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1
UGCNETDec2007II: 2
The number of edges in a complete graph with ‘n’ vertices is equal to : $n(n1)$ $\large\frac{n(n1)}{2}$ $n^2$ $2n1$
asked
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Graph Theory
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jothee
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106k
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10
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ugcnetdec2007ii
0
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2
UGCNETDec2006II: 2
The proposition ~ q ∨ p is equivalent to :
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1 day
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Mathematical Logic
by
jothee
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106k
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14
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ugcnetdec2006ii
0
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1
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3
UGCNETDec2006II: 3
The number of edges in a complete graph with N vertices is equal to: $N (N−1)$ $2N−1$ $N−1$ $N(N−1)/2$
asked
1 day
ago
in
Graph Theory
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jothee
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106k
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10
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ugcnetdec2006ii
0
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1
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4
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
asked
3 days
ago
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Set Theory & Algebra
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jothee
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7
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ugcnetdec2004ii
0
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1
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5
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)
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3 days
ago
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Graph Theory
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jothee
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106k
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11
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ugcnetdec2004ii
0
votes
0
answers
6
UGCNETDec2004II: 23
Weighted graph : Is a bidirectional graph. Is directed graph. Is graph in which number associated with arc. Eliminates table method.
asked
3 days
ago
in
Graph Theory
by
jothee
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106k
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4
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ugcnetdec2004ii
0
votes
1
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7
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.
asked
Feb 17
in
Set Theory & Algebra
by
vivek_mishra
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653
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150
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jest
functions
sets
+4
votes
4
answers
8
GATE2020CS1
Consider the functions $e^{x}$ $x^{2}\sin x$ $\sqrt{x^{3}+1}$ Which of the above functions is/are increasing everywhere in $[ 0,1]$? Ⅲ only Ⅱ only Ⅱ and Ⅲ only Ⅰ and Ⅲ only
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Feb 12
in
Mathematical Logic
by
Arjun
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435k
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1.6k
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gate2020cs
engineeringmathematics
+3
votes
4
answers
9
GATE2020CS39
Which one of the following predicate formulae is NOT logically valid? Note that $W$ is a predicate formula without any free occurrence of $x$. $\forall x (p(x) \vee W) \equiv \forall x \: ( px) \vee W$ ... $\exists x(p(x) \rightarrow W) \equiv \forall x \: p(x) \rightarrow W$
asked
Feb 12
in
Mathematical Logic
by
Arjun
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435k
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1.9k
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gate2020cs
engineeringmathematics
+3
votes
6
answers
10
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 ______.
asked
Feb 12
in
Combinatory
by
Arjun
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435k
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1.4k
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gate2020cs
numericalanswers
engineeringmathematics
+2
votes
3
answers
11
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______________
asked
Feb 12
in
Mathematical Logic
by
Arjun
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(
435k
points)

985
views
gate2020cs
numericalanswers
+2
votes
3
answers
12
GATE2020CS52
Graph $G$ is obtained by adding vertex $s$ to $K_{3,4}$ and making $s$ adjacent to every vertex of $K_{3,4}$. The minimum number of colours required to edgecolour $G$ is _______
asked
Feb 12
in
Graph Theory
by
Arjun
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435k
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1.2k
views
gate2020cs
numericalanswers
grab
graphtheory
0
votes
3
answers
13
TIFR2020B11
Which of the following graphs are bipartite? Only $(1)$ Only $(2)$ Only $(2)$ and $(3)$ None of $(1),(2),(3)$ All of $(1),(2),(3)$
asked
Feb 11
in
Graph Theory
by
Lakshman Patel RJIT
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61.2k
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89
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tifr2020
engineeringmathematics
graphtheory
graphcoloring
+3
votes
2
answers
14
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
asked
Jan 13
in
Mathematical Logic
by
Satbir
Boss
(
25.3k
points)

368
views
isro2020
discretemathematics
mathematicallogic
propositionallogic
normal
+1
vote
1
answer
15
ISRO202076
If $A=\{x,y,z\}$ and $B=\{u,v,w,x\}, $ and the universe is $\{s,t,u,v,w,x,y,z\}$ Then $(A \cup \bar{B}) \cap (A \cap B)$ is equal to $\{u,v,w,x\}$ $\{ \ \}$ $\{u,v,w,x,y,z\}$ $\{u,v,w\}$
asked
Jan 13
in
Set Theory & Algebra
by
Satbir
Boss
(
25.3k
points)

192
views
isro2020
discretemathematics
settheory&algebra
sets
easy
0
votes
1
answer
16
$\textbf{NTA NET DEC 2019 (group)}$
Consider the following statements: $\mathbf{S_1:}\;\;$If a group $\mathbf{(G,*)}$ is of order $\mathbf n$ and $\mathrm {a \in G}$ is such that $\mathrm {a^m=e}$ for some integer $\mathrm {m \le n}$ then $\mathbf m$ must divide $\mathbf n$ ... $(3)\;\;\;\text{Niether}\; \mathrm{S_1}\;\text{nor}\;\mathrm{S_2}$
asked
Dec 29, 2019
in
Set Theory & Algebra
by
Sanjay Sharma
Boss
(
49.5k
points)

140
views
ugcnetdec2019ii
grouptheory
+1
vote
1
answer
17
NTA NET DEC2019( shortest distance)
Consider a weighted directed graph. The current shortest distance from sources S to node x is represented by d[v] = 29 . d[u] = 15 , w[u,v] = 12. What is the updated value of d[v]based on current information? 1) 29 2) 27 3) 25 4) 17
asked
Dec 22, 2019
in
Graph Theory
by
Sanjay Sharma
Boss
(
49.5k
points)

147
views
+3
votes
0
answers
18
The Interesting combination sum problems
Find the number of possible solutions for $x,y,z$ for each the following cases. $Case\ 1.$ Case of unlimited repetition. $x + y +z = 10$ and $x \geq 0\ , y \geq 0,\ z \geq 0 $ $Case\ 2 $ Case of unlimited repetition with variable lower bounds $x + y +z = 10$ and ... variable. $x + y +z = 10$ and $8 \geq x \geq 1\ , \ 20 \geq y \geq 2 \ , 12 \geq z \geq 3\ $
asked
Nov 1, 2019
in
Combinatory
by
Satbir
Boss
(
25.3k
points)

244
views
permutationandcombination
+2
votes
2
answers
19
ISI2014DCG1
Let $(1+x)^n = C_0+C_1x+C_2x^2+ \dots + C_nx^n$, $n$ being a positive integer. The value of $\left( 1+\dfrac{C_0}{C_1} \right) \left( 1+\dfrac{C_1}{C_2} \right) \cdots \left( 1+\dfrac{C_{n1}}{C_n} \right)$ is $\left( \frac{n+1}{n+2} \right) ^n$ $ \frac{n^n}{n!} $ $\left( \frac{n}{n+1} \right) ^n$ $ \frac{(n+1)^n}{n!} $
asked
Sep 23, 2019
in
Combinatory
by
Arjun
Veteran
(
435k
points)

202
views
isi2014dcg
permutationandcombination
binomialtheorem
+1
vote
1
answer
20
ISI2014DCG5
Consider the sets defined by the real solutions of the inequalities $A = \{(x,y):x^2+y^4 \leq 1\} \:\:\:\:\:\:\: B=\{(x,y):x^4+y^6 \leq 1\}$ Then $B \subseteq A$ $A \subseteq B$ Each of the sets $A – B, \: B – A$ and $A \cap B$ is nonempty none of the above
asked
Sep 23, 2019
in
Set Theory & Algebra
by
Arjun
Veteran
(
435k
points)

115
views
isi2014dcg
sets
+2
votes
1
answer
21
ISI2014DCG15
Let $\mathbb{N}=\{1,2,3, \dots\}$ be the set of natural numbers. For each $n \in \mathbb{N}$, define $A_n=\{(n+1)k, \: k \in \mathbb{N} \}$. Then $A_1 \cap A_2$ equals $A_3$ $A_4$ $A_5$ $A_6$
asked
Sep 23, 2019
in
Set Theory & Algebra
by
Arjun
Veteran
(
435k
points)

59
views
isi2014dcg
sets
algebra
+2
votes
3
answers
22
ISI2014DCG18
$^nC_0+2^nC_1+3^nC_2+\cdots+(n+1)^nC_n$ equals $2^n+n2^{n1}$ $2^nn2^{n1}$ $2^n$ none of these
asked
Sep 23, 2019
in
Combinatory
by
Arjun
Veteran
(
435k
points)

