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 $\emptyset$.
16 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
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
15 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 $0$ $1$ $1$ ... $Q_{A} Q_{B} Q_{C} Q_{D}$ after the fourth clock pulse is $0000$ $1111$ $1001$ $1000$
19 votes
3 answers
5
The Boolean expression $A \oplus B \oplus A$ is equivalent to $AB + \bar {A}\bar B$ $\bar{A}B+A\bar{B}$ $B$ $\bar{A}$
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?
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.
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.
13 votes
6 answers
9
Show that the conclusion $(r \to q)$ follows from the premises: $p, (p \to q) \vee (p \wedge (r \to q))$
16 votes
6 answers
10
Give a regular expression over the alphabet $\{0, 1\}$ to denote the set of proper non-null substrings of the string $0110$.
4 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 $3$.
27 votes
6 answers
12
What is the generating function $G(z)$ for the sequence of Fibonacci numbers?
20 votes
4 answers
13
Solve the recurrence equations: $T(n) = T(n - 1)+ n$ $T(1) = 1$
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.
11 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?
3 votes
1 answer
16
Specify an adjacency-lists representation of the undirected graph given above.
9 votes
3 answers
17
Show that the number of odd-degree vertices in a finite graph is even.
19 votes
2 answers
18
How many one-to-one functions are there from a set $A$ with $n$ elements onto itself?
12 votes
2 answers
19
How many binary relations are there on a set $A$ with $n$ elements?
7 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.
14 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
10 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
11 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) $g ([5, 1, 8, 9])$
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.
2 votes
1 answer
25
Give the character format for data transmission in asynchronous serial mode.
5 votes
5 answers
26
What is cache memory? What is rationale of using cache memory?
21 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.
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.
16 votes
2 answers
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.
13 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.