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GATE 1987 Computer Science Questions
Recent questions tagged gate1987
–1
vote
0
answers
1
GATE CSE 1987 | Question: 17a
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 $\emptyset$.
makhdoom ghaya
asked
in
Others
Nov 16, 2016
by
makhdoom ghaya
644
views
gate1987
out-of-gate-syllabus
21
votes
3
answers
2
GATE CSE 1987 | Question: 16-a
A Boolean function $f$ is to be realized only by $\text{NOR}$ gates. Its $K$-map is given below: The realization is
makhdoom ghaya
asked
in
Digital Logic
Nov 15, 2016
by
makhdoom ghaya
3.1k
views
gate1987
digital-logic
k-map
0
votes
0
answers
3
GATE CSE 1987 | Question: 15a
Fig. below shows the circuit diagram of a wien bridge oscillator using an op-amp. 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
makhdoom ghaya
asked
in
Integrated Circuits
Nov 15, 2016
by
makhdoom ghaya
583
views
gate1987
integrated-circuits
out-of-gate-syllabus
17
votes
3
answers
4
GATE CSE 1987 | Question: 13-a
The below figure shows four $\text{D}$-type flip-flops connected as a shift register using a $\text{XOR}$ ... $Q_{A} Q_{B} Q_{C} Q_{D}$ after the fourth clock pulse is $0000$ $1111$ $1001$ $1000$
makhdoom ghaya
asked
in
Digital Logic
Nov 15, 2016
by
makhdoom ghaya
2.6k
views
gate1987
digital-logic
circuit-output
sequential-circuit
digital-counter
shift-registers
26
votes
3
answers
5
GATE CSE 1987 | Question: 12-a
The Boolean expression $A \oplus B \oplus A$ is equivalent to $AB + \overline {A}\;\;\overline B$ $\overline{A}\;B+A\;\overline{B}$ $B$ $\overline{A}$
makhdoom ghaya
asked
in
Digital Logic
Nov 15, 2016
by
makhdoom ghaya
3.1k
views
gate1987
digital-logic
boolean-algebra
easy
1
vote
2
answers
6
GATE CSE 1987 | Question: 11c
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: $\begin{array}{|c|cccc|}\hline\textbf{JOBS} && \textbf{Machines} \\ & \textbf{$ ... Using the assignment method find the assignment involving minimum cost. Is this an optimal assignment?
makhdoom ghaya
asked
in
Algorithms
Nov 15, 2016
by
makhdoom ghaya
898
views
gate1987
algorithms
descriptive
out-of-gate-syllabus
0
votes
0
answers
7
GATE CSE 1987 | Question: 11b
Use Simpson's rule with $h=0.25$ to evaluate $ V= \int_{0}^{1} \frac{1}{1+x} dx$ correct to three decimal places.
makhdoom ghaya
asked
in
Numerical Methods
Nov 15, 2016
by
makhdoom ghaya
548
views
gate1987
numerical-methods
simpsons-rule
out-of-gate-syllabus
0
votes
0
answers
8
GATE CSE 1987 | Question: 11a
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.
makhdoom ghaya
asked
in
Numerical Methods
Nov 15, 2016
by
makhdoom ghaya
414
views
gate1987
numerical-methods
out-of-gate-syllabus
19
votes
8
answers
9
GATE CSE 1987 | Question: 10e
Show that the conclusion $(r \to q)$ follows from the premises$:p, (p \to q) \vee (p \wedge (r \to q))$
makhdoom ghaya
asked
in
Mathematical Logic
Nov 15, 2016
by
makhdoom ghaya
3.3k
views
gate1987
mathematical-logic
propositional-logic
proof
descriptive
22
votes
6
answers
10
GATE CSE 1987 | Question: 10d
Give a regular expression over the alphabet $\{0, 1\}$ to denote the set of proper non-null substrings of the string $0110$.
makhdoom ghaya
asked
in
Theory of Computation
Nov 15, 2016
by
makhdoom ghaya
4.2k
views
gate1987
theory-of-computation
regular-expression
descriptive
6
votes
1
answer
11
GATE CSE 1987 | Question: 10c
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 multiple of $3$.
makhdoom ghaya
asked
in
Digital Logic
Nov 15, 2016
by
makhdoom ghaya
1.7k
views
gate1987
digital-logic
digital-counter
descriptive
34
votes
8
answers
12
GATE CSE 1987 | Question: 10b
What is the generating function $G(z)$ for the sequence of Fibonacci numbers?
makhdoom ghaya
asked
in
Combinatory
Nov 15, 2016
by
makhdoom ghaya
7.4k
views
gate1987
combinatory
generating-functions
descriptive
23
votes
4
answers
13
GATE CSE 1987 | Question: 10a
Solve the recurrence equations: $T(n) = T(n - 1)+ n$ $T(1) = 1$
makhdoom ghaya
asked
in
Algorithms
Nov 15, 2016
by
makhdoom ghaya
4.2k
views
gate1987
algorithms
recurrence-relation
descriptive
3
votes
1
answer
14
GATE CSE 1987 | Question: 9f
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.
makhdoom ghaya
asked
in
Set Theory & Algebra
Nov 15, 2016
by
makhdoom ghaya
601
views
gate1987
set-theory&algebra
group-theory
group-isomorphism
descriptive
out-of-gate-syllabus
21
votes
2
answers
15
GATE CSE 1987 | Question: 9e
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?