99
views
isi2014dcg
permutationandcombination
binomialtheorem
+2
votes
0
answers
23
ISI2014DCG32
Consider $30$ multiplechoice questions, each with four options of which exactly one is correct. Then the number of ways one can get only the alternate questions correctly answered is $3^{15}$ $2^{31}$ $2 \times \begin{pmatrix} 30 \\ 15 \end{pmatrix}$ $2 \times 3^{15}$
asked
Sep 23, 2019
in
Combinatory
by
Arjun
Veteran
(
435k
points)

110
views
isi2014dcg
permutationandcombination
+1
vote
1
answer
24
ISI2014DCG34
The following sum of $n+1$ terms $2 + 3 \times \begin{pmatrix} n \\ 1 \end{pmatrix} + 5 \times \begin{pmatrix} n \\ 2 \end{pmatrix} + 9 \times \begin{pmatrix} n \\ 3 \end{pmatrix} + 17 \times \begin{pmatrix} n \\ 4 \end{pmatrix} + \cdots$ up to $n+1$ terms is equal to $3^{n+1}+2^{n+1}$ $3^n \times 2^n$ $3^n + 2^n$ $2 \times 3^n$
asked
Sep 23, 2019
in
Combinatory
by
Arjun
Veteran
(
435k
points)

68
views
isi2014dcg
permutationandcombination
binomialtheorem
summation
+1
vote
1
answer
25
ISI2014DCG35
Let $A$ and $B$ be disjoint sets containing $m$ and $n$ elements respectively, and let $C=A \cup B$. Then the number of subsets $S$ (of $C$) which contains $p$ elements and also has the property that $S \cap A$ contains $q$ ... $\begin{pmatrix} m \\ pq \end{pmatrix} \times \begin{pmatrix} n \\ q \end{pmatrix}$
asked
Sep 23, 2019
in
Set Theory & Algebra
by
Arjun
Veteran
(
435k
points)

55
views
isi2014dcg
sets
disjointsets
+1
vote
1
answer
26
ISI2014DCG41
The number of permutations of the letters $a, b, c$ and $d$ such that $b$ does not follow $a,c$ does not follow $b$, and $c$ does not follow $d$, is $11$ $12$ $13$ $14$
asked
Sep 23, 2019
in
Combinatory
by
Arjun
Veteran
(
435k
points)

69
views
isi2014dcg
permutationandcombination
+2
votes
1
answer
27
ISI2014DCG63
If $^nC_{r1}=36$, $^nC_r=84$ an $^nC_{r+1}=126$ then $r$ is equal to $1$ $2$ $3$ none of these
asked
Sep 23, 2019
in
Combinatory
by
Arjun
Veteran
(
435k
points)

48
views
isi2014dcg
permutationandcombination
+1
vote
1
answer
28
ISI2014DCG66
Consider all possible words obtained by arranging all the letters of the word $\textbf{AGAIN}$. These words are now arranged in the alphabetical order, as in a dictionary. The fiftieth word in this arrangement is $\text{IAANG}$ $\text{NAAGI}$ $\text{NAAIG}$ $\text{IAAGN}$
asked
Sep 23, 2019
in
Combinatory
by
Arjun
Veteran
(
435k
points)

57
views
isi2014dcg
permutationandcombination
arrangements
+1
vote
2
answers
29
ISI2014DCG71
Five letters $A, B, C, D$ and $E$ are arranged so that $A$ and $C$ are always adjacent to each other and $B$ and $E$ are never adjacent to each other. The total number of such arrangements is $24$ $16$ $12$ $32$
asked
Sep 23, 2019
in
Combinatory
by
Arjun
Veteran
(
435k
points)

59
views
isi2014dcg
permutationandcombination
arrangements
circularpermutation
+1
vote
1
answer
30
ISI2014DCG72
The sum $\sum_{k=1}^n (1)^k \:\: {}^nC_k \sum_{j=0}^k (1)^j \: \: {}^kC_j$ is equal to $1$ $0$ $1$ $2^n$
asked
Sep 23, 2019
in
Combinatory
by
Arjun
Veteran
(
435k
points)

56
views
isi2014dcg
permutationandcombination
summation
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