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Recent questions and answers in Discrete Mathematics
0
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1
answer
1
UGCNETDec2007II: 2
The number of edges in a complete graph with ‘n’ vertices is equal to : $n(n1)$ $\large\frac{n(n1)}{2}$ $n^2$ $2n1$
answered
3 days
ago
in
Graph Theory
by
chirudeepnamini
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5.3k
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19
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ugcnetdec2007ii
0
votes
1
answer
2
UGCNETDec2006II: 3
The number of edges in a complete graph with N vertices is equal to: $N (N−1)$ $2N−1$ $N−1$ $N(N−1)/2$
answered
5 days
ago
in
Graph Theory
by
Sanjay Sharma
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49.6k
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13
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ugcnetdec2006ii
0
votes
1
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3
UGCNETDec2004II: 4
The following lists are the degrees of all the vertices of a graph : $1,2,3,4,5$ $3,4,5,6,7$ $1, 4, 5, 8, 6$ $3,4,5,6$ (i) and (ii) (iii) and (iv) (iii) and (ii) (ii) and (iv)
answered
5 days
ago
in
Graph Theory
by
Divya Devi
(
23
points)

16
views
ugcnetdec2004ii
+10
votes
5
answers
4
GATE19871xxii
The equation $7x^{7}+14x^{6}+12x^{5}+3x^{4}+12x^{3}+10x^{2}+5x+7=0$ has All complex roots At least one real root Four pairs of imaginary roots None of the above
answered
5 days
ago
in
Set Theory & Algebra
by
SatyamK
(
229
points)

561
views
gate1987
polynomials
0
votes
0
answers
5
UGCNETDec2006II: 2
The proposition ~ q ∨ p is equivalent to :
asked
5 days
ago
in
Mathematical Logic
by
jothee
Veteran
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107k
points)

21
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ugcnetdec2006ii
0
votes
1
answer
6
UGCNETDec2004II: 2
If $f (x)=x+1\:\text{and}\:g(x)=x+3$ then $f 0 f 0 f 0 f$ is : $g$ $g+1$ $g^4$ None of these
answered
6 days
ago
in
Set Theory & Algebra
by
Shobhit Joshi
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5.5k
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11
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ugcnetdec2004ii
0
votes
0
answers
7
UGCNETDec2004II: 23
Weighted graph : Is a bidirectional graph. Is directed graph. Is graph in which number associated with arc. Eliminates table method.
asked
6 days
ago
in
Graph Theory
by
jothee
Veteran
(
107k
points)

5
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ugcnetdec2004ii
0
votes
2
answers
8
NIELIT ScientistB Dec 2017_44
On a set A = {a, b, c, d} a binary operation * is defined as given in the following table. * a b c d a b c d a c b d c b d a b d a c d a c b The relation is : (A) Commutative but not associative (B) Neither commutative nor associative (C) Both commutative and associative (D) Associative but not commutative
answered
Mar 19
in
Set Theory & Algebra
by
topper98
Junior
(
589
points)

152
views
0
votes
1
answer
9
NIELIT ScientistB Dec 2017_51
Let $u$ and $v$ be two vectors in R2 whose Euclidean norms satisfy $u=2v$. What is the value of $\alpha$ such that $w=u+\alpha v$ bisects the angle between $u$ and $v$ ? (A) 2 (B) 1 (C) 1/2 (D) 2
answered
Mar 19
in
Set Theory & Algebra
by
topper98
Junior
(
589
points)

107
views
0
votes
2
answers
10
NIELIT ScientistB Dec 2017_24
Using bisection method, one root of X4X1 lies between 1 and 2. After second iteration the root may lie in interval : (A) (1.25, 1.5) (B) (1, 1.25) (C) (1, 1.5) (D) None of the options
answered
Mar 19
in
Set Theory & Algebra
by
topper98
Junior
(
589
points)

205
views
0
votes
2
answers
11
NIELIT July 2017_75
Choose the most appropriate definition of plane graph A) A simple graph which is isomorphic to Hamiltonian graph B) A graph drawn in a plane such away that if the vertex set of graph can be partitioned into two non  empty disjoint subset X and Y in such a way ... A graph drawn in a plane in such a way that any pair of edges meet only at their end vertices D) None of the option
answered
Mar 19
in
Graph Theory
by
topper98
Junior
(
589
points)

340
views
+3
votes
5
answers
12
NIELIT July 2017_73
For the graph shown, which of the following paths is a Hamilton circuit ? A) ABCDCFDEFAEA B) AEDCBAF C) AEFDCBA D) AFCDEBA
answered
Mar 19
in
Graph Theory
by
topper98
Junior
(
589
points)

628
views
0
votes
2
answers
13
NIELIT July 2017_72
The following graph has no Euler circuit because A) It has 7 vertices B) It is evenvalent (all vertices have even valence) C) It is not connected D) It does not have an Euler circuit
answered
Mar 19
in
Graph Theory
by
topper98
Junior
(
589
points)

361
views
0
votes
2
answers
14
NIELIT July 2017_71
Consider the following graph L and find the bridges, if any A) No bridge B) {d, e} C) {c, d} D) {c, d} and {c, f}
answered
Mar 19
in
Graph Theory
by
topper98
Junior
(
589
points)

395
views
+1
vote
1
answer
15
ISI2016PCBCS8
Consider all possible trees with $n$ nodes. Let $k$ be the number of nodes with degree greater than 1 in a given tree. What is the maximum possible value of $k$? Justify your answer. Consider $2n$ committees, each having at least $2n$ persons, formed from a group of $4n$ persons. Prove that there exists at least one person who belongs to at least $n$ committees.
answered
Mar 18
in
Combinatory
by
Falahamin
(
21
points)

46
views
isi2016pcbcs
permutationandcombination
descriptive
0
votes
1
answer
16
ISI2016MMA25
A integer is said to be a $\textbf{palindrome}$ if it reads the same forward or backward. For example, the integer $14541$ is a $5$digit palindrome and $12345$ is not a palindrome. How many $8$digit palindromes are prime? $0$ $1$ $11$ $19$
answered
Mar 18
in
Combinatory
by
Falahamin
(
21
points)

24
views
isi2016mmamma
permutationandcombination
+3
votes
3
answers
17
GATE2020CS45
For $n>2$, let $a \in \{0,1\}^n$ be a nonzero vector. Suppose that $x$ is chosen uniformly at random from $\{0,1\}^n$. Then, the probability that $\displaystyle{} \Sigma_{i=1}^n a_i x_i$ is an odd number is______________
answered
Mar 17
in
Mathematical Logic
by
felics moses 1
(
119
points)

1k
views
gate2020cs
numericalanswers
+13
votes
6
answers
18
GATE201938
Let $G$ be any connected, weighted, undirected graph. $G$ has a unique minimum spanning tree, if no two edges of $G$ have the same weight. $G$ has a unique minimum spanning tree, if, for every cut of $G$, there is a unique minimumweight edge crossing the cut. Which of the following statements is/are TRUE? I only II only Both I and II Neither I nor II
answered
Mar 17
in
Graph Theory
by
immanujs
Active
(
3.3k
points)

4.7k
views
gate2019
engineeringmathematics
discretemathematics
graphtheory
graphconnectivity
+4
votes
6
answers
19
GATE2020CS42
The number of permutations of the characters in LILAC so that no character appears in its original position, if the two L’s are indistinguishable, is ______.
answered
Mar 15
in
Combinatory
by
felics moses 1
(
119
points)

1.5k
views
gate2020cs
numericalanswers
engineeringmathematics
0
votes
1
answer
20
JEST 2020
X AND Y is an arbitrary sets, F: $X\rightarrow Y$ show that a and b are equivalent F is oneone For all set Z and function g1: $Z\rightarrow X$ and g2: $Z\rightarrow X$, if $g1 \neq g2$ implies $f \bigcirc g1 \neq f \bigcirc g2$ Where $\bigcirc$ is a fucntion composition.
answered
Mar 12
in
Set Theory & Algebra
by
commenter commenter
Active
(
1.6k
points)

150
views
jest
functions
sets
+20
votes
4
answers
21
GATE19961.4
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
answered
Mar 11
in
Set Theory & Algebra
by
vivekgatecs2020
(
137
points)

2.2k
views
gate1996
settheory&algebra
grouptheory
normal
+1
vote
2
answers
22
ISI2017MMA26
Let $n$ be the number of ways in which $5$ men and $7$ women can stand in a queue such that all the women stand consecutively. Let $m$ be the number of ways in which the same $12$ persons can stand in a queue such that exactly $6$ women stand consecutively. Then the value of $\frac{m}{n}$ is $5$ $7$ $\frac{5}{7}$ $\frac{7}{5}$
answered
Mar 9
in
Combinatory
by
kraken_wizard
(
41
points)

93
views
isi2017mma
engineeringmathematics
discretemathematics
permutationandcombination
0
votes
3
answers
23
NIELIT ScientistB Dec 2017_56
Let G be a simple undirected graph on $n=3x$ vertices ($x>=1$) with chromatic number 3, then maximum number of edges in G is : (A) $n(n1)/2$ (B) $n^{n2}$ (C) $nx$ (D) $n$
answered
Mar 8
in
Graph Theory
by
vivekgatecs2020
(
137
points)

460
views
+28
votes
3
answers
24
GATE20021.4
The minimum number of colours required to colour the vertices of a cycle with $n$ nodes in such a way that no two adjacent nodes have the same colour is $2$ $3$ $4$ $n2 \left \lfloor \frac{n}{2} \right \rfloor+2$
answered
Mar 7
in
Graph Theory
by
vivekgatecs2020
(
137
points)

3.1k
views
gate2002
graphtheory
graphcoloring
normal
+33
votes
4
answers
25
GATE20093
Which one of the following is TRUE for any simple connected undirected graph with more than $2$ vertices? No two vertices have the same degree. At least two vertices have the same degree. At least three vertices have the same degree. All vertices have the same degree.
answered
Mar 7
in
Graph Theory
by
vivekgatecs2020
(
137
points)

2.7k
views
gate2009
graphtheory
normal
degreeofgraph
+2
votes
2
answers
26
Let a relation R be defined on the set of all real numbers by a R b <=> 1 + ab > 0 thus R is ?
answered
Mar 3
in
Set Theory & Algebra
by
MKraza
(
11
points)

7.4k
views
+2
votes
2
answers
27
Zeal Test Series 2019: Graph Theory  Graph Coloring
what is index ?
answered
Mar 2
in
Graph Theory
by
Parth Narodia
(
23
points)

167
views
zeal
graphtheory
graphcoloring
zeal2019
+25
votes
6
answers
28
GATE20057
The time complexity of computing the transitive closure of a binary relation on a set of $n$ elements is known to be: $O(n)$ $O(n \log n)$ $O \left( n^{\frac{3}{2}} \right)$ $O\left(n^3\right)$
answered
Mar 2
in
Set Theory & Algebra
by
Pratyush Priyam Kuan
Active
(
1.1k
points)

6.9k
views
gate2005
settheory&algebra
normal
relations
+14
votes
3
answers
29
GATE20023
Let $A$ be a set of $n(>0)$ elements. Let $N_r$ be the number of binary relations on $A$ and let $N_f$ be the number of functions from $A$ to $A$ Give the expression for $N_r,$ in terms of $n.$ Give the expression for $N_f,$ terms of $n.$ Which is larger for all possible $n,N_r$ or $N_f$
answered
Mar 2
in
Set Theory & Algebra
by
Pratyush Priyam Kuan
Active
(
1.1k
points)

932
views
gate2002
settheory&algebra
normal
descriptive
relations
+25
votes
4
answers
30
GATE20002.5
A relation $R$ is defined on the set of integers as $xRy$ iff $(x + y)$ is even. Which of the following statements is true? $R$ is not an equivalence relation $R$ is an equivalence relation having 1 equivalence class $R$ is an equivalence relation having 2 equivalence classes $R$ is an equivalence relation having 3 equivalence classes
answered
Mar 2
in
Set Theory & Algebra
by
Pratyush Priyam Kuan
Active
(
1.1k
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3.4k
views
gate2000
settheory&algebra
relations
normal
+12
votes
4
answers
31
GATE19993
Mr. X claims the following: If a relation R is both symmetric and transitive, then R is reflexive. For this, Mr. X offers the following proof: “From xRy, using symmetry we get yRx. Now because R is transitive xRy and yRx together imply xRx. Therefore, R is reflexive”. Give an example of a relation R which is symmetric and transitive but not reflexive.
answered
Mar 2
in
Set Theory & Algebra
by
Pratyush Priyam Kuan
Active
(
1.1k
points)

979
views
gate1999
settheory&algebra
relations
normal
descriptive
+12
votes
3
answers
32
GATE19981.6
Suppose $A$ is a finite set with $n$ elements. The number of elements in the largest equivalence relation of A is $n$ $n^2$ $1$ $n+1$
answered
Mar 2
in
Set Theory & Algebra
by
Pratyush Priyam Kuan
Active
(
1.1k
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3.1k
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gate1998
settheory&algebra
relations
easy
0
votes
1
answer
33
website
There is 4 coins 1 paisa, 5 paise, 10 paise, 25 paise using these coins we have to make 50 paisa how many combination can we make ?
answered
Mar 1
in
Combinatory
by
smsubham
Boss
(
16k
points)

46
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permutationandcombination
+1
vote
2
answers
34
MadeEasy Test Series: Mathematical Logic  First Order Logic
Pardon for the screenshot though. No idea of latex.
answered
Mar 1
in
Mathematical Logic
by
Madhab
Loyal
(
6.2k
points)

204
views
madeeasytestseries
firstorderlogic
mathematicallogic
+3
votes
2
answers
35
Rosen 7e Exercise6.5 question 45.b page 433
How many ways can n books be placed on k distinguishable shelves if no two books are the same, and the positions of the books on the shelves matter?
answered
Mar 1
in
Combinatory
by
smsubham
Boss
(
16k
points)

213
views
kennethrosen
discretemathematics
permutationandcombination
+25
votes
5
answers
36
GATE2017221
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 ______
answered
Mar 1
in
Set Theory & Algebra
by
Pratyush Priyam Kuan
Active
(
1.1k
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4.3k
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gate20172
settheory&algebra
lattice
numericalanswers
normal
+3
votes
2
answers
37
ISRO202073
Given that $B(a)$ means “$a$ is a bear” $F(a)$ means “$a$ is a fish” and $E(a,b)$ means “$a $ eats $b$” Then what is the best meaning of $\forall x [F(x) \to \forall y(E(y,x)\rightarrow b(y))]$ Every fish is eaten by some bear Bears eat only fish Every bear eats fish Only bears eat fish
answered
Mar 1
in
Mathematical Logic
by
Madhab
Loyal
(
6.2k
points)

369
views
isro2020
discretemathematics
mathematicallogic
propositionallogic
normal
+2
votes
2
answers
38
GATE19882xviii
Show that if $G$ is a group such that $(a, b)^2 = a^2.b^2$ for all $a, b$ belonging to $G$, then $G$ is an abelian.
answered
Feb 29
in
Set Theory & Algebra
by
Pratyush Priyam Kuan
Active
(
1.1k
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291
views
gate1988
descriptive
grouptheory
+11
votes
4
answers
39
TIFR2013B16
Consider a function $T_{k, n}: \left\{0, 1\right\}^{n}\rightarrow \left\{0, 1\right\}$ which returns $1$ if at least $k$ of its $n$ inputs are $1$. Formally, $T_{k, n}(x)=1$ if $\sum ^{n}_{1} x_{i}\geq k$. Let $y \in \left\{0, 1\right\}^{n}$ be such that $y$ ... $y_{i}$ is omitted) is equivalent to $T_{k1}, n(y)$ $T_{k, n}(y)$ $y_{i}$ $\neg y_{i}$ None of the above.
answered
Feb 29
in
Set Theory & Algebra
by
Pratyush Priyam Kuan
Active
(
1.1k
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465
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tifr2013
settheory&algebra
functions
+13
votes
3
answers
40
TIFR2012B1
For $x, y\in \left\{0, 1\right\}^{n}$, let $x ⊕ y$ be the element of $\left\{0, 1\right\}^{n}$ obtained by the componentwise exclusiveor of $x$ and $y$. A Boolean function $F:\left\{0, 1\right\}^{n}\rightarrow\left\{0, 1\right\}$ is said to be linear if $F(x ⊕ y)= F(x) ⊕ F(y)$ ... from $\left\{0, 1\right\}^{n}$ to $\left\{0, 1\right\}$ is. $2^{2n}$ $2^{n+1}$ $2^{n1}+1$ $n!$ $2^{n}$
answered
Feb 29
in
Set Theory & Algebra
by
Pratyush Priyam Kuan
Active
(
1.1k
points)

638
views
tifr2012
settheory&algebra
functions
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