers
11
GATE CSE 1988 | Question: 13ib
Verify whether the following mapping is a homomorphism. If so, determine its kernel. $\overline{G}=G$
Verify whether the following mapping is a homomorphism. If so, determine its kernel.$\overline{G}=G$
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477
views
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asked
Dec 20, 2016
Graph Theory
gate1988
normal
descriptive
group-theory
group-homomorphism
out-of-gate-syllabus
+
–
1
votes
0
answers
12
GATE CSE 1988 | Question: 13ia
Verify whether the following mapping is a homomorphism. If so, determine its kernel. $G$ is the group of non zero real numbers under multiplication.
Verify whether the following mapping is a homomorphism. If so, determine its kernel.$G$ is the group of non zero real numbers under multiplication.
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440
views
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asked
Dec 20, 2016
Set Theory & Algebra
gate1988
normal
descriptive
group-theory
group-homomorphism
out-of-gate-syllabus
+
–
5
votes
3
answers
13
GATE CSE 1988 | Question: 12iv
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.
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 lea...
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1.3k
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asked
Dec 20, 2016
Databases
gate1988
normal
descriptive
databases
sql
+
–
10
votes
3
answers
14
GATE CSE 1988 | Question: 12iii
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'))
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 (sele...
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2.0k
views
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asked
Dec 20, 2016
Databases
gate1988
normal
descriptive
databases
sql
+
–
5
votes
1
answer
15
GATE CSE 1988 | Question: 12iic
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).
Using Armstrong’s axioms of functional dependency derive the following rules:$\{ x \rightarrow y, \: z \subset y \} \mid= x \rightarrow z$(Note: $x \rightarrow y$ denot...
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1.3k
views
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Dec 20, 2016
Databases
gate1988
normal
descriptive
databases
database-normalization
+
–
4
votes
1
answer
16
GATE CSE 1988 | Question: 12iib
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).
Using Armstrong’s axioms of functional dependency derive the following rules:$\{ x \rightarrow y, \: wy \rightarrow z \} \mid= xw \rightarrow z$(Note: $x \rightarrow y$...
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1.0k
views
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asked
Dec 20, 2016
Databases
gate1988
normal
descriptive
databases
database-normalization
+
–
8
votes
1
answer
17
GATE CSE 1988 | Question: 12iia
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).
Using Armstrong’s axioms of functional dependency derive the following rules:$\{ x \rightarrow y, \: x \rightarrow z \} \mid= x \rightarrow yz$(Note: $x \rightarrow y$ ...
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1.3k
views
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asked
Dec 19, 2016
Databases
gate1988
easy
descriptive
databases
database-normalization
+
–
9
votes
1
answer
18
GATE CSE 1988 | Question: 12i
What are the three axioms of functional dependency for the relational databases given by Armstrong.
What are the three axioms of functional dependency for the relational databases given by Armstrong.
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1.8k
views
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asked
Dec 19, 2016
Databases
gate1988
normal
descriptive
databases
database-normalization
+
–
7
votes
4
answers
19
GATE CSE 1988 | Question: 11
A number of processes could be in a deadlock state if none of them can execute due to non-availability 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 ... Is the system currently in a safe state? If yes, explain why.
A number of processes could be in a deadlock state if none of them can execute due to non-availability of sufficient resources. Let $P_i, 0 \leq i \leq 4$ represent five...
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3.0k
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Dec 19, 2016
Operating System
gate1988
normal
descriptive
operating-system
resource-allocation
+
–
14
votes
3
answers
20
GATE CSE 1988 | Question: 10iib
Given below is solution for the critical section problem of two processes $P_0$ and $P_1$ ... until false Determine of the above solution is correct. If it is incorrect, demonstrate with an example how it violates the conditions.
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 fa...
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4.0k
views
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Dec 19, 2016
Operating System
gate1988
descriptive
operating-system
process-synchronization
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–
1
votes
1
answer
21
GATE CSE 1988 | Question: 10iia
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; ... 1...10] of real; begin i:=0; While i:<=10 do begin a[i]:=0; i:=i+1 end; end.
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; whi...
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808
views
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asked
Dec 19, 2016
Compiler Design
gate1988
descriptive
compiler-design
intermediate-code
pascal
out-of-gate-syllabus
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–
4
votes
2
answers
22
GATE CSE 1988 | Question: 10ib
Consider the following grammar: $S \rightarrow S$ $S \rightarrow SS \mid a \mid \epsilon$ Indicate the shift-reduce and reduce-reduce conflict (if any) in the various states of the $\text{LR(0)}$ parser.
Consider the following grammar:$S \rightarrow S$$S \rightarrow SS \mid a \mid \epsilon$Indicate the shift-reduce and reduce-reduce conflict (if any) in the various states...