makhdoom ghaya
asked
in
Set Theory & Algebra
Nov 15, 2016
by
makhdoom ghaya
2.2k
views
gate1987
set-theory&algebra
relations
descriptive
11
votes
1
answer
16
GATE CSE 1987 | Question: 9d
Specify an adjacency-lists representation of the undirected graph given above.
makhdoom ghaya
asked
in
Graph Theory
Nov 15, 2016
by
makhdoom ghaya
1.2k
views
gate1987
graph-theory
easy
graph-connectivity
descriptive
14
votes
3
answers
17
GATE CSE 1987 | Question: 9c
Show that the number of odd-degree vertices in a finite graph is even.
makhdoom ghaya
asked
in
Graph Theory
Nov 15, 2016
by
makhdoom ghaya
1.3k
views
gate1987
graph-theory
degree-of-graph
descriptive
proof
22
votes
2
answers
18
GATE CSE 1987 | Question: 9b
How many one-to-one functions are there from a set $A$ with $n$ elements onto itself?
makhdoom ghaya
asked
in
Set Theory & Algebra
Nov 15, 2016
by
makhdoom ghaya
3.3k
views
gate1987
set-theory&algebra
functions
descriptive
21
votes
2
answers
19
GATE CSE 1987 | Question: 9a
How many binary relations are there on a set $A$ with $n$ elements?
makhdoom ghaya
asked
in
Set Theory & Algebra
Nov 15, 2016
by
makhdoom ghaya
5.1k
views
gate1987
set-theory&algebra
relations
descriptive
12
votes
1
answer
20
GATE CSE 1987 | Question: 8a
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 ... group of readers make waiting writers starve? Can writers starve readers? Explain in two sentences why the solution is incorrect.
makhdoom ghaya
asked
in
Operating System
Nov 15, 2016
by
makhdoom ghaya
2.2k
views
gate1987
operating-system
process-synchronization
descriptive
16
votes
3
answers
21
GATE CSE 1987 | Question: 7b
Construct a binary tree whose preorder traversal is $K\;L\;N\;M\;P\;R\;Q\;S\;T$ and inorder traversal is $N\;L\;K\;P\;R\;M\;S\;Q\;T$
makhdoom ghaya
asked
in
DS
Nov 15, 2016
by
makhdoom ghaya
4.1k
views
gate1987
data-structures
binary-tree
descriptive
15
votes
1
answer
22
GATE CSE 1987 | Question: 7a
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; ... = remainder - divisor; (*C*) end; (*D*) quotient := quotient - 1; remainder := remainder + divisor; (*E*) end
makhdoom ghaya
asked
in
Programming
Nov 14, 2016
by
makhdoom ghaya
1.8k
views
gate1987
programming
loop-invariants
descriptive
14
votes
3
answers
23
GATE CSE 1987 | Question: 6a
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 ... $f ([32, 16, 8], [9, 11, 12])$ $g ([5, 1, 8, 9])$
makhdoom ghaya
asked
in
DS
Nov 14, 2016
by
makhdoom ghaya
2.1k
views
gate1987
data-structures
linked-list
descriptive
1
vote
0
answers
24
GATE CSE 1987 | Question: 5a
Eight $7$-segment 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.
makhdoom ghaya
asked
in
CO and Architecture
Nov 12, 2016
by
makhdoom ghaya
308
views
gate1987
co-and-architecture
input-output
descriptive
out-of-gate-syllabus
2
votes
1
answer
25
GATE CSE 1987 | Question: 4c
Give the character format for data transmission in asynchronous serial mode.
makhdoom ghaya
asked
in
Computer Networks
Nov 12, 2016
by
makhdoom ghaya
548
views
gate1987
serial-communication
descriptive
out-of-gate-syllabus
8
votes
4
answers
26
GATE CSE 1987 | Question: 4b
What is cache memory? What is rationale of using cache memory?
makhdoom ghaya
asked
in
CO and Architecture
Nov 12, 2016
by
makhdoom ghaya
1.5k
views
gate1987
co-and-architecture
cache-memory
descriptive
25
votes
3
answers
27
GATE CSE 1987 | Question: 4a
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 checking $4$ status bits. Provision to hold $128$ words in the control memory.
makhdoom ghaya
asked
in
CO and Architecture
Nov 12, 2016
by
makhdoom ghaya
4.2k
views
gate1987
co-and-architecture
microprogramming
descriptive
1
vote
0
answers
28
GATE CSE 1987 | Question: 3a
Design an $8 \times 8$ multiplier using five $4$-bits adders and $4$ ROM's each programmed to realise $4 \times 4$ multiplier.
makhdoom ghaya
asked
in
Digital Logic
Nov 12, 2016
by
makhdoom ghaya
488
views
gate1987
digital-logic
adder
descriptive
unsolved
19
votes
2
answers
29
GATE CSE 1987 | Question: 2n
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.
makhdoom ghaya
asked
in
Databases
Nov 9, 2016
by
makhdoom ghaya
2.4k
views
gate1987
databases
database-normalization
true-false
15
votes
2
answers
30
GATE CSE 1987 | Question: 2m
State whether the following statements are TRUE or FALSE: The problem as to whether a Turing machine $M$ accepts input $w$ is undecidable.
makhdoom ghaya
asked
in
Theory of Computation
Nov 9, 2016
by
makhdoom ghaya
3.2k
views
gate1987
theory-of-computation
turing-machine
decidability
true-false
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