Register
GATE 1987 Computer Science Questions

Recent questions tagged gate1987

4 4 votes
0 0 answers
1.9k
1.9k views
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...
User Avatar
36 36 votes
5 answers 5 answers
8.8k
8.8k views
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    
User Avatar
1 1 vote
0 0 answers
1.7k
1.7k views
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 th...
User Avatar
30 30 votes
4 answers 4 answers
6.5k
6.5k views
GATE CSE 1987 | Question: 13-a
The below figure shows four $\text{D}$-type flip-flops connected as a shift register using a $\text{XOR}$ gate. The initial state and three subsequent states for three cl...
User Avatar
39 39 votes
7 answers 7 answers
10.4k
10.4k views
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$$\overline{A}$
User Avatar
2 2 votes
2 answers 2 answers
2.5k
2.5k views
GATE CSE 1987 | Question: 11c
The relative costs of assigning jobs $J_{1}, J_{2}$ and $J_{3}$ to machines $M_{1}, M_{2}$ and $M_{3}$ are given below:$$\begin{array}{|c|cccc|}\hline\textbf{JOBS} && \te...
User Avatar
1 1 vote
0 0 answers
1.2k
1.2k views
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.
User Avatar
1 1 vote
0 0 answers
794
794 views
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.
User Avatar
40 40 votes
13 answers 13 answers
12.2k
12.2k views
GATE CSE 1987 | Question: 10e
Show that the conclusion $(r \to q)$ follows from the premises$:p, (p \to q) \vee (p \wedge (r \to q))$
User Avatar
36 36 votes
6 answers 6 answers
9.8k
9.8k views
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 $0110$.
User Avatar
10 10 votes
1 answers 1 answer
4.9k
4.9k views
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 $3$.
User Avatar
45 45 votes
10 answers 10 answers
16.9k
16.9k views
GATE CSE 1987 | Question: 10b
What is the generating function $G(z)$ for the sequence of Fibonacci numbers?
User Avatar
33 33 votes
7 answers 7 answers
9.6k
9.6k views
GATE CSE 1987 | Question: 10a
Solve the recurrence equations:$T(n) = T(n - 1)+ n$$T(1) = 1$
User Avatar
5 5 votes
1 1 answer
1.7k
1.7k views
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, ...
User Avatar
40 40 votes
5 answers 5 answers
7.1k
7.1k views
GATE CSE 1987 | Question: 9e
How many true inclusion relations are there of the form $A \subseteq B$, where $A$ and $B$ are subsets of a set $S$ with $n$ elements?
User Avatar
21 21 votes
1 answers 1 answer
3.4k
3.4k views
GATE CSE 1987 | Question: 9d
Specify an adjacency-lists representation of the undirected graph given above.
User Avatar
21 21 votes
3 answers 3 answers
3.7k
3.7k views
GATE CSE 1987 | Question: 9c
Show that the number of odd-degree vertices in a finite graph is even.
User Avatar
31 31 votes
3 answers 3 answers
7.5k
7.5k views
GATE CSE 1987 | Question: 9b
How many one-to-one functions are there from a set $A$ with $n$ elements onto itself?
User Avatar
32 32 votes
5 answers 5 answers
8.8k
8.8k views
GATE CSE 1987 | Question: 9a
How many binary relations are there on a set $A$ with $n$ elements?
User Avatar
20 20 votes
1 1 answer
6.0k
6.0k views
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: initia...
User Avatar
29 29 votes
3 answers 3 answers
8.3k
8.3k views
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$N\;L\;K\;P\;R\;M\;S\;Q\;T$
User Avatar
20 20 votes
2 2 answers
5.3k
5.3k views
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, quot...
User Avatar
36 36 votes
3 answers 3 answers
6.1k
6.1k views
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 an...
User Avatar
1 1 vote
0 0 answers
732
732 views
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 circu...
User Avatar
2 2 votes
1 answers 1 answer
1.3k
1.3k views
GATE CSE 1987 | Question: 4c
Give the character format for data transmission in asynchronous serial mode.
User Avatar
16 16 votes
5 answers 5 answers
4.1k
4.1k views
GATE CSE 1987 | Question: 4b
What is cache memory? What is rationale of using cache memory?
User Avatar
34 34 votes
4 answers 4 answers
10.9k
10.9k views
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 ...
User Avatar
1 1 vote
0 0 answers
1.0k
1.0k views
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.
User Avatar
50 50 votes
6 answers 6 answers
9.3k
9.3k views
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...
User Avatar
19 19 votes
5 answers 5 answers
6.7k
6.7k views
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.
User Avatar
Page: