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UGC NET CSE | December 2019 | Part 2 | Question: 41
When using Dijkstra's algorithm to find shortest path in a graph, which of the following statement is not true? It can find shortest path within the same graph data structure Every time a new node is visited, we choose the ... Shortest path always passes through least number of vertices The graph needs to have a non-negative weight on every edge
When using Dijkstra’s algorithm to find shortest path in a graph, which of the following statement is not true?It can find shortest path within the same graph data stru...
885
views
answered
Aug 13, 2021
Others
ugcnetcse-dec2019-paper2
+
–
10
answers
2
GATE CSE 2010 | Question: 39
Let $L=\{ w \in \:(0+1)^* \mid w\text{ has even number of }1s \}$. i.e., $L$ is the set of all the bit strings with even numbers of $1$s. Which one of the regular expressions below represents $L$? $(0^*10^*1)^*$ $0^*(10^*10^*)^*$ $0^*(10^*1)^*0^*$ $0^*1(10^*1)^*10^*$
Let $L=\{ w \in \:(0+1)^* \mid w\text{ has even number of }1s \}$. i.e., $L$ is the set of all the bit strings with even numbers of $1$s. Which one of the regular express...
22.1k
views
commented
Sep 9, 2020
Theory of Computation
gatecse-2010
theory-of-computation
regular-expression
normal
+
–
8
answers
3
GATE CSE 2014 Set 2 | Question: 50
Consider the following relation on subsets of the set $S$ of integers between $1$ and $2014$. For two distinct subsets $U$ and $V$ of $S$ we say $U\:<\:V$ if the minimum element in the symmetric difference of the two sets is in $U$. Consider the ... $S1$ is true and $S2$ is false $S2$ is true and $S1$ is false Neither $S1$ nor $S2$ is true
Consider the following relation on subsets of the set $S$ of integers between $1$ and $2014$. For two distinct subsets $U$ and $V$ of $S$ we say $U\:<\:V$ if the minimum ...
15.6k
views
commented
Sep 6, 2020
Set Theory & Algebra
gatecse-2014-set2
set-theory&algebra
normal
set-theory
+
–
3
answers
4
GATE CSE 2004 | Question: 56
Consider three IP networks $A, B$ and $C$. Host $H_A$ in network $A$ sends messages each containing $180$ bytes of application data to a host $H_C$ in network $C$. The $\text{TCP}$ layer prefixes $20$ byte header to the message. This passes ... $200$ $220$ $240$ $260$
Consider three IP networks $A, B$ and $C$. Host $H_A$ in network $A$ sends messages each containing $180$ bytes of application data to a host $H_C$ in network $C$. The $\...
22.8k
views
commented
Sep 3, 2020
Computer Networks
gatecse-2004
computer-networks
ip-addressing
tcp
normal
+
–
6
answers
5
GATE CSE 2004 | Question: 78
Two $n$ bit binary strings, $S_1$ and $S_2$ are chosen randomly with uniform probability. The probability that the Hamming distance between these strings (the number of bit positions where the two strings differ) is equal to $d$ is $\dfrac{^{n}C_{d}}{2^{n}}$ $\dfrac{^{n}C_{d}}{2^{d}}$ $\dfrac{d}{2^{n}}$ $\dfrac{1}{2^{d}}$
Two $n$ bit binary strings, $S_1$ and $S_2$ are chosen randomly with uniform probability. The probability that the Hamming distance between these strings (the number of b...
7.3k
views
answered
Aug 31, 2020
Probability
gatecse-2004
probability
normal
uniform-distribution
+
–
11
answers
6
GATE CSE 2005 | Question: 52
A random bit string of length n is constructed by tossing a fair coin n times and setting a bit to 0 or 1 depending on outcomes head and tail, respectively. The probability that two such randomly generated strings are not identical is: $\frac{1}{2^n}$ $1 - \frac{1}{n}$ $\frac{1}{n!}$ $1 - \frac{1}{2^n}$
A random bit string of length n is constructed by tossing a fair coin n times and setting a bit to 0 or 1 depending on outcomes head and tail, respectively. The probabili...
