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GATE 1988 Computer Science Questions

Recent questions tagged gate1988

0 votes
0 answers
1
GATE1988-17i-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 transportation problem ... i). 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 at the origins and the requirements at the destinations. The transportation problem implied by ... question(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 jothee 196 views
0 votes
0 answers
2
GATE1988-16ii-iii
If $x \| \underline{x} \| \infty = 1< i^{max} < n \: \: max \: \: ( \mid x1 \mid ) $ for the vector $\underline{x} = (x1, x2 \dots x_n)$ ... 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.
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 jothee 231 views
4 votes
2 answers
3
GATE1988-16i
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 $P$ 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.
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 $P$ 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 jothee 899 views
3 votes
1 answer
4
GATE1988-15
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 $F2=A$ ? $F2=B$ ? $F2=C$ ? $F2=D$ ? $M=(Q, \Sigma, \delta, q_0, F)$ $M2=(Q2, \Sigma, \delta_2, q_{00}, F2)$ ... $D=\{\langle p, q, r \rangle \mid p \in Q; q \in F\}$
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 jothee 403 views
0 votes
0 answers
5
GATE1988-14ii
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-formed formula, given above, cannot be satisfied for any interpretation.
asked Dec 20, 2016 in Mathematical Logic jothee 251 views
0 votes
1 answer
6
GATE1988-14i
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 clausal form.
asked Dec 20, 2016 in Mathematical Logic jothee 262 views
9 votes
4 answers
7
GATE1988-13iv
Solve the recurrence equations: $T(n)= T( \frac{n}{2})+1$ $T(1)=1$
Solve the recurrence equations: $T(n)= T( \frac{n}{2})+1$ $T(1)=1$
asked Dec 20, 2016 in Algorithms jothee 1.5k views
4 votes
2 answers
8
GATE1988-13iii
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.
asked Dec 20, 2016 in Graph Theory jothee 503 views
15 votes
1 answer
9
GATE1988-13ii
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.
asked Dec 20, 2016 in Set Theory & Algebra jothee 1.1k views
0 votes
0 answers
10
GATE1988-13ic
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 $G$.
asked Dec 20, 2016 in Set Theory & Algebra jothee 225 views
0 votes
0 answers
11
GATE1988-13ib
Verify whether the following mapping is a homomorphism. If so, determine its kernel. $\bar{G}=G$
Verify whether the following mapping is a homomorphism. If so, determine its kernel. $\bar{G}=G$
asked Dec 20, 2016 in Graph Theory jothee 166 views
0 votes
0 answers
12
GATE1988-13ia
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.
asked Dec 20, 2016 in Set Theory & Algebra jothee 174 views
3 votes
2 answers
13
GATE1988-12iv
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 least two attributes of each of these relations.
asked Dec 20, 2016 in Databases jothee 580 views
4 votes
2 answers
14
GATE1988-12iii
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 (select PNO from P Where COLOUR='BLUE'))
asked Dec 20, 2016 in Databases jothee 692 views
3 votes
1 answer
15
GATE1988-12iic
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: $x \rightarrow y$ 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 jothee 457 views
3 votes
1 answer
16
GATE1988-12iib
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: $x \rightarrow y$ 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 jothee 406 views
4 votes
1 answer
17
GATE1988-12iia
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: $x \rightarrow y$ 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 jothee 509 views
6 votes
1 answer
18
GATE1988-12i
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.
asked Dec 19, 2016 in Databases jothee 683 views
5 votes
4 answers
19
GATE1988-11
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 data ... 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 processes and let there be four resources types $r_j, 0 \leq j \leq 3$. Suppose the following data structures have been used ... Is the system currently in a safe state? If yes, explain why.
asked Dec 19, 2016 in Operating System jothee 1.2k views
7 votes
2 answers
20
GATE1988-10iib
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.
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) where ... i]:=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 jothee 1.3k views
0 votes
1 answer
21
GATE1988-10iia
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; var i:integer ... [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; 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; a: array [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 jothee 446 views
0 votes
3 answers
22
GATE1988-10ib
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 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 of the LR(0) parser.
asked Dec 19, 2016 in Compiler Design jothee 534 views
6 votes
2 answers
23
GATE1988-10ia
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.
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 jothee 1.1k views
7 votes
1 answer
24
GATE1988-9iii
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. ...
asked Dec 19, 2016 in CO and Architecture jothee 1.4k views
1 vote
0 answers
25
GATE1988-9ii
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 below Note-that $SP$ is the stack pointer and $R_i$ represents $i^{th}$ ...
asked Dec 19, 2016 in CO and Architecture jothee 203 views
2 votes
3 answers
26
GATE1988-9i
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 T2 ADD T1 STORE Z Give the arithmetic expression implemented by the fragment.
asked Dec 19, 2016 in CO and Architecture jothee 697 views
0 votes
0 answers
27
GATE1988-8iv
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 R; Q; exception 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; exception when BAD-Format => ... handler body 1 end R; begin R; Q; exception when BAD-FORMAT => ... handler body 2 end P; Under what conditions are the two handler bodies 1 and 2 executed?
asked Dec 19, 2016 in Programming jothee 185 views
0 votes
0 answers
28
GATE1988-8iii
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.
asked Dec 19, 2016 in Programming jothee 153 views
3 votes
2 answers
29
GATE1988-8ii
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 statement and f as a function.
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 jothee 1k views
2 votes
1 answer
30
GATE1988-8i
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, 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.
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, say z; assign to ... the 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 jothee 722 views
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