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Gate 2016
The minimum number of colours that is sufficient to vertex-colour any planar graph is ________. I am confused with the question's language. please correct me if I have a wrong assumption. We need to tell the minimum colors required for a planar graph. Suppose I start ... is only fixed to 4. I understand the answer not to be less than 4. What does the word "any" means here?
TusharRana
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Graph Theory
Feb 8
by
TusharRana
175
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0
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0
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62
Combinatorics & Probability
A rumor is spread randomly among a group of 10 people by successively having one person call someone, who calls someone, and so on. A person can pass the rumor on to anyone except the individual who just called. (a) By how many different paths can a rumor ... in $N$ calls? (c) What is the probability that if $A$ starts the rumor, then $A$ receives the third calls?
Debargha Mitra Roy
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in
Combinatory
Feb 8
by
Debargha Mitra Roy
132
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combinatory
counting
0
votes
0
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63
how i give free mock test on previous year
Shruti bhurse
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Others
Feb 7
by
Shruti bhurse
73
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query
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64
#self doubt
Can someone please verify it ? isn't should be 8. https://www.toppr.com/ask/question/the-cardinality-of-the-power-set-of-left-phi-left-phiright-left-phi-left/ Let S={ϕ,{ϕ},{ϕ,{ϕ}}} P(s)= Power Set of set S P(s)={ϕ,{ϕ},{ϕ,{ϕ}},{ϕ,{ϕ,{ϕ}}},{{ϕ},{ϕ,{ϕ}}},{ϕ,{ϕ},{ϕ,{ϕ}}}} n(P(s))=6.
Dknights
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in
Set Theory & Algebra
Feb 6
by
Dknights
109
views
discrete-mathematics
4
votes
0
answers
65
GO Classes Test Series 2024 | Mock GATE | Test 14 | Question: 31
DeMorgan's Laws ensure that Closure under intersection and complementation imply closure under union. Closure under intersection and union imply closure under complementation. Closure under union and complementation imply closure ... Closure under any two of union, intersection, and complementation implies closure under all three.
GO Classes
asked
in
Theory of Computation
Feb 5
by
GO Classes
301
views
goclasses2024-mockgate-14
theory-of-computation
closure-property
multiple-selects
1-mark
4
votes
0
answers
66
GO Classes Test Series 2024 | Mock GATE | Test 14 | Question: 40
Consider the following schema (primary keys are underlined): Which of the following queries returns the department numbers of those departments for which there are no courses being offered?
GO Classes
asked
in
Databases
Feb 5
by
GO Classes
274
views
goclasses2024-mockgate-14
databases
sql
2-marks
3
votes
0
answers
67
GO Classes Test Series 2024 | Mock GATE | Test 14 | Question: 47
A $\text{stable sort}$ preserves the order of values that are equal with respect to the comparison function. We have a list of three-dimensional points $[(7, 1, 8),(3, 5, 7),(6, 1, 4),(6, 5, 9),(0, 2, 5),(9, 0, 9)].$ We sort these in ascending order by the ... $[(9, 0, 9),(6, 1, 4),(7, 1, 8),(0, 2, 5),(3, 5, 7),(6, 5, 9)]$
GO Classes
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in
Algorithms
Feb 5
by
GO Classes
185
views
goclasses2024-mockgate-14
algorithms
sorting
2-marks
4
votes
0
answers
68
GO Classes Test Series 2024 | Mock GATE | Test 14 | Question: 51
Consider the following forwarding table in a router that uses longest prefix matching to forward packets. Assume that 4-bit addressing is used. ... $X=0$ and $Y=00$ $X=01$ and $Y=00$ $X=010$ and $Y=00$ $X=00$ and $Y=0$
GO Classes
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in
Computer Networks
Feb 5
by
GO Classes
322
views
goclasses2024-mockgate-14
computer-networks
ip-packet
multiple-selects
2-marks
4
votes
0
answers
69
GO Classes Test Series 2024 | Mock GATE | Test 14 | Question: 53
The grammar shown below is LL(k) for some value of k. What is the smallest value of k for which this grammar is LL(k)?