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2.2k
views
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asked
Dec 19, 2016
Compiler Design
gate1988
compiler-design
descriptive
grammar
parsing
+
–
10
votes
2
answers
23
GATE CSE 1988 | Question: 10ia
Consider the following grammar: $S \rightarrow S$ $S \rightarrow SS \mid a \mid \epsilon$ Construct the collection of sets of $\text{LR (0)}$ items for this grammar and draw its goto graph.
Consider the following grammar:$S \rightarrow S$$S \rightarrow SS \mid a \mid \epsilon$Construct the collection of sets of $\text{LR (0)}$ items for this grammar and draw...
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3.6k
views
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asked
Dec 19, 2016
Compiler Design
gate1988
compiler-design
descriptive
grammar
parsing
+
–
12
votes
1
answer
24
GATE CSE 1988 | Question: 9iii
In the program scheme given below indicate the instructions containing any operand needing relocation for position independent behaviour. Justify your answer. ...
In the program scheme given below indicate the instructions containing any operand needing relocation for position independent behaviour. Justify your answer.$$\begin{arr...
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3.5k
views
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asked
Dec 19, 2016
CO and Architecture
gate1988
normal
descriptive
co-and-architecture
addressing-modes
+
–
1
votes
0
answers
25
GATE CSE 1988 | Question: 9ii
The code for the implementation of a sub-routine to convert positive numeric data from binary to appropriate character string in a $PDP-11$ like machine has been given below Note-that $SP$ is the stack pointer and $R_i$ represents $i^{th}$ ...
The code for the implementation of a sub-routine to convert positive numeric data from binary to appropriate character string in a $PDP-11$ like machine has been given be...
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491
views
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asked
Dec 19, 2016
CO and Architecture
gate1988
normal
descriptive
co-and-architecture
unsolved
+
–
7
votes
3
answers
26
GATE CSE 1988 | Question: 9i
The following program fragment was written in an assembly language for a single address computer with one accumulator register: LOAD B MULT C STORE T1 ADD A STORE T2 MULT T2 ADD T1 STORE Z Give the arithmetic expression implemented by the fragment.
The following program fragment was written in an assembly language for a single address computer with one accumulator register:LOAD B MULT C STORE T1 ADD A STORE T2 MULT ...
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1.7k
views
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asked
Dec 19, 2016
CO and Architecture
gate1988
normal
descriptive
co-and-architecture
machine-instruction
+
–
1
votes
0
answers
27
GATE CSE 1988 | Question: 8iv
Consider the following Ada program: Procedure P is BAD-FORMAT: exception Procedure Q is begin ... if S/='b' then raise BAD-FORMAT end if; ... end Q; Procedure R is begin Q; exception when BAD-Format => ... handler body 1 end R; begin ... when BAD-FORMAT => ... handler body 2 end P; Under what conditions are the two handler bodies $1$ and $2$ executed?
Consider the following Ada program:Procedure P is BAD-FORMAT: exception Procedure Q is begin ... if S/='b' then raise BAD-FORMAT end if; ... end Q; Procedure R is begin Q...
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488
views
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asked
Dec 19, 2016
Programming in C
gate1988
normal
descriptive
programming
ada
out-of-gate-syllabus
+
–
0
votes
1
answer
28
GATE CSE 1988 | Question: 8iii
Write a LISP function to compute the product of all the numbers in a list. Assume that the list contains only number.
Write a LISP function to compute the product of all the numbers in a list. Assume that the list contains only number.
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464
views
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asked
Dec 19, 2016
Programming in C
gate1988
descriptive
programming
lisp
out-of-gate-syllabus
+
–
4
votes
2
answers
29
GATE CSE 1988 | Question: 8ii
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 statements and $f$ as a function.
Consider the two program segments below:for i:=1 to f(x) by 1 do S endi:=1; While i<=f(x) do S i:=i+1 endUnder what conditions are these two programs equivalent? Treat $S...
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2.2k
views
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asked
Dec 19, 2016
Programming in C
gate1988
programming
descriptive
loop-invariants
+
–
5
votes
1
answer
30
GATE CSE 1988 | Question: 8i
Consider the procedure declaration: Procedure P (k: integer) where the parameter passing mechanism is call-by-value-result. 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, ... P using z for k; set A [i] to z; Explain your answer. If this is incorrect implementation, suggest a correct one.
Consider the procedure declaration:Procedure P (k: integer)where the parameter passing mechanism is call-by-value-result. Is it correct if the call, P (A[i]), where A is ...
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1.7k
views
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asked
Dec 19, 2016
Compiler Design
gate1988
descriptive
compiler-design
runtime-environment
parameter-passing
+
–
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