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Hot questions in Discrete Mathematics
111
votes
9
answers
1
GATE CSE 2012 | Question: 38
Let $G$ be a complete undirected graph on $6$ vertices. If vertices of $G$ are labeled, then the number of distinct cycles of length $4$ in $G$ is equal to $15$ $30$ $90$ $360$
gatecse
asked
in
Graph Theory
Sep 12, 2014
by
gatecse
34.5k
views
gatecse-2012
graph-theory
normal
marks-to-all
counting
13
votes
3
answers
2
relation
Number of relations $S$ over set $\{0,1,2,3 \}$ such that $(x,y) \in S \Rightarrow x = y$
Lakshman Bhaiya
asked
in
Set Theory & Algebra
Dec 27, 2017
by
Lakshman Bhaiya
44.5k
views
set-theory&algebra
relations
76
votes
12
answers
3
GATE CSE 1994 | Question: 1.6, ISRO2008-29
The number of distinct simple graphs with up to three nodes is $15$ $10$ $7$ $9$
Kathleen
asked
in
Graph Theory
Oct 4, 2014
by
Kathleen
34.3k
views
gate1994
graph-theory
graph-connectivity
combinatory
normal
isro2008
counting
100
votes
10
answers
4
GATE CSE 2014 Set 1 | Question: 51
Consider an undirected graph $G$ where self-loops are not allowed. The vertex set of $G$ is $\{(i,j) \mid1 \leq i \leq 12, 1 \leq j \leq 12\}$. There is an edge between $(a,b)$ and $(c,d)$ if $|a-c| \leq 1$ and $|b-d| \leq 1$. The number of edges in this graph is______.
go_editor
asked
in
Graph Theory
Sep 28, 2014
by
go_editor
26.5k
views
gatecse-2014-set1
graph-theory
numerical-answers
normal
graph-connectivity
38
votes
9
answers
5
GATE CSE 2014 Set 2 | Question: 3
The maximum number of edges in a bipartite graph on $12$ vertices is____
go_editor
asked
in
Graph Theory
Sep 28, 2014
by
go_editor
26.8k
views
gatecse-2014-set2
graph-theory
graph-connectivity
numerical-answers
normal
100
votes
11
answers
6
GATE CSE 2016 Set 2 | Question: 01
Consider the following expressions: $false$ $Q$ $true$ $P\vee Q$ $\neg Q\vee P$ The number of expressions given above that are logically implied by $P \wedge (P \Rightarrow Q)$ is ___________.
Akash Kanase
asked
in
Mathematical Logic
Feb 12, 2016
by
Akash Kanase
19.5k
views
gatecse-2016-set2
mathematical-logic
normal
numerical-answers
propositional-logic
91
votes
9
answers
7
GATE CSE 2016 Set 1 | Question: 28
A function $f: \Bbb{N^+} \rightarrow \Bbb{N^+}$ , defined on the set of positive integers $\Bbb{N^+}$, satisfies the following properties: $f(n)=f(n/2)$ if $n$ is even $f(n)=f(n+5)$ if $n$ is odd Let $R=\{ i \mid \exists{j} : f(j)=i \}$ be the set of distinct values that $f$ takes. The maximum possible size of $R$ is ___________.
Sandeep Singh
asked
in
Set Theory & Algebra
Feb 12, 2016
by
Sandeep Singh
21.2k
views
gatecse-2016-set1
set-theory&algebra
functions
normal
numerical-answers
32
votes
14
answers
8
GATE CSE 2019 | Question: 12
Let $G$ be an undirected complete graph on $n$ vertices, where $n > 2$. Then, the number of different Hamiltonian cycles in $G$ is equal to $n!$ $(n-1)!$ $1$ $\frac{(n-1)!}{2}$
Arjun
asked
in
Graph Theory
Feb 7, 2019
by
Arjun
20.9k
views
gatecse-2019
engineering-mathematics
discrete-mathematics
graph-theory
graph-connectivity
1-mark
57
votes
17
answers
9
GATE CSE 2016 Set 1 | Question: 26
The coefficient of $x^{12}$ in $\left(x^{3}+x^{4}+x^{5}+x^{6}+\dots \right)^{3}$ is ___________.
Sandeep Singh
asked
in
Combinatory
Feb 12, 2016
by
Sandeep Singh
25.5k
views
gatecse-2016-set1
combinatory
generating-functions
normal
numerical-answers
19
votes
18
answers
10
GATE CSE 2019 | Question: 21
The value of $3^{51} \text{ mod } 5$ is _____
Arjun
asked
in
Combinatory
Feb 7, 2019
by
Arjun
17.9k
views
gatecse-2019
numerical-answers
combinatory
modular-arithmetic
1-mark
33
votes
6
answers
11
GATE CSE 1996 | Question: 1.4
Which of the following statements is FALSE? The set of rational numbers is an abelian group under addition The set of integers in an abelian group under addition The set of rational numbers form an abelian group under multiplication The set of real numbers excluding zero is an abelian group under multiplication
Kathleen
asked
in
Set Theory & Algebra
Oct 9, 2014
by
Kathleen
22.8k
views
gate1996
set-theory&algebra
group-theory
normal
54
votes
6
answers
12
GATE CSE 1997 | Question: 6.3
The number of equivalence relations of the set $\{1,2,3,4\}$ is $15$ $16$ $24$ $4$
Kathleen
asked
in
Set Theory & Algebra
Sep 29, 2014
by
Kathleen
21.1k
views
gate1997
set-theory&algebra
relations
normal
32
votes
9
answers
13
GATE CSE 2015 Set 1 | Question: 54
Let G be a connected planar graph with 10 vertices. If the number of edges on each face is three, then the number of edges in G is_______________.
