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Featured
Most answered questions in Engineering Mathematics
3
votes
6
answers
161
UGC NET CSE | January 2017 | Part 2 | Question: 6
In propositional logic if $\left ( P \rightarrow Q \right )\wedge \left ( R \rightarrow S \right )$ and $\left ( P \vee R \right )$ are two premises such that $\begin{array}{c} (P \to Q) \wedge (R \to S) \\ P \vee R \\ \hline Y \\ \hline \end{array}$ $Y$ is the premise : $P \vee R$ $P \vee S$ $Q \vee R$ $Q \vee S$
go_editor
asked
in
Mathematical Logic
Mar 24, 2020
by
go_editor
2.9k
views
ugcnetjan2017ii
discrete-mathematics
propositional-logic
28
votes
6
answers
162
GATE CSE 2020 | Question: 52
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 edge-colour $G$ is _______
Arjun
asked
in
Graph Theory
Feb 12, 2020
by
Arjun
13.5k
views
gatecse-2020
numerical-answers
graph-theory
graph-coloring
2-marks
40
votes
6
answers
163
GATE CSE 2019 | Question: 38
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 minimum-weight edge crossing the cut. Which of the following statements is/are TRUE? I only II only Both I and II Neither I nor II
Arjun
asked
in
Graph Theory
Feb 7, 2019
by
Arjun
20.4k
views
gatecse-2019
engineering-mathematics
discrete-mathematics
graph-theory
graph-connectivity
2-marks
8
votes
6
answers
164
TIFR CSE 2019 | Part A | Question: 1
Let $X$ be a set with $n$ elements. How many subsets of $X$ have odd cardinality? $n$ $2^n$ $2^{n/2}$ $2^{n-1}$ Can not be determined without knowing whether $n$ is odd or even
Arjun
asked
in
Set Theory & Algebra
Dec 18, 2018
by
Arjun
3.4k
views
tifr2019
engineering-mathematics
discrete-mathematics
set-theory&algebra
set-theory
52
votes
6
answers
165
GATE CSE 2018 | Question: 27
Let $N$ be the set of natural numbers. Consider the following sets, $P:$ Set of Rational numbers (positive and negative) $Q:$ Set of functions from $\{0,1\}$ to $N$ $R:$ Set of functions from $N$ to $\{0, 1\}$ $S:$ Set of finite subsets of $N$ Which of the above sets are countable? $Q$ and $S$ only $P$ and $S$ only $P$ and $R$ only $P, Q$ and $S$ only
gatecse
asked
in
Set Theory & Algebra
Feb 14, 2018
by
gatecse
21.8k
views
gatecse-2018
set-theory&algebra
countable-uncountable-set
normal
2-marks
23
votes
6
answers
166
GATE CSE 2018 | Question: 17
Consider a matrix $A= uv^T$ where $u=\begin{pmatrix}1 \\ 2 \end{pmatrix} , v = \begin{pmatrix}1 \\1 \end{pmatrix}$. Note that $v^T$ denotes the transpose of $v$. The largest eigenvalue of $A$ is ____
gatecse
asked
in
Linear Algebra
Feb 14, 2018
by
gatecse
10.2k
views
gatecse-2018
linear-algebra
eigen-value
normal
numerical-answers
1-mark
1
vote
6
answers
167
ISRO-DEC2017-6
The proposition $(P\Rightarrow Q)\wedge (Q\Rightarrow P)$ is a Tautology Contradiction Contingency Absurdity
gatecse
asked
in
Mathematical Logic
Dec 17, 2017
by
gatecse
2.5k
views
isrodec2017
30
votes
6
answers
168
TIFR CSE 2018 | Part A | Question: 9
How many ways are there to assign colours from range $\left\{1,2,\ldots,r\right\}$ to vertices of the following graph so that adjacent vertices receive distinct colours? $r^{4}$ $r^{4} - 4r^{3}$ $r^{4}-5r^{3}+8r^{2}-4r$ $r^{4}-4r^{3}+9r^{2}-3r$ $r^{4}-5r^{3}+10r^{2}-15r$
Rohit Gupta 8
asked
in
Graph Theory
Dec 10, 2017
by
Rohit Gupta 8
4.6k
views
tifr2018
graph-theory
graph-coloring
16
votes
6
answers
169
TIFR CSE 2018 | Part A | Question: 6
What is the minimum number of students needed in a class to guarantee that there are at least $6$ students whose birthdays fall in the same month ? $6$ $23$ $61$ $72$ $91$
Arjun
asked
in
Combinatory
Dec 10, 2017
by
Arjun
3.4k
views
tifr2018
pigeonhole-principle
combinatory
1
vote
6
answers
170
UGC NET CSE | November 2017 | Part 2 | Question: 8
Let $P$ and $Q$ be two propositions $\neg (P \leftrightarrow Q)$ is equivalent to $P\leftrightarrow \neg Q$ $\neg P\leftrightarrow Q$ $\neg P \leftrightarrow \neg Q$ $Q\rightarrow P$
