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Featured
Hot questions in Engineering Mathematics
69
votes
5
answers
1
GATE CSE 2010 | Question: 30
Suppose the predicate $F(x, y, t)$ is used to represent the statement that person $x$ can fool person $y$ at time $t$. Which one of the statements below expresses best the meaning of the formula, $\qquad∀x∃y∃t(¬F(x,y,t))$ Everyone can ... time No one can fool everyone all the time Everyone cannot fool some person all the time No one can fool some person at some time
gatecse
asked
in
Mathematical Logic
Sep 21, 2014
by
gatecse
70.0k
views
gatecse-2010
mathematical-logic
easy
first-order-logic
83
votes
6
answers
2
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
111
votes
9
answers
3
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
34.7k
views
gatecse-2012
graph-theory
normal
marks-to-all
counting
13
votes
3
answers
4
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
5
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
34.7k
views
gate1994
graph-theory
graph-connectivity
combinatory
normal
isro2008
counting
97
votes
8
answers
6
GATE CSE 2014 Set 2 | Question: 47
The product of the non-zero eigenvalues of the matrix is ____ $\begin{pmatrix} 1 & 0 & 0 & 0 & 1 \\ 0 & 1 & 1 & 1 & 0 \\ 0 & 1 & 1 & 1 & 0 \\ 0 & 1 & 1 & 1 & 0 \\ 1 & 0 & 0 & 0 & 1 \end{pmatrix}$
go_editor
asked
in
Linear Algebra
Sep 28, 2014
by
go_editor
37.0k
views
gatecse-2014-set2
linear-algebra
eigen-value
normal
numerical-answers
77
votes
7
answers
7
GATE CSE 2018 | Question: 26
Consider a matrix P whose only eigenvectors are the multiples of $\begin{bmatrix} 1 \\ 4 \end{bmatrix}$. Consider the following statements. P does not have an inverse P has a repeated eigenvalue P cannot be diagonalized Which one of the ... III are necessarily true Only II is necessarily true Only I and II are necessarily true Only II and III are necessarily true
gatecse
asked
in
Linear Algebra
Feb 14, 2018
by
gatecse
27.2k
views
gatecse-2018
linear-algebra
matrix
eigen-value
normal
2-marks
100
votes
10
answers
8
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
26.7k
views
gatecse-2014-set1
graph-theory
numerical-answers
normal
graph-connectivity
43
votes
14
answers
9
GATE CSE 2021 Set 2 | Question: 24
Suppose that $P$ is a $4 \times 5$ matrix such that every solution of the equation $\text{Px=0}$ is a scalar multiple of $\begin{bmatrix} 2 & 5 & 4 &3 & 1 \end{bmatrix}^T$. The rank of $P$ is __________
Arjun
asked
in
Linear Algebra
Feb 18, 2021
by
Arjun
18.1k
views
gatecse-2021-set2
numerical-answers
linear-algebra
matrix
rank-of-matrix
1-mark
38
votes
9
answers
10
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
100
votes
11
answers
11
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
19.7k
views
gatecse-2016-set2
mathematical-logic
normal
numerical-answers
propositional-logic
91
votes
9
answers
12
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
21.5k
views
gatecse-2016-set1
set-theory&algebra
functions
normal
numerical-answers
72
votes
8
answers
13
GATE IT 2005 | Question: 32
An unbiased coin is tossed repeatedly until the outcome of two successive tosses is the same. Assuming that the trials are independent, the expected number of tosses is $3$ $4$ $5$ $6$
Ishrat Jahan
asked
in
Probability
Nov 3, 2014
by
Ishrat Jahan
29.5k
views
gateit-2005
probability
binomial-distribution
expectation
normal
42
votes
8
answers
14
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
17.0k
views
gatecse-2020
first-order-logic
mathematical-logic
2-marks
88
votes
5
answers
15
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
20.9k
views
gatecse-2015-set2
mathematical-logic
normal
first-order-logic
32
votes
14
answers
16
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
21.1k
views
gatecse-2019
engineering-mathematics
discrete-mathematics
graph-theory
graph-connectivity
1-mark
48
votes
7
answers
17
GATE CSE 1996 | Question: 1.7
Let $Ax = b$ be a system of linear equations where $A$ is an $m \times n$ matrix and $b$ is a $m \times 1$ column vector and $X$ is an $n \times1$ column vector of unknowns. Which of the following is false? The system has a solution if and ... a unique solution. The system will have only a trivial solution when $m=n$, $b$ is the zero vector and $\text{rank}(A) =n$.
Kathleen
asked
in
Linear Algebra
Oct 9, 2014
by
Kathleen
21.3k
views
gate1996
linear-algebra
system-of-equations
normal
67
votes
9
answers
18
GATE CSE 2017 Set 1 | Question: 3
Let $c_{1}.....c_{n}$ be scalars, not all zero, such that $\sum_{i=1}^{n}c_{i}a_{i}$ = 0 where $a_{i}$ are column vectors in $R^{n}$. Consider the set of linear equations $Ax = b$ ... has a unique solution at $x=J_{n}$ where $J_{n}$ denotes a $n$-dimensional vector of all 1. no solution infinitely many solutions finitely many solutions
Arjun
asked
in
Linear Algebra
Feb 14, 2017
by
Arjun
20.2k
views
gatecse-2017-set1
linear-algebra
system-of-equations
normal
57
votes
17
answers
19
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
25.8k
views
gatecse-2016-set1
combinatory
generating-functions
normal
numerical-answers
19
votes
18
answers
20
GATE CSE 2019 | Question: 21
The value of $3^{51} \text{ mod } 5$ is _____
Arjun
asked
in
Combinatory
Feb 7, 2019
by
Arjun
18.1k
views
gatecse-2019
numerical-answers
combinatory
modular-arithmetic
1-mark
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