8.4k
views
answered
Aug 31, 2020
Probability
gatecse-2005
probability
binomial-distribution
easy
+
–
2
answers
7
GATE CSE 2019 | Question: 32
Let the set of functional dependencies $F=\{QR \rightarrow S, \: R \rightarrow P, \: S \rightarrow Q \}$ hold on a relation schema $X=(PQRS)$. $X$ is not in BCNF. Suppose $X$ is decomposed into two schemas $Y$ and $Z$ ... and $Z$ is dependency preserving and lossless Which of the above statements is/are correct? Both I and II I only II only Neither I nor II
Let the set of functional dependencies $F=\{QR \rightarrow S, \: R \rightarrow P, \: S \rightarrow Q \}$ hold on a relation schema $X=(PQRS)$. $X$ is not in BCNF. Suppose...
13.1k
views
commented
Aug 29, 2020
Databases
gatecse-2019
databases
database-normalization
2-marks
+
–
9
answers
8
GATE CSE 2001 | Question: 2.1
How many $4$-digit even numbers have all $4$ digits distinct? $2240$ $2296$ $2620$ $4536$
How many $4$-digit even numbers have all $4$ digits distinct?$2240$$2296$$2620$$4536$
12.5k
views
answered
Aug 26, 2020
Combinatory
gatecse-2001
combinatory
normal
+
–
3
answers
9
ISRO2009-56
A simple graph ( a graph without parallel edge or loops) with $n$ vertices and $k$ components can have at most $n$ edges $n-k$ edges $(n-k) (n-k+1)$ edges $(n-k) (n-k+1)/2$ edges
A simple graph ( a graph without parallel edge or loops) with $n$ vertices and $k$ components can have at most$n$ edges$n-k$ edges$(n-k) (n-k+1)$ edges$(n-k) (n-k+1)/2$ e...
3.4k
views
answered
Aug 26, 2020
Graph Theory
isro2009
graph-theory
graph-connectivity
+
–
2
answers
10
GATE CSE 1991 | Question: 01,viii
The weighted external path length of the binary tree in figure is ______
The weighted external path length of the binary tree in figure is ______
13.6k
views
commented
Aug 24, 2020
DS
gate1991
binary-tree
data-structures
normal
numerical-answers
+
–
7
answers
11
GATE CSE 2019 | Question: 30
Consider three $4$-variable functions $f_1, f_2$, and $f_3$, which are expressed in sum-of-minterms as $f_1=\Sigma(0,2,5,8,14),$ $f_2=\Sigma(2,3,6,8,14,15),$ $f_3=\Sigma (2,7,11,14)$ For the following circuit with one AND gate and one XOR gate the output function $f$ can be ... as: $\Sigma(7,8,11)$ $\Sigma (2,7,8,11,14)$ $\Sigma (2,14)$ $\Sigma (0,2,3,5,6,7,8,11,14,15)$
Consider three $4$-variable functions $f_1, f_2$, and $f_3$, which are expressed in sum-of-minterms as$f_1=\Sigma(0,2,5,8,14),$$f_2=\Sigma(2,3,6,8,14,15),$$f_3=\Sigma (2,...
14.2k
views
answered
Aug 22, 2020
Digital Logic
gatecse-2019
digital-logic
k-map
digital-circuits
2-marks
+
–
2
answers
12
GATE CSE 2016 Set 1 | Question: 46
Consider the following Syntax Directed Translation Scheme $( SDTS )$, with non-terminals $\{S,A \}$ and terminals $\{a,b \}$. $S \to aA \quad \{\text{print }1\}$ $S \to a \quad \{\text{print }2\}$ $A \to Sb \quad \{\text{print }3\}$ Using the above $SDTS$ ... printed by a bottom-up parser, for the input $aab$ is: $1 \ 3 \ 2 $ $2 \ 2 \ 3 $ $2 \ 3 \ 1 $ syntax error
Consider the following Syntax Directed Translation Scheme $( SDTS )$, with non-terminals $\{S,A \}$ and terminals $\{a,b \}$. $S \to aA \quad \{\text{print }1\}...
