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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

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

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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

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

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

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

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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

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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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

1 vote

0 answers

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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

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

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

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

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

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

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

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