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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 gate1987
GATE 1987 Computer Science Questions
–1
vote
0
answers
1
GATE198717a
A voltage source e(t) $50 \sin 100$ is connected to a resistor R of 3 ohms in series with an inductor L of $0.04$ henries at time $t$ (in seconds) = 0. The expression for the current in the circuit for $1=0$ is of the form. $i(t) = Ae^{kt} + B sing (100t  \emptyset)$ Find the values of $A, K, B$ and $\emptyset$.
asked
Nov 16, 2016
in
Others
by
makhdoom ghaya
Boss
(
40k
points)

213
views
gate1987
+12
votes
4
answers
2
GATE198716a
A Boolean function $f$ is to be realized only by NOR gates. Its Kmap is given below: The realization is
asked
Nov 15, 2016
in
Digital Logic
by
makhdoom ghaya
Boss
(
40k
points)

563
views
gate1987
digitallogic
kmap
0
votes
0
answers
3
GATE198715a
Fig. below shows the circuit diagram of a wien bridge oscillator using an opamp. The frequency of oscillation is given by $f= 1/2 \pi CR$. To have the system oscillate the ratio $R_{2}/R_{1}$ should be $0.5$ $29$ $2$ Any value
asked
Nov 15, 2016
in
Integrated Circuits
by
makhdoom ghaya
Boss
(
40k
points)

179
views
gate1987
nongate
integratedcircuits
+11
votes
2
answers
4
GATE198713a
The below figure shows four Dtype flipflops connnected as a shift register using an $XOR$ gate. The initial state and three subsequent states for three clock pulses are also given. State $Q_{A}$ $Q_{B}$ $Q_{C}$ $Q_{D}$ Initial $1$ $1$ $1$ $1$ After the first ... clock $0$ $0$ $0$ $1$ The state $Q_{A} Q_{B} Q_{C} Q_{D}$ after the fourth clock pulse is $0000$ $1111$ $1001$ $1000$
asked
Nov 15, 2016
in
Digital Logic
by
makhdoom ghaya
Boss
(
40k
points)

536
views
gate1987
digitallogic
circuitoutput
shiftregisters
+13
votes
3
answers
5
GATE198712a
The Boolean expression $A \oplus B \oplus A$ is equivalent to $AB + \bar {A}\bar B$ $\bar{A}B+A\bar{B}$ $B$ $\bar{A}$
asked
Nov 15, 2016
in
Digital Logic
by
makhdoom ghaya
Boss
(
40k
points)

502
views
gate1987
digitallogic
booleanexpressions
easy
0
votes
2
answers
6
GATE198711c
The relative costs of assigning jobs $J_{1}, J_{2}$ and $J_{3}$ to machines $M_{1}, M_{2}$ and $M_{3}$ are given below: Using the assignment method find the assignment involving minimum cost. Is this an optimal assignment?
asked
Nov 15, 2016
in
Algorithms
by
makhdoom ghaya
Boss
(
40k
points)

203
views
gate1987
algorithms
0
votes
0
answers
7
GATE198711b
Use Simpson's rule with $h=0.25$ to evaluate $ V= \int_{0}^{1} \frac{1}{1+x} dx$ correct to three decimal places.
asked
Nov 15, 2016
in
Numerical Methods
by
makhdoom ghaya
Boss
(
40k
points)

164
views
gate1987
nongate
numericalmethods
simpsonsrule
0
votes
0
answers
8
GATE198711a
Given $f(300)=2,4771; f(304) = 2.4829; f(305) = 2.4843$ and $f(307) = 2.4871$ find $f(301)$ using Lagrange's interpolation formula.
asked
Nov 15, 2016
in
Numerical Methods
by
makhdoom ghaya
Boss
(
40k
points)

124
views
gate1987
nongate
numericalmethods
+8
votes
3
answers
9
GATE198710e
Show that the conclusion $(r \to q)$ follows from the premises: $p, (p \to q) \vee (p \wedge (r \to q))$
asked
Nov 15, 2016
in
Mathematical Logic
by
makhdoom ghaya
Boss
(
40k
points)