10.5k
views
commented
Aug 19, 2020
Compiler Design
gatecse-2016-set1
compiler-design
syntax-directed-translation
normal
+
–
7
answers
13
GATE IT 2006 | Question: 21
Consider the following first order logic formula in which $R$ is a binary relation symbol. $∀x∀y (R(x, y) \implies R(y, x))$ The formula is satisfiable and valid satisfiable and so is its negation unsatisfiable but its negation is valid satisfiable but its negation is unsatisfiable
Consider the following first order logic formula in which $R$ is a binary relation symbol.$∀x∀y (R(x, y) \implies R(y, x))$The formula issatisfiable and validsatisfia...
13.2k
views
answered
Aug 18, 2020
Mathematical Logic
gateit-2006
mathematical-logic
normal
first-order-logic
+
–
2
answers
14
relations and functions
367
views
answered
Aug 15, 2020
2
answers
15
relations and functions
A binary relation R on Z × Z is defined as follows: (a, b) R (c, d) iff a = c or b = d Consider the following propositions: 1. R is reflexive. 2. R is symmetric. 3. R is antisymmetric. Which one of the above statements is True?
A binary relation R on Z × Z is defined as follows: (a, b) R (c, d) iff a = c or b = dConsider the following propo...
630
views
answered
Aug 15, 2020
9
answers
16
GATE CSE 2014 Set 3 | Question: 25
Host A (on TCP/IP v4 network A) sends an IP datagram D to host B (also on TCP/IP v4 network B). Assume that no error occurred during the transmission of D. When D reaches B, which of the following IP header field(s) may be different from that of the original datagram ... $\text{ii}$ only $\text{ii}$ and $\text{iii}$ only $\text{i, ii}$ and $\text{iii}$
Host A (on TCP/IP v4 network A) sends an IP datagram D to host B (also on TCP/IP v4 network B). Assume that no error occurred during the transmission of D. When D reaches...
16.2k
views
commented
Aug 13, 2020
Computer Networks
gatecse-2014-set3
computer-networks
ip-packet
normal
+
–
7
answers
17
GATE CSE 2004 | Question: 26
The number of different $n \times n $ symmetric matrices with each element being either 0 or 1 is: (Note: $\text{power} \left(2, X\right)$ is same as $2^X$) $\text{power} \left(2, n\right)$ $\text{power} \left(2, n^2\right)$ $\text{power} \left(2,\frac{ \left(n^2+ n \right) }{2}\right)$ $\text{power} \left(2, \frac{\left(n^2 - n\right)}{2}\right)$
The number of different $n \times n $ symmetric matrices with each element being either 0 or 1 is: (Note: $\text{power} \left(2, X\right)$ is same as $2^X$)$\text{power} ...
12.4k
views
answered
Aug 10, 2020
Linear Algebra
gatecse-2004
linear-algebra
normal
matrix
+
–
4
answers
18
GATE CSE 2015 Set 3 | Question: 53
Language $L_1$ is polynomial time reducible to language $L_2$. Language $L_3$ is polynomial time reducible to language $L_2$, which in turn polynomial time reducible to language $L_4$. Which of the following is/are true? $\text{ if } L_4 \in P, \text{ then } L_2 \in P$ ... $\text{ if } L_4 \in P, \text{ then } L_3 \in P$ II only III only I and IV only I only
Language $L_1$ is polynomial time reducible to language $L_2$. Language $L_3$ is polynomial time reducible to language $L_2$, which in turn polynomial time reducible to l...