GO Classes
asked
in
Compiler Design
Feb 5
by
GO Classes
835
views
goclasses2024-mockgate-14
numerical-answers
compiler-design
parsing
ll-parser
2-marks
3
votes
0
answers
70
GO Classes Test Series 2024 | Mock GATE | Test 14 | Question: 60
The logic circuit above is used to compare two unsigned 2-bit numbers, $X_1 X_0=X$ and $Y_1 Y_0=Y$, where $X_0$ and $Y_0$ are the least significant bits. (A small circle on any line in a logic diagram indicates logical NOT.) Which of the following always makes the output $Z$ have the value 1? $X\gt Y$ $X\lt Y$ $X=Y$ $X \neq Y$
GO Classes
asked
in
Digital Logic
Feb 5
by
GO Classes
288
views
goclasses2024-mockgate-14
digital-logic
combinational-circuit
digital-circuits
2-marks
4
votes
0
answers
71
GO Classes Test Series 2024 | Mock GATE | Test 14 | Question: 65
Which of the following statements are true for every language $\mathrm{L} \subseteq\{0,1\}^*?$ $L^{\star}$ is infinite. $L$ is accepted by some DFA if and only if $L$ is accepted by some NFA. If $\mathrm{L}$ is the ... $\mathrm{L}$ is undecidable. If $\mathrm{L}$ is the union of two decidable languages, then $\mathrm{L}$ is decidable.
GO Classes
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in
Theory of Computation
Feb 5
by
GO Classes
552
views
goclasses2024-mockgate-14
theory-of-computation
decidability
multiple-selects
2-marks
0
votes
0
answers
72
Memory Based GATE DA 2024 | Question: 5
Consider a matrix \(M \in \mathbb{R}^{3 \times 3}\) and let \(U\) be a 2-dimensional subspace such that \(M\) is a projection onto \(U\). Which of the following statements are true? \(M^3 = M\) \(M^2 = M\) The nullspace of \(M\) is 1-dimensional. The nullspace of \(M\) is 2-dimensional.
GO Classes
asked
in
Linear Algebra
Feb 4
by
GO Classes
197
views
gate2024-da-memory-based
goclasses
linear-algebra
vector-space
0
votes
0
answers
73
Memory Based GATE DA 2024 | Question: 11
Consider a dataset with a raw score \(x = 75\), a mean \(\mu = 70\), and a standard deviation \(\sigma = 5\). Calculate the Z-score using the formula \(z = \frac{x - \mu}{\sigma}\).
GO Classes
asked
in
Probability
Feb 4
by
GO Classes
163
views
gate2024-da-memory-based
goclasses
probability
normal-distribution
numerical-answers
0
votes
0
answers
74
Memory Based GATE DA 2024 | Question: 12
Consider the following table: $ \begin{array}{cccc} & A & B & C \\ Person 1 & 10,000 & 20,000 & 20,000 \\ Person 2 & 20,000 & 15,000 & 15,000 \\ & x \% & 15 \% & 15 \% \end{array} $ After a year, if Person 1's mutual fund value is 500 more than Person 2's, determine the value of \(x\).
GO Classes
asked
in
Quantitative Aptitude
Feb 4
by
GO Classes
176
views
gate2024-da-memory-based
goclasses
quantitative-aptitude
percentage
numerical-answers
1
vote
0
answers
75
Memory Based GATE DA 2024 | Question: 15
Consider the joint probability density function given by: $ f(x, y)= \begin{cases} 2xy & \text{if } 0 < x < 2 \text{ and } 0 < y < x \\ 0 & \text{otherwise} \end{cases} $ \noindent Determine the conditional expectation $E(Y | X = 1.5)$.
GO Classes
asked
in
Probability
Feb 4
by
GO Classes
179
views
gate2024-da-memory-based
goclasses
probability
expectation
numerical-answers
0
votes
0
answers
76
Memory Based GATE DA 2024 | Question: 17
Consider the following SQL query: \[ \begin{aligned} &\text{SELECT * FROM Raider, Team} \\ &\text{WHERE Raider.id = Team.id} \\ &\text{AND City = 'Jaipur'} \\ &\text{AND Raid_points \textgreater 200; ... {aligned} \] Determine the number of rows returned by the SQL query, given the conditions specified for the City and Raid points.