Arjun
asked
in
Mathematical Logic
Nov 5, 2017
by
Arjun
2.3k
views
ugcnetcse-nov2017-paper2
discrete-mathematics
mathematical-logic
63
votes
6
answers
171
GATE CSE 2017 Set 2 | Question: 26
$P$ and $Q$ are considering to apply for a job. The probability that $P$ applies for the job is $\dfrac{1}{4},$ the probability that $P$ applies for the job given that $Q$ applies for the job is $\dfrac{1}{2},$ and the probability that $Q$ applies for the ... $\left(\dfrac{5}{6}\right)$ $\left(\dfrac{7}{8}\right)$ $\left(\dfrac{11}{12}\right)$
Arjun
asked
in
Probability
Feb 14, 2017
by
Arjun
12.4k
views
gatecse-2017-set2
probability
conditional-probability
83
votes
6
answers
172
GATE CSE 2017 Set 1 | Question: 31
Let $A$ be $n\times n$ real valued square symmetric matrix of rank $2$ with $\sum_{i=1}^{n}\sum_{j=1}^{n}A^{2}_{ij} = 50.$ Consider the following statements. One eigenvalue must be in $\left [ -5,5 \right ]$ The eigenvalue ... than $5$ Which of the above statements about eigenvalues of $A$ is/are necessarily CORRECT? Both I and II I only II only Neither I nor II
Arjun
asked
in
Linear Algebra
Feb 14, 2017
by
Arjun
44.4k
views
gatecse-2017-set1
linear-algebra
eigen-value
normal
36
votes
6
answers
173
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
11.8k
views
gatecse-2017-set2
set-theory&algebra
lattice
numerical-answers
normal
6
votes
6
answers
174
Gate ECE 2017 Eigen Value
For the given matrix A, one of the Eigenvalue is real $A=\begin{bmatrix} 1 &2 &3 &4 &5 \\ 5 &1 &2 &3 &4 \\ 4&5 &1 &2 &3 \\ 3&4 &5 &1 &2 \\ 2 &3 &4 &5 &1 \end{bmatrix}$ The real Eigen value is:
yg92
asked
in
Linear Algebra
Feb 8, 2017
by
yg92
5.3k
views
matrix
eigen-value
20
votes
6
answers
175
GATE CSE 1988 | Question: 1vii
The complement(s) of the element $'a'$ in the lattice shown in below figure is (are) ____
go_editor
asked
in
Set Theory & Algebra
Dec 10, 2016
by
go_editor
4.6k
views
gate1988
descriptive
lattice
set-theory&algebra
21
votes
6
answers
176
GATE CSE 1989 | Question: 1-iv
The transitive closure of the relation $\left\{(1, 2), (2, 3), (3, 4), (5, 4)\right\}$ on the set $\left\{1, 2, 3, 4, 5\right\}$ is ___________.
makhdoom ghaya
asked
in
Set Theory & Algebra
Nov 27, 2016
by
makhdoom ghaya
7.1k
views
gate1989
set-theory&algebra
relations
descriptive
29
votes
6
answers
177
GATE CSE 1990 | Question: 3-x
Indicate which of the following well-formed formulae are valid: $\left(P\Rightarrow Q\right) {\wedge} \left(Q \Rightarrow R\right) \Rightarrow \left(P \Rightarrow R\right)$ ...
makhdoom ghaya
asked
in
Mathematical Logic
Nov 22, 2016
by
makhdoom ghaya
9.3k
views
gate1990
normal
mathematical-logic
propositional-logic
multiple-selects
1
vote
6
answers
178
GATE Overflow | Mathematics | Test 1 | Question: 2
Four couples decide to form a committee of four members. The number of different committees that can be formed in which no couple finds a place is? 10 12 14 16
Bikram
asked
in
Combinatory
Aug 6, 2016
by
Bikram
703
views
go-mathematics-1
combinatory
19
votes
6
answers
179
CMI2013-A-06
A simple graph is one in which there are no self-loops and each pair of distinct vertices is connected by at most one edge. Let $G$ be a simple graph on $8$ vertices such that there is a vertex of degree $1$, a vertex of degree $2$, a vertex of degree $3$, a vertex ... degree $6$ and a vertex of degree $7$. Which of the following can be the degree of the last vertex? $3$ $0$ $5$ $4$
go_editor
asked
in
Graph Theory
May 23, 2016
by
go_editor
5.3k
views
cmi2013
graph-theory
normal
degree-of-graph
89
votes
6
answers
180
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
17.7k
views
gatecse-2006
graph-theory
normal
degree-of-graph
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