378
views
gate1987
mathematicallogic
propositionallogic
proof
descriptive
+11
votes
5
answers
10
GATE198710d
Give a regular expression over the alphabet $\{0, 1\}$ to denote the set of proper nonnull substrings of the string $0110$.
asked
Nov 15, 2016
in
Theory of Computation
by
makhdoom ghaya
Boss
(
40k
points)

651
views
gate1987
theoryofcomputation
regularexpressions
+1
vote
1
answer
11
GATE198710c
Give a minimal DFA that performs as a $\mod  3,\;$ $1$'s counter, i.e. outputs a $1$ each time the number of $1$'s in the input sequence is a sequence is a multiple of $3$.
asked
Nov 15, 2016
in
Digital Logic
by
makhdoom ghaya
Boss
(
40k
points)

176
views
gate1987
digitallogic
digitalcounter
+12
votes
5
answers
12
GATE198710b
What is the generating function $G(z)$ for the sequence of Fibonacci numbers?
asked
Nov 15, 2016
in
Combinatory
by
makhdoom ghaya
Boss
(
40k
points)

833
views
gate1987
permutationsandcombinations
generatingfunctions
descriptive
+14
votes
3
answers
13
GATE198710a
Solve the recurrence equations: $T(n) = T(n  1)+ n$ $T(1) = 1$
asked
Nov 15, 2016
in
Algorithms
by
makhdoom ghaya
Boss
(
40k
points)

537
views
gate1987
algorithms
recurrence
+2
votes
0
answers
14
GATE19879f
Give the composition tables (Cayley Tables) of the two non isomorphic groups of order 4 with elements $e, a, b, c$ where $c$ is the identity element. Use the order $e, a, b, c$ for the rows and columns.
asked
Nov 15, 2016
in
Set Theory & Algebra
by
makhdoom ghaya
Boss
(
40k
points)

123
views
gate1987
groupisomorphism
settheory&algebra
+7
votes
0
answers
15
GATE19879e
How many true inclusion relations are there of the from $A \subseteq B$, where $A$ and $B$ are subsets of a set $S$ with $n$ elements?
asked
Nov 15, 2016
in
Set Theory & Algebra
by
makhdoom ghaya
Boss
(
40k
points)

336
views
gate1987
settheory&algebra
relations
+2
votes
0
answers
16
GATE19879d
Specify an adjacencylists representation of the undirected graph given above.
asked
Nov 15, 2016
in
Graph Theory
by
makhdoom ghaya
Boss
(
40k
points)

144
views
gate1987
graphtheory
easy
+2
votes
2
answers
17
GATE19879c
Show that the number of odddegree vertices in a finite graph is even.
asked
Nov 15, 2016
in
Graph Theory
by
makhdoom ghaya
Boss
(
40k
points)

195
views
gate1987
graphtheory
degreeofgraph
descriptive
+8
votes
2
answers
18
GATE19879b
How many onetoone functions are there from a set $A$ with $n$ elements onto itself?
asked
Nov 15, 2016
in
Set Theory & Algebra
by
makhdoom ghaya
Boss
(
40k
points)

445
views
gate1987
settheory&algebra
functions
descriptive
+7
votes
2
answers
19
GATE19879a
How many binary relations are there on a set $A$ with $n$ elements?
asked
Nov 15, 2016
in
Set Theory & Algebra
by
makhdoom ghaya
Boss
(
40k
points)

510
views
gate1987
settheory&algebra
relations
descriptive
+3
votes
0
answers
20
GATE19878a
Consider the following proposal to the "readers and writers problem." Shared variables and semaphores: aw, ar, rw, rr : interger; mutex, reading, writing: semaphore: initial values of variables and states of semaphores: ar=rr=aw=rw=0 ... a group of readers make waiting writers starve? Can writers starve readers? Explain in two sentences why the solution is incorrect.
asked
Nov 15, 2016
in
Operating System
by
makhdoom ghaya
Boss
(
40k
points)