GO Classes
asked
in
Databases
Feb 4
by
GO Classes
145
views
gate2024-da-memory-based
goclasses
databases
sql
numerical-answers
0
votes
0
answers
77
Memory Based GATE DA 2024 | Question: 18
Consider a directed acyclic graph (DAG) with vertices labeled as P, Q, R, S, T, U, and V. Which of the following sequences represents a possible topological sort of the graph? PRQVSUT PQRSVUT PQRSTUV PRQSVUT
GO Classes
asked
in
Algorithms
Feb 4
by
GO Classes
119
views
gate2024-da-memory-based
goclasses
algorithms
graph-algorithm
topological-sort
1
vote
0
answers
78
Memory Based GATE DA 2024 | Question: 19
Consider the function \(f(n)\), which represents the maximum number of comparisons in binary search on a sorted array of size \(n\). Which of the following recursive relationships correctly defines \(f(n)\)? \(f(n) = f\left(\lfloor \frac{n}{2} \rfloor\right) ... \rfloor\right)\) \(f(n) = f\left(\lfloor \frac{n}{2} \rfloor\right) + 1\) None of the above
GO Classes
asked
in
Algorithms
Feb 4
by
GO Classes
151
views
gate2024-da-memory-based
goclasses
algorithms
binary-search
recurrence-relation
0
votes
0
answers
79
Memory Based GATE DA 2024 | Question: 20
Consider the following Python code: S[1] = [1] x = [6, 3, 5, 4, 10] for i in range(2, len(x)): S[i] = [1] if x[i - 1]
GO Classes
asked
in
Programming
Feb 4
by
GO Classes
98
views
gate2024-da-memory-based
goclasses
programming
programming-in-python
0
votes
0
answers
80
Memory Based GATE DA 2024 | Question: 21
What does the following Python code do? \begin{verbatim} def fun(D, S_1, S_2): if S_1 < S_2: D[S_1], D[S_2] = D[S_2], D[S_1] fun(D, S_1 + 1, S_2 - 1) \end{verbatim}
GO Classes
asked
in
Programming
Feb 4
by
GO Classes
89
views
gate2024-da-memory-based
goclasses
programming
programming-in-python
0
votes
0
answers
81
Memory Based GATE DA 2024 | Question: 22
Given the array \( [4, 3, 2, 1, 5] \), which of the following sorting algorithms can successfully sort the array in exactly two passes? Bubble Sort Insertion Sort Selection Sort Merge Sort
GO Classes
asked
in
Algorithms
Feb 4
by
GO Classes
138
views
gate2024-da-memory-based
goclasses
algorithms
sorting
0
votes
0
answers
82
Memory Based GATE DA 2024 | Question: 27
Consider performing Depth-First Search (DFS) on an undirected and unweighted graph $\bar{G}$ starting at vertex $S$. For any vertex $u$ in $G$, where $d[u]$ is the length of the shortest path from $S$ to $u$, let $(u \geqslant v)$ be an edge in ... $v$, then in the above DFS, the edge $(u, v)$ becomes: A forward edge A back edge A cross edge A tree edge
GO Classes
asked
in
Algorithms
Feb 4
by
GO Classes
151
views
gate2024-da-memory-based
goclasses
algorithms
graph-algorithm
depth-first-search
1
vote
0
answers
83
Memory Based GATE DA 2024 | Question: 28
Consider a function \(f\) with \(f^1(X^*) = 0\) and \(f^{1l}(X^*) > 0\). Based on these conditions, determine the nature of the critical point \(X^*\) for the function \(f(X)\). \(X^*\) is a local maximum \(X^*\) is a local minimum \(X^*\) is a global maximum \(X^*\) is a global minimum
GO Classes
asked
in
Calculus
Feb 4
by
GO Classes
144
views
gate2024-da-memory-based
goclasses
calculus
maxima-minima
0
votes
0
answers
84
Memory Based GATE DA 2024 | Question: 31
Consider the scenario where there was growth in dairy farms in a city, and coincidentally, there was a mutation in the gene of people in that locality, enabling them to digest milk products. Based on the above paragraph, choose the ... the mutation in the gene of people. Select the most appropriate conclusion that can be drawn from the given information.
