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GATE 1993 Computer Science Questions and Solutions

Recent questions tagged gate1993

19 votes
2 answers
3
GATE CSE 1993 | Question: 6.2
If the state machine described in figure should have a stable state, the restriction on the inputs is given by $a.b=1$ $a+b=1$ $\bar{a} + \bar{b} =0$ $\overline{a.b}=1$ $\overline{a+b} =1$
If the state machine described in figure should have a stable state, the restriction on the inputs is given by$a.b=1$$a+b=1$$\bar{a} + \bar{b} =0$$\overline{a.b}=1$$\over...
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30 votes
4 answers
4
GATE CSE 1993 | Question: 28
Let $\left(\{ p,q \},*\right)$ be a semigroup where $p*p=q$. Show that: $p*q=q*p$ and $q*q=q$
Let $\left(\{ p,q \},*\right)$ be a semigroup where $p*p=q$. Show that:$p*q=q*p$ and$q*q=q$
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32 votes
4 answers
5
GATE CSE 1993 | Question: 27
Draw the state transition of a deterministic finite state automaton which accepts all strings from the alphabet $\{a,b\}$, such that no string has $3$ consecutive occurrences of the letter $b$.
Draw the state transition of a deterministic finite state automaton which accepts all strings from the alphabet $\{a,b\}$, such that no string has $3$ consecutive occurre...
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25 votes
4 answers
9
GATE CSE 1993 | Question: 22
Write a concurrent program using $\text{parbegin-parend}$ and semaphores to represent the precedence constraints of the statements $S_1$ to $S_6$, as shown in figure below.
Write a concurrent program using $\text{parbegin-parend}$ and semaphores to represent the precedence constraints of the statements $S_1$ to $S_6$, as shown in figure belo...
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18 votes
3 answers
13
GATE CSE 1993 | Question: 18
Show that proposition $C$ is a logical consequence of the formula$A\wedge \left(A \to \left(B \vee C\right)\right) \wedge \left( B \to \neg A\right)$using truth tables.
Show that proposition $C$ is a logical consequence of the formula$$A\wedge \left(A \to \left(B \vee C\right)\right) \wedge \left( B \to \neg A\right)$$using truth tables....
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42 votes
4 answers
14
GATE CSE 1993 | Question: 17
Out of a group of $21$ persons, $9$ eat vegetables, $10$ eat fish and $7$ eat eggs. $5$ persons eat all three. How many persons eat at least two out of the three dishes?
Out of a group of $21$ persons, $9$ eat vegetables, $10$ eat fish and $7$ eat eggs. $5$ persons eat all three. How many persons eat at least two out of the three dishes?
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19 votes
2 answers
15
GATE CSE 1993 | Question: 16
Prove by the principal of mathematical induction that for any binary tree, in which every non-leaf node has $2$-descendants, the number of leaves in the tree is one more than the number of non-leaf nodes.
Prove by the principal of mathematical induction that for any binary tree, in which every non-leaf node has $2$-descendants, the number of leaves in the tree is one more ...
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17 votes
2 answers
22
GATE CSE 1993 | Question: 9
Assume that only half adders are available in your laboratory. Show that any binary function can be implemented using half adders only.
Assume that only half adders are available in your laboratory. Show that any binary function can be implemented using half adders only.
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41 votes
5 answers
23
GATE CSE 1993 | Question: 8.7
$\displaystyle \sum_{1\leq k\leq n} O(n)$, where $O(n)$ stands for order $n$ is: $O(n)$ $O(n^2)$ $O(n^3)$ $O(3n^2)$ $O(1.5n^2)$
$\displaystyle \sum_{1\leq k\leq n} O(n)$, where $O(n)$ stands for order $n$ is:$O(n)$$O(n^2)$$O(n^3)$$O(3n^2)$$O(1.5n^2)$
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28 votes
3 answers
24
GATE CSE 1993 | Question: 8.6
Let $A$ and $B$ be sets with cardinalities $m$ and $n$ respectively. The number of one-one mappings from $A$ to $B$, when $m < n$, is $m^n$ $^nP_m$ $^mC_n$ $^nC_m$ $^mP_n$
Let $A$ and $B$ be sets with cardinalities $m$ and $n$ respectively. The number of one-one mappings from $A$ to $B$, when $m < n$, is$m^n$$^nP_m$$^mC_n$$^nC_m$$^mP_n$
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27 votes
3 answers
26
GATE CSE 1993 | Question: 8.4
Let A be a finite set of size n. The number of elements in the power set of $A\times A$ is: $2^{2^n}$ $2^{n^2}$ $\left(2^n\right)^2$ $\left(2^2\right)^n$ None of the above
Let A be a finite set of size n. The number of elements in the power set of $A\times A$ is:$2^{2^n}$$2^{n^2}$$\left(2^n\right)^2$$\left(2^2\right)^n$None of the above
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24 votes
4 answers
28
GATE CSE 1993 | Question: 8.2
The proposition $p \wedge (\sim p \vee q)$ is: a tautology logically equivalent to $p \wedge q$ logically equivalent to $p \vee q$ a contradiction none of the above
The proposition $p \wedge (\sim p \vee q)$ is:a tautologylogically equivalent to $p \wedge q$logically equivalent to $p \vee q$a contradictionnone of the above
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28 votes
3 answers
30
GATE CSE 1993 | Question: 7.10
Assume that the following jobs are to be executed on a single processor system ... time (completion time) for job $p$ if scheduling is round robin with time slice $1$ $4$ $10$ $11$ $12$ None of the above
Assume that the following jobs are to be executed on a single processor system$$\begin{array}{|c|c|} \hline \textbf{Job Id} & \textbf{CPU Burst Time} \\\hline \text{p} ...
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