243
views
gate1987
operatingsystem
processsynchronization
readerwriter
+11
votes
3
answers
21
GATE19877b
Construct a binary tree whose preorder traversal is K L N M P R Q S T and inorder traversal is N L K P R M S Q T
asked
Nov 15, 2016
in
DS
by
makhdoom ghaya
Boss
(
40k
points)

375
views
gate1987
datastructure
binarytree
+3
votes
0
answers
22
GATE19877a
List the invariant assertions at points $A, B, C, D$ and $E$ in program given below: Program division (input, output) Const dividend = 81; divisor = 9; Var remainder, quotient:interger begin (*(dividend >= 0) AND (divisor > 0)*) remainder := dividend; quotient := 9; ... := remainder  divisor; (*C*) end; (*D*) quotient := quotient  1; remainder := remainder + divisor; (*E*) end
asked
Nov 14, 2016
in
Programming
by
makhdoom ghaya
Boss
(
40k
points)

158
views
gate1987
programming
loopinvariants
+7
votes
3
answers
23
GATE19876a
A list of $n$ elements is commonly written as a sequence of $n$ elements enclosed in a pair of square brackets. For example. $[10, 20, 30]$ is a list of three elements and $[]$ is a nil list. Five functions are defined below: $car (l)$ returns the first element of its argument list $l$; $cdr ( ... $ What do the following compute? (a) $f ([32, 16, 8], [9, 11, 12])$ (b) $g ([5, 1, 8, 9])$
asked
Nov 14, 2016
in
DS
by
makhdoom ghaya
Boss
(
40k
points)

402
views
gate1987
datastructure
linkedlists
0
votes
0
answers
24
GATE19875a
Eight 7segment LED displays and a keyboard consisting of 28 keys are to be interfaced to a microprocessor based system. Give the block diagram of the interface circuit using minimum number of port lines from any programmable I/O chip. Use any other IC chip if necessary.
asked
Nov 12, 2016
in
Others
by
makhdoom ghaya
Boss
(
40k
points)

85
views
gate1987
nongate
interfacing
+2
votes
1
answer
25
GATE19874c
Give the character format for data transmission in asynchronous serial mode.
asked
Nov 12, 2016
in
Computer Networks
by
makhdoom ghaya
Boss
(
40k
points)

163
views
gate1987
serialcommunication
nongate
0
votes
1
answer
26
GATE19874b
What is cache memory? What is rationale of using cache memory?
asked
Nov 12, 2016
in
CO & Architecture
by
makhdoom ghaya
Boss
(
40k
points)

128
views
gate1987
coandarchitecture
cachememory
+7
votes
3
answers
27
GATE19874a
Find out the width of the control memory of a horizontal microprogrammed control unit, given the following specifications: $16$ control lines for the processor consisting of ALU and $7$ registers. Conditional branching facility by cheeking $4$ status bits. Provision to hold $128$ words in the control memory.
asked
Nov 12, 2016
in
CO & Architecture
by
makhdoom ghaya
Boss
(
40k
points)

316
views
gate1987
coandarchitecture
microprogramming
0
votes
0
answers
28
GATE19873a
Design an $8 \times 8$ multiplier using five 4bits adders and 4 ROM's each programmed to realise $4 \times 4$ multiplier.
asked
Nov 12, 2016
in
Digital Logic
by
makhdoom ghaya
Boss
(
40k
points)

112
views
gate1987
digitallogic
adder
+10
votes
1
answer
29
GATE19872n
State whether the following statements are TRUE or FALSE: A relation $r$ with schema $(X, Y)$ satisfies the function dependency $X \rightarrow Y$, The tuples $\langle 1, 2\rangle$ and $\langle 2, 2 \rangle$ can both be in $r$ simultaneously.
asked
Nov 9, 2016
in
Databases
by
makhdoom ghaya
Boss
(
40k
points)

256
views
gate1987
databases
functionaldependencies
+7
votes
2
answers
30
GATE19872m
State whether the following statements are TRUE or FALSE: The problem as to whether a Turing machine $M$ accepts input $w$ is undecidable.
asked
Nov 9, 2016
in
Theory of Computation
by
makhdoom ghaya
Boss
(
40k
points)

352
views
gate1987
theoryofcomputation
turingmachine
decidability
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