GO Classes
asked
in
Verbal Aptitude
Feb 4
by
GO Classes
139
views
gate2024-da-memory-based
goclasses
verbal-aptitude
passage-reading
0
votes
0
answers
85
Memory Based GATE DA 2024 | Question: 32
Consider two admissible heuristic functions, \(h_1\) and \(h_2\). Determine which of the following combinations are admissible: \(\frac{h_1}{h_2}\) \(\left(h_2 > 0\right)\) \\ \(h_1 \cdot \tilde{h}_2\) \\ \(\left| h_1 - h_2 \right|\) \\ \(h_1 + h_2\)
GO Classes
asked
in
Artificial Intelligence
Feb 4
by
GO Classes
155
views
gate2024-da-memory-based
goclasses
artificial-intelligence
0
votes
0
answers
86
Memory Based GATE DA 2024 | Question: 34
BFS DFS question asking the number of nodes expanded BFS = DFS BFS $ DFS None
GO Classes
asked
in
Algorithms
Feb 4
by
GO Classes
110
views
gate2024-da-memory-based
goclasses
algorithms
graph-algorithm
depth-first-search
breadth-first-search
0
votes
0
answers
87
Memory Based GATE DA 2024 | Question: 35
Conditional probability \[ \begin{aligned} & \mathrm{P}(\mathrm{U}, \mathrm{V}, \mathrm{W}, \mathrm{X}, \mathrm{Y}) & = \mathrm{P}(\mathrm{U}) \cdot \mathrm{P}(\mathrm{V}) \cdot \mathrm{P}(\mathrm{W} / \mathrm{U}, \mathrm{V}) \cdot \mathrm{P}(\mathrm{X} / \mathrm{W}) \cdot \mathrm{P}(\mathrm{Y} / \mathrm{W}) \end{aligned} \]
GO Classes
asked
in
Probability
Feb 4
by
GO Classes
129
views
gate2024-da-memory-based
goclasses
probability
conditional-probability
0
votes
0
answers
88
Memory Based GATE DA 2024 | Question: 36
In the context of K-Nearest Neighbors ($\mathrm{KNN}$), what is the minimum odd value of $\mathrm{K}$ such that the diamond ($\diamond$) shaped data point gets classified as ($\square$)?
GO Classes
asked
in
Machine Learning
Feb 4
by
GO Classes
153
views
gate2024-da-memory-based
goclasses
machine-learning
numerical-answers
0
votes
0
answers
89
Memory Based GATE DA 2024 | Question: 37
Consider the vectors: \[ \begin{aligned} & X_1=\begin{bmatrix} 1 \\ 0 \end{bmatrix}, \quad X_2=\begin{bmatrix} 0 \\ 1 \end{bmatrix}, \quad X_3=\begin{bmatrix} 0 \\ -1 \end{bmatrix}, \\ & X_4=\begin{bmatrix} -1 \\ 0 \end{bmatrix}, \ ... vectors? Select the correct option: $X_1, X_2, X_5$ $X_1, X_2, X_3, X_4, X_5, X_6$ $X_3, X_4$ $X_1, X_2, X_3, X_4$
GO Classes
asked
in
Machine Learning
Feb 4
by
GO Classes
98
views
gate2024-da-memory-based
goclasses
machine-learning
0
votes
0
answers
90
Memory Based GATE DA 2024 | Question: 38
Consider a scenario with \(k\)-binary attributes for a two-class classification task using Naive Bayes. What is the total number of parameters needed? Choose the correct option: \(2k + 1\) \(2^k + 1\) \(2^{k+1} + 1\) \(k^2 + 1\)
GO Classes
asked
in
Machine Learning
Feb 4
by
GO Classes
128
views
gate2024-da-memory-based
goclasses
machine-learning
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