makhdoom ghaya
asked
in
Graph Theory
Feb 14, 2015
by
makhdoom ghaya
24.3k
views
gatecse-2015-set1
graph-theory
graph-connectivity
normal
graph-planarity
numerical-answers
89
votes
6
answers
14
GATE CSE 2006 | Question: 72
The $2^n$ vertices of a graph $G$ corresponds to all subsets of a set of size $n$, for $n \geq 6$. Two vertices of $G$ are adjacent if and only if the corresponding sets intersect in exactly two elements. The maximum degree of a vertex in $G$ is: $\binom{\frac{n}{2}}{2}.2^{\frac{n}{2}}$ $2^{n-2}$ $2^{n-3}\times 3$ $2^{n-1}$
go_editor
asked
in
Graph Theory
Apr 24, 2016
by
go_editor
17.6k
views
gatecse-2006
graph-theory
normal
degree-of-graph
91
votes
12
answers
15
GATE CSE 2015 Set 3 | Question: 24
In a room there are only two types of people, namely $\text{Type 1}$ and $\text{Type 2}$. $\text{Type 1}$ people always tell the truth and $\text{Type 2}$ people always lie. You give a fair coin to a person in that room, without knowing which type ... person is of $\text{Type 2}$, then the result is tail If the person is of $\text{Type 1}$, then the result is tail
go_editor
asked
in
Mathematical Logic
Feb 14, 2015
by
go_editor
17.4k
views
gatecse-2015-set3
mathematical-logic
difficult
logical-reasoning
87
votes
5
answers
16
GATE CSE 2015 Set 2 | Question: 55
Which one of the following well-formed formulae is a tautology? $\forall x \, \exists y \, R(x,y) \, \leftrightarrow \, \exists y \, \forall x \, R(x, y)$ ... $\forall x \, \forall y \, P(x,y) \, \rightarrow \, \forall x \, \forall y \, P(y, x)$
go_editor
asked
in
Mathematical Logic
Feb 13, 2015
by
go_editor
20.4k
views
gatecse-2015-set2
mathematical-logic
normal
first-order-logic
51
votes
15
answers
17
GATE CSE 2015 Set 2 | Question: 40
The number of onto functions (surjective functions) from set $X = \{1, 2, 3, 4\}$ to set $Y=\{a,b,c\}$ is ______.
go_editor
asked
in
Set Theory & Algebra
Feb 13, 2015
by
go_editor
19.1k
views
gatecse-2015-set2
set-theory&algebra
functions
normal
numerical-answers
111
votes
6
answers
18
GATE CSE 2003 | Question: 33
Consider the following formula and its two interpretations \(I_1\) and \(I_2\). \(\alpha: (\forall x)\left[P_x \Leftrightarrow (\forall y)\left[Q_{xy} \Leftrightarrow \neg Q_{yy} \right]\right] \Rightarrow (\forall x)\left[\neg P_x\right]\) \(I_1\) : Domain: ... I_1\) does not Neither \(I_1\) nor \(I_2\) satisfies \(\alpha\) Both \(I_1\) and \(I_2\) satisfies \(\alpha\)
Kathleen
asked
in
Mathematical Logic
Sep 16, 2014
by
Kathleen
15.5k
views
gatecse-2003
mathematical-logic
difficult
first-order-logic
71
votes
7
answers
19
GATE CSE 2017 Set 1 | Question: 02
Consider the first-order logic sentence $F:\forall x(\exists yR(x,y))$. Assuming non-empty logical domains, which of the sentences below are implied by $F$? $\exists y(\exists xR(x,y))$ $\exists y(\forall xR(x,y))$ $\forall y(\exists xR(x,y))$ $¬\exists x(\forall y¬R(x,y))$ IV only I and IV only II only II and III only
khushtak
asked
in
Mathematical Logic
Feb 14, 2017
by
khushtak
17.0k
views
gatecse-2017-set1
mathematical-logic
first-order-logic
41
votes
7
answers
20
GATE CSE 2020 | Question: 39
Which one of the following predicate formulae is NOT logically valid? Note that $W$ is a predicate formula without any free occurrence of $x$. $\forall x (p(x) \vee W) \equiv \forall x \: ( px) \vee W$ ... $\exists x(p(x) \rightarrow W) \equiv \forall x \: p(x) \rightarrow W$
Arjun
asked
in
Mathematical Logic
Feb 12, 2020
by
Arjun
16.7k
views
gatecse-2020
first-order-logic
mathematical-logic
2-marks
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