9.0k
views
answered
Aug 9, 2020
Theory of Computation
gatecse-2015-set3
theory-of-computation
decidability
normal
+
–
8
answers
19
GATE CSE 2018 | Question: 15
Two people, $P$ and $Q$, decide to independently roll two identical dice, each with $6$ faces, numbered $1$ to $6$. The person with the lower number wins. In case of a tie, they roll the dice repeatedly until there is no tie. Define a ... and that all trials are independent. The probability (rounded to $3$ decimal places) that one of them wins on the third trial is ____
Two people, $P$ and $Q$, decide to independently roll two identical dice, each with $6$ faces, numbered $1$ to $6$. The person with the lower number wins. In case of a ti...
10.8k
views
answered
Aug 9, 2020
Probability
gatecse-2018
probability
normal
numerical-answers
1-mark
+
–
5
answers
20
GATE CSE 1995 | Question: 2.23
A finite state machine with the following state table has a single input $x$ and a single out $z$ ... $C$ is: $01$ $10$ $101$ $110$
A finite state machine with the following state table has a single input $x$ and a single out $z$.$$\begin{array}{|c|ll|}\hline\textbf{present state} & \qquad \textbf{nex...
11.3k
views
commented
Aug 7, 2020
Theory of Computation
gate1995
theory-of-computation
finite-automata
normal
+
–
1
answer
21
GATE CSE 1997 | Question: 4.10
The trapezoidal method to numerically obtain $\int_a^b f(x) dx$ has an error E bounded by $\frac{b-a}{12} h^2 \max f’’(x), x \in [a, b]$ where $h$ is the width of the trapezoids. The minimum number of trapezoids guaranteed to ensure $E \leq 10^{-4}$ in computing $\ln 7$ using $f=\frac{1}{x}$ is 60 100 600 10000
The trapezoidal method to numerically obtain $\int_a^b f(x) dx$ has an error E bounded by $\frac{b-a}{12} h^2 \max f’’(x), x \in [a, b]$ where $h$ is the widt...
1.5k
views
commented
Aug 5, 2020
Numerical Methods
gate1997
numerical-methods
trapezoidal-rule
normal
+
–
5
answers
22
GATE CSE 2000 | Question: 1.4
Let $S$ and $T$ be languages over $\Sigma=\{a,b\}$ represented by the regular expressions $(a+b^*)^*$ and $(a+b)^*$, respectively. Which of the following is true? $S \subset T$ $T \subset S$ $S = T$ $S \cap T = \phi$
Let $S$ and $T$ be languages over $\Sigma=\{a,b\}$ represented by the regular expressions $(a+b^*)^*$ and $(a+b)^*$, respectively. Which of the following is true?$S \subs...
11.4k
views
commented
Aug 4, 2020
Theory of Computation
gatecse-2000
theory-of-computation
regular-expression
easy
+
–
21
answers
23
GATE CSE 2016 Set 1 | Question: 54
For a host machine that uses the token bucket algorithm for congestion control, the token bucket has a capacity of $1$ $\text{megabyte}$ and the maximum output rate is $20$ $\text{megabytes}$ per $\text{second}$. Tokens arrive at a rate to ... to send $12$ $\text{megabytes}$ of data. The minimum time required to transmit the data is _____________ $\text{seconds}$.
For a host machine that uses the token bucket algorithm for congestion control, the token bucket has a capacity of $1$ $\text{megabyte}$ and the maximum output rate is $2...
41.7k
views
commented
Aug 2, 2020
Computer Networks
gatecse-2016-set1
computer-networks
token-bucket
normal
numerical-answers
+
–
3
answers
24
GATE CSE 2008 | Question: 21
The minimum number of equal length subintervals needed to approximate $\int_1^2 xe^x\,dx$ to an accuracy of at least $\frac{1}{3}\times10^{-6}$ using the trapezoidal rule is 1000e 1000 100e 100
The minimum number of equal length subintervals needed to approximate $\int_1^2 xe^x\,dx$ to an accuracy of at least $\frac{1}{3}\times10^{-6}$ using the trapezoidal rule...
