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Highest voted questions in Discrete Mathematics
38
votes
2
answers
151
GATE CSE 2015 Set 2 | Question: 16
Let $R$ be the relation on the set of positive integers such that $aRb$ and only if $a$ and $b$ are distinct and let have a common divisor other than $1.$ Which one of the following statements about $R$ is true? $R$ is ... but not symmetric not transitive $R$ is transitive but not reflexive and not symmetric $R$ is symmetric but not reflexive and not transitive
go_editor
asked
in
Set Theory & Algebra
Feb 12, 2015
by
go_editor
7.6k
views
gatecse-2015-set2
set-theory&algebra
relations
normal
38
votes
3
answers
152
GATE IT 2008 | Question: 25
In how many ways can $b$ blue balls and $r$ red balls be distributed in $n$ distinct boxes? $\frac{(n+b-1)!\,(n+r-1)!}{(n-1)!\,b!\,(n-1)!\,r!}$ $\frac{(n+(b+r)-1)!}{(n-1)!\,(n-1)!\,(b+r)!}$ $\frac{n!}{b!\,r!}$ $\frac{(n + (b + r) - 1)!} {n!\,(b + r - 1)}$
Ishrat Jahan
asked
in
Combinatory
Oct 27, 2014
by
Ishrat Jahan
8.3k
views
gateit-2008
combinatory
normal
38
votes
9
answers
153
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
26.9k
views
gatecse-2014-set2
graph-theory
graph-connectivity
numerical-answers
normal
38
votes
7
answers
154
GATE CSE 1999 | Question: 2.2
Two girls have picked $10$ roses, $15$ sunflowers and $15$ daffodils. What is the number of ways they can divide the flowers among themselves? $1638$ $2100$ $2640$ None of the above
Kathleen
asked
in
Combinatory
Sep 23, 2014
by
Kathleen
12.0k
views
gate1999
combinatory
normal
38
votes
4
answers
155
GATE CSE 2005 | Question: 11
Let $G$ be a simple graph with $20$ vertices and $100$ edges. The size of the minimum vertex cover of G is $8$. Then, the size of the maximum independent set of $G$ is: $12$ $8$ less than $8$ more than $12$
gatecse
asked
in
Graph Theory
Sep 21, 2014
by
gatecse
11.5k
views
gatecse-2005
graph-theory
normal
graph-connectivity
38
votes
9
answers
156
GATE CSE 2001 | Question: 2.1
How many $4$-digit even numbers have all $4$ digits distinct? $2240$ $2296$ $2620$ $4536$
Kathleen
asked
in
Combinatory
Sep 14, 2014
by
Kathleen
12.4k
views
gatecse-2001
combinatory
normal
37
votes
9
answers
157
GATE CSE 2019 | Question: 10
Let $G$ be an arbitrary group. Consider the following relations on $G$: $R_1: \forall a , b \in G, \: a R_1 b \text{ if and only if } \exists g \in G \text{ such that } a = g^{-1}bg$ ... $R_1$ and $R_2$ $R_1$ only $R_2$ only Neither $R_1$ nor $R_2$
Arjun
asked
in
Set Theory & Algebra
Feb 7, 2019
by
Arjun
17.1k
views
gatecse-2019
engineering-mathematics
discrete-mathematics
set-theory&algebra
group-theory
1-mark
37
votes
4
answers
158
TIFR CSE 2017 | Part B | Question: 1
A vertex colouring with three colours of a graph $G=(V, E)$ is a mapping $c: V \rightarrow \{R, G, B\}$ so that adjacent vertices receive distinct colours. Consider the following undirected graph. How many vertex colouring with three colours does this graph have? $3^9$ $6^3$ $3 \times 2^8$ $27$ $24$
go_editor
asked
in
Graph Theory
Dec 23, 2016
by
go_editor
3.9k
views
tifr2017
graph-theory
graph-coloring
37
votes
5
answers
159
GATE CSE 1989 | Question: 4-i
How many substrings (of all lengths inclusive) can be formed from a character string of length $n$? Assume all characters to be distinct, prove your answer.
makhdoom ghaya
asked
in
Combinatory
Nov 29, 2016
by
makhdoom ghaya
6.8k
views
gate1989
descriptive
combinatory
normal
proof
37
votes
6
answers
160
TIFR CSE 2010 | Part B | Question: 36
In a directed graph, every vertex has exactly seven edges coming in. What can one always say about the number of edges going out of its vertices? Exactly seven edges leave every vertex. Exactly seven edges leave some vertex. Some vertex has at least seven edges leaving it. The number of edges coming out of vertex is odd. None of the above.
