Recent questions tagged gate1988

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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.

asked Dec 20, 2016 in Others by jothee Veteran | 155 views

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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.

asked Dec 20, 2016 in Linear Algebra by jothee Veteran | 173 views

+3 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.

asked Dec 20, 2016 in Linear Algebra by jothee Veteran | 436 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 $F2=A$ ? $F2=B$ ? $F2=C$ ? $F2=D$ ? $M=(Q, \Sigma, \delta, q_0, F)$ $M2=(Q2, \Sigma, \delta_2, q_{00}, F2)$ ... $D=\{\langle p, q, r \rangle \mid p \in Q; q \in F\}$

asked Dec 20, 2016 in Theory of Computation by jothee Veteran | 300 views

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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.

asked Dec 20, 2016 in Mathematical Logic by jothee Veteran | 208 views

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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.

asked Dec 20, 2016 in Mathematical Logic by jothee Veteran | 200 views

+8 votes

5 answers

7

GATE1988-13iv
Solve the recurrence equations: $T(n)= T( \frac{n}{2})+1$ $T(1)=1$

asked Dec 20, 2016 in Algorithms by jothee Veteran | 758 views

+3 votes

2 answers

8

GATE1988-13iii
Are the two digraphs shown in the above figure isomorphic? Justify your answer.

asked Dec 20, 2016 in Graph Theory by jothee Veteran | 390 views

+13 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.

asked Dec 20, 2016 in Set Theory & Algebra by jothee Veteran | 675 views

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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 $G$.

asked Dec 20, 2016 in Set Theory & Algebra by jothee Veteran | 169 views

0 votes

0 answers

11

GATE1988-13ib
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 | 114 views

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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.

asked Dec 20, 2016 in Set Theory & Algebra by jothee Veteran | 133 views

+1 vote

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.

asked Dec 20, 2016 in Databases by jothee Veteran | 270 views

+2 votes

1 answer

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'))

asked Dec 20, 2016 in Databases by jothee Veteran | 239 views

+2 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).

asked Dec 20, 2016 in Databases by jothee Veteran | 219 views

+2 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).

asked Dec 20, 2016 in Databases by jothee Veteran | 194 views

+3 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).

asked Dec 19, 2016 in Databases by jothee Veteran | 198 views

+4 votes

1 answer

18

GATE1988-12i
What are the three axioms of functional dependency for the relational databases given by Armstrong.

asked Dec 19, 2016 in Databases by jothee Veteran | 248 views

+4 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.

asked Dec 19, 2016 in Operating System by jothee Veteran | 705 views

+1 vote

1 answer

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.

asked Dec 19, 2016 in Operating System by jothee Veteran | 456 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.

asked Dec 19, 2016 in Compiler Design by jothee Veteran | 328 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.

asked Dec 19, 2016 in Compiler Design by jothee Veteran | 385 views

+3 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.

asked Dec 19, 2016 in Compiler Design by jothee Veteran | 491 views

+3 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. ...

asked Dec 19, 2016 in CO and Architecture by jothee Veteran | 429 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 $i^{th}$ ...

asked Dec 19, 2016 in CO and Architecture by jothee Veteran | 148 views

+1 vote

2 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.

asked Dec 19, 2016 in CO and Architecture by jothee Veteran | 236 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?

asked Dec 19, 2016 in Programming by jothee Veteran | 135 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.

asked Dec 19, 2016 in Programming by jothee Veteran | 112 views

+2 votes

1 answer

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.

asked Dec 19, 2016 in Programming by jothee Veteran | 473 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.

asked Dec 19, 2016 in Compiler Design by jothee Veteran | 404 views

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