3.0k
views
answered
Aug 1, 2020
Numerical Methods
gatecse-2008
normal
numerical-methods
trapezoidal-rule
non-gate
+
–
1
answer
25
GATE CSE 1988 | Question: 1i
Loosely speaking, we can say that a numerical method is unstable if errors introduced into the computation grow at _________ rate as the computation proceeds.
Loosely speaking, we can say that a numerical method is unstable if errors introduced into the computation grow at _________ rate as the computation proceeds.
548
views
answered
Jul 31, 2020
Numerical Methods
gate1988
numerical-methods
out-of-gate-syllabus
+
–
7
answers
26
GATE CSE 2011 | Question: 31
Given $i = \sqrt{-1}$, what will be the evaluation of the definite integral $\int \limits_0^{\pi/2} \dfrac{\cos x +i \sin x} {\cos x - i \sin x} dx$ ? $0$ $2$ $-i$ $i$
Given $i = \sqrt{-1}$, what will be the evaluation of the definite integral $\int \limits_0^{\pi/2} \dfrac{\cos x +i \sin x} {\cos x - i \sin x} dx$ ?$0$$2$$-i$$i$
10.8k
views
commented
Jul 29, 2020
Calculus
gatecse-2011
calculus
integration
normal
+
–
11
answers
27
GATE CSE 2014 Set 1 | Question: 47
A function $f(x)$ is continuous in the interval $[0,2]$. It is known that $f(0) = f(2) = -1$ and $f(1) = 1$. Which one of the following statements must be true? There exists a $y$ in the interval $(0,1)$ such that $f(y) = f(y+1)$ For every $y$ ... the function in the interval $(0,2)$ is $1$ There exists a $y$ in the interval $(0,1)$ such that $f(y)$ = $-f(2-y)$
A function $f(x)$ is continuous in the interval $[0,2]$. It is known that $f(0) = f(2) = -1$ and $f(1) = 1$. Which one of the following statements must be true?There exis...
20.7k
views
commented
Jul 29, 2020
Calculus
gatecse-2014-set1
calculus
continuity
normal
+
–
8
answers
28
GATE CSE 2006 | Question: 46
Station $A$ needs to send a message consisting of $9$ packets to Station $B$ using a sliding window (window size $3$) and go-back-$n$ error control strategy. All packets are ready and immediately available for transmission. If every $5$th packet that $A$ ... what is the number of packets that $A$ will transmit for sending the message to $B$? $12$ $14$ $16$ $18$
Station $A$ needs to send a message consisting of $9$ packets to Station $B$ using a sliding window (window size $3$) and go-back-$n$ error control strategy. All packets ...
40.7k
views
commented
Jul 28, 2020
Computer Networks
gatecse-2006
computer-networks
sliding-window
normal
+
–
5
answers
29
GATE IT 2007 | Question: 65
Consider a selection of the form $\sigma_{A\leq 100} (r)$, where $r$ is a relation with $1000$ tuples. Assume that the attribute values for $A$ among the tuples are uniformly distributed in the interval $[0, 500].$ Which one of the following options is the best estimate of the number of tuples returned by the given selection query ? $50$ $100$ $150$ $200$
Consider a selection of the form $\sigma_{A\leq 100} (r)$, where $r$ is a relation with $1000$ tuples. Assume that the attribute values for $A$ among the tuples are unifo...
12.5k
views
commented
Jul 26, 2020
Databases
gateit-2007
databases
relational-calculus
probability
normal
+
–
9
answers
30
GATE CSE 2008 | Question: 1
$\displaystyle \lim_{x \to \infty}\frac{x-\sin x}{x+\cos x}$ equals $1$ $-1$ $\infty$ $-\infty$
$\displaystyle \lim_{x \to \infty}\frac{x-\sin x}{x+\cos x}$ equals$1$$-1$$\infty$$-\infty$
9.9k
views
commented
Jul 25, 2020
Calculus
gatecse-2008
calculus
limits
easy
+
–
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