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GATE 1987 Computer Science Questions

Recent questions tagged gate1987

–2 votes
0 answers
1
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 makhdoom ghaya 335 views
15 votes
4 answers
2
A Boolean function $f$ is to be realized only by $NOR$ gates. Its $K-map$ is given below: The realization is
asked Nov 15, 2016 in Digital Logic makhdoom ghaya 1.3k views
0 votes
0 answers
3
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
asked Nov 15, 2016 in Integrated Circuits makhdoom ghaya 261 views
13 votes
3 answers
4
The below figure shows four D-type flip-flops connected as a shift register using a $XOR$ 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 $0$ $1$ $1$ $1$ ... $0$ $0$ $0$ $1$ 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 makhdoom ghaya 1.1k views
14 votes
3 answers
5
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 makhdoom ghaya 1.1k views
0 votes
2 answers
6
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: $\begin{array}{|c|cccc|}\hline\textbf{JOBS} && \textbf{Machines} \\ & \textbf{$M_{1}$} & \textbf{$M_{2}$} & \textbf{$ ... Using the assignment method find the assignment involving minimum cost. Is this an optimal assignment?
asked Nov 15, 2016 in Algorithms makhdoom ghaya 490 views
0 votes
0 answers
7
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 makhdoom ghaya 282 views
0 votes
0 answers
8
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 makhdoom ghaya 204 views
12 votes
6 answers
9
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 makhdoom ghaya 1k views
14 votes
5 answers
10
Give a regular expression over the alphabet $\{0, 1\}$ to denote the set of proper non-null substrings of the string $0110$.
asked Nov 15, 2016 in Theory of Computation makhdoom ghaya 1.6k views
3 votes
1 answer
11
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 $3$.
asked Nov 15, 2016 in Digital Logic makhdoom ghaya 574 views
25 votes
6 answers
12
What is the generating function $G(z)$ for the sequence of Fibonacci numbers?
asked Nov 15, 2016 in Combinatory makhdoom ghaya 3.1k views
17 votes
3 answers
13
Solve the recurrence equations: $T(n) = T(n - 1)+ n$ $T(1) = 1$
asked Nov 15, 2016 in Algorithms makhdoom ghaya 1.7k views
2 votes
1 answer
14
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 makhdoom ghaya 245 views
9 votes
1 answer
15
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 makhdoom ghaya 764 views
2 votes
1 answer
16
Specify an adjacency-lists representation of the undirected graph given above.
asked Nov 15, 2016 in Graph Theory makhdoom ghaya 511 views
8 votes
2 answers
17
Show that the number of odd-degree vertices in a finite graph is even.
asked Nov 15, 2016 in Graph Theory makhdoom ghaya 486 views
16 votes
2 answers
18
How many one-to-one functions are there from a set $A$ with $n$ elements onto itself?
asked Nov 15, 2016 in Set Theory & Algebra makhdoom ghaya 1.2k views
11 votes
2 answers
19
How many binary relations are there on a set $A$ with $n$ elements?
asked Nov 15, 2016 in Set Theory & Algebra makhdoom ghaya 1.7k views
4 votes
1 answer
20
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 reading_value = ... Can 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 makhdoom ghaya 733 views
13 votes
3 answers
21
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 makhdoom ghaya 1.2k views
8 votes
1 answer
22
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; (*A*) ... 1; remainder := remainder - divisor; (*C*) end; (*D*) quotient := quotient - 1; remainder := remainder + divisor; (*E*) end
asked Nov 14, 2016 in Programming makhdoom ghaya 657 views
9 votes
3 answers
23
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 $l$; $cdr (l)$ ... $f ([32, 16, 8], [9, 11, 12])$ (b) $g ([5, 1, 8, 9])$
asked Nov 14, 2016 in DS makhdoom ghaya 887 views
0 votes
0 answers
24
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.
asked Nov 12, 2016 in Others makhdoom ghaya 142 views
2 votes
1 answer
25
Give the character format for data transmission in asynchronous serial mode.
asked Nov 12, 2016 in Computer Networks makhdoom ghaya 286 views
2 votes
3 answers
26
What is cache memory? What is rationale of using cache memory?
asked Nov 12, 2016 in CO and Architecture makhdoom ghaya 387 views
18 votes
3 answers
27
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.
asked Nov 12, 2016 in CO and Architecture makhdoom ghaya 1.1k views
0 votes
0 answers
28
Design an $8 \times 8$ multiplier using five 4-bits adders and 4 ROM's each programmed to realise $4 \times 4$ multiplier.
asked Nov 12, 2016 in Digital Logic makhdoom ghaya 238 views
14 votes
1 answer
29
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 makhdoom ghaya 676 views
11 votes
2 answers
30
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 makhdoom ghaya 937 views
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