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GATE 1987 Computer Science Questions

Recent questions tagged gate1987

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
A Boolean function $f$ is to be realized only by $\text{NOR}$ gates. Its $K$-map is given below:The realization is
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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
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...
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18 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 $0000$ $1111$ $1001$ $1000$
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...
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28 votes
3 answers
5
GATE CSE 1987 | Question: 12-a
The Boolean expression $A \oplus B \oplus A$ is equivalent to $AB + \overline {A}\;\;\overline B$ $\overline{A}\;B+A\;\overline{B}$ $B$ $\overline{A}$
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}$
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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.
Use Simpson's rule with $h=0.25$ to evaluate $ V= \int_{0}^{1} \frac{1}{1+x} dx$ correct to three decimal places.
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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.
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.
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23 votes
9 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))$
Show that the conclusion $(r \to q)$ follows from the premises$:p, (p \to q) \vee (p \wedge (r \to q))$
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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$.
Give a regular expression over the alphabet $\{0, 1\}$ to denote the set of proper non-null substrings of the string $0110$.
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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$.
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$.
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36 votes
8 answers
12
GATE CSE 1987 | Question: 10b
What is the generating function $G(z)$ for the sequence of Fibonacci numbers?
What is the generating function $G(z)$ for the sequence of Fibonacci numbers?
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24 votes
4 answers
13
GATE CSE 1987 | Question: 10a
Solve the recurrence equations: $T(n) = T(n - 1)+ n$ $T(1) = 1$
Solve the recurrence equations:$T(n) = T(n - 1)+ n$$T(1) = 1$
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25 votes
2 answers
15
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?
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?
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11 votes
1 answer
16
GATE CSE 1987 | Question: 9d
Specify an adjacency-lists representation of the undirected graph given above.
Specify an adjacency-lists representation of the undirected graph given above.
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15 votes
3 answers
17
GATE CSE 1987 | Question: 9c
Show that the number of odd-degree vertices in a finite graph is even.
Show that the number of odd-degree vertices in a finite graph is even.
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24 votes
3 answers
18
GATE CSE 1987 | Question: 9b
How many one-to-one functions are there from a set $A$ with $n$ elements onto itself?
How many one-to-one functions are there from a set $A$ with $n$ elements onto itself?
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25 votes
4 answers
19
GATE CSE 1987 | Question: 9a
How many binary relations are there on a set $A$ with $n$ elements?
How many binary relations are there on a set $A$ with $n$ elements?
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18 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 $N\;L\;K\;P\;R\;M\;S\;Q\;T$
Construct a binary tree whose preorder traversal is$K\;L\;N\;M\;P\;R\;Q\;S\;T$and inorder traversal is$N\;L\;K\;P\;R\;M\;S\;Q\;T$
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2 votes
1 answer
25
GATE CSE 1987 | Question: 4c
Give the character format for data transmission in asynchronous serial mode.
Give the character format for data transmission in asynchronous serial mode.
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10 votes
4 answers
26
GATE CSE 1987 | Question: 4b
What is cache memory? What is rationale of using cache memory?
What is cache memory? What is rationale of using cache memory?
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1 votes
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.
Design an $8 \times 8$ multiplier using five $4$-bits adders and $4$ ROM's each programmed to realise $4 \times 4$ multiplier.
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21 votes
3 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.
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...
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14 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.
State whether the following statements are TRUE or FALSE:The problem as to whether a Turing machine $M$ accepts input $w$ is undecidable.
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