makhdoom ghaya
asked
in
Graph Theory
Oct 10, 2015
by
makhdoom ghaya
5.7k
views
tifr2010
graph-theory
degree-of-graph
37
votes
8
answers
161
GATE IT 2005 | Question: 31
Let $f$ be a function from a set $A$ to a set $B$, $g$ a function from $B$ to $C$, and $h$ a function from $A$ to $C$, such that $h(a) = g(f(a))$ for all $a ∈ A.$ Which of the following statements is always true for all such functions $f$ and $g$? ... is onto $h$ is onto $\implies$ $f$ is onto $h$ is onto $\implies$ $g$ is onto $h$ is onto $\implies$ $f$ and $g$ are onto
Ishrat Jahan
asked
in
Set Theory & Algebra
Nov 3, 2014
by
Ishrat Jahan
8.8k
views
gateit-2005
set-theory&algebra
functions
normal
37
votes
3
answers
162
GATE IT 2004 | Question: 4
Let $R_{1}$ be a relation from $A = \left \{ 1,3,5,7 \right \}$ to $B = \left \{ 2,4,6,8 \right \}$ and $R_{2}$ be another relation from $B$ to $C = \{1, 2, 3, 4\}$ as defined below: An element $x$ in $A$ is related to an element $y$ in $B$ (under $R_{1}$) if $x + y$ is ... $R_{1}R_{2} = \{(3, 2), (3, 4), (5, 1), (5, 3), (7, 1)\} $
Ishrat Jahan
asked
in
Set Theory & Algebra
Nov 1, 2014
by
Ishrat Jahan
10.1k
views
gateit-2004
set-theory&algebra
relations
normal
37
votes
7
answers
163
GATE IT 2006 | Question: 11
If all the edge weights of an undirected graph are positive, then any subset of edges that connects all the vertices and has minimum total weight is a Hamiltonian cycle grid hypercube tree
Ishrat Jahan
asked
in
Graph Theory
Oct 31, 2014
by
Ishrat Jahan
8.7k
views
gateit-2006
graph-theory
graph-connectivity
normal
37
votes
11
answers
164
GATE CSE 2014 Set 3 | Question: 53
The CORRECT formula for the sentence, "not all Rainy days are Cold" is $\forall d (\text{Rainy}(d) \wedge \text{~Cold}(d))$ $\forall d ( \text{~Rainy}(d) \to \text{Cold}(d))$ $\exists d(\text{~Rainy}(d) \to \text{Cold}(d))$ $\exists d(\text{Rainy}(d) \wedge \text{~Cold}(d))$
go_editor
asked
in
Mathematical Logic
Sep 28, 2014
by
go_editor
7.7k
views
gatecse-2014-set3
mathematical-logic
easy
first-order-logic
37
votes
7
answers
165
GATE CSE 2004 | Question: 77
The minimum number of colours required to colour the following graph, such that no two adjacent vertices are assigned the same color, is $2$ $3$ $4$ $5$
Kathleen
asked
in
Graph Theory
Sep 18, 2014
by
Kathleen
12.5k
views
gatecse-2004
graph-theory
graph-coloring
easy
37
votes
8
answers
166
GATE CSE 2006 | Question: 28
A logical binary relation $\odot$ ... $(\sim A\odot B)$ $\sim(A \odot \sim B)$ $\sim(\sim A\odot\sim B)$ $\sim(\sim A\odot B)$
Rucha Shelke
asked
in
Set Theory & Algebra
Sep 18, 2014
by
Rucha Shelke
5.7k
views
gatecse-2006
set-theory&algebra
binary-operation
37
votes
6
answers
167
GATE CSE 2014 Set 1 | Question: 1
Consider the statement "Not all that glitters is gold Predicate glitters$(x)$ is true if $x$ glitters and predicate gold$(x)$ is true if $x$ ... $\exists x: \text{glitters}(x)\wedge \neg \text{gold}(x)$
gatecse
asked
in
Mathematical Logic
Sep 15, 2014
by
gatecse
6.5k
views
gatecse-2014-set1
mathematical-logic
first-order-logic
37
votes
4
answers
168
GATE CSE 2000 | Question: 2.4
A polynomial $p(x)$ satisfies the following: $p(1) = p(3) = p(5) = 1$ $p(2) = p(4) = -1$ The minimum degree of such a polynomial is $1$ $2$ $3$ $4$
Kathleen
asked
in
Set Theory & Algebra
Sep 14, 2014
by
Kathleen
7.6k
views
gatecse-2000
set-theory&algebra
normal
polynomials
36
votes
6
answers
169
GATE CSE 2017 Set 2 | Question: 21
Consider the set $X=\{a, b, c, d, e\}$ under partial ordering $R=\{(a,a), (a, b), (a, c), (a, d), (a, e), (b, b), (b, c), (b, e), (c, c), (c, e), (d, d), (d, e), (e, e) \}$ The Hasse diagram of the partial order $(X, R)$ is shown below. The minimum number of ordered pairs that need to be added to $R$ to make $(X, R)$ a lattice is ______
khushtak
asked
in
Set Theory & Algebra
Feb 14, 2017
by
khushtak
11.6k
views
gatecse-2017-set2
set-theory&algebra
lattice
numerical-answers
normal
36
votes
8
answers
170
GATE CSE 1987 | Question: 10b
What is the generating function $G(z)$ for the sequence of Fibonacci numbers?
makhdoom ghaya
asked
in
Combinatory
Nov 14, 2016
by
makhdoom ghaya
9.7k
views
gate1987
combinatory
generating-functions
descriptive
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