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Featured
Hot questions in Engineering Mathematics
11
votes
3
answers
1
relation
Number of relations $S$ over set $\{0,1,2,3 \}$ such that $(x,y) \in S \Rightarrow x = y$
Lakshman Patel RJIT
asked
in
Set Theory & Algebra
Dec 27, 2017
by
Lakshman Patel RJIT
44.0k
views
set-theory&algebra
relations
64
votes
12
answers
2
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
27.4k
views
gate1994
graph-theory
combinatory
normal
isro2008
counting
76
votes
9
answers
3
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
28.4k
views
gatecse-2014-set2
linear-algebra
eigen-value
normal
numerical-answers
97
votes
8
answers
4
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
27.9k
views
gatecse-2012
graph-theory
normal
marks-to-all
counting
37
votes
8
answers
5
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
24.2k
views
gatecse-2014-set2
graph-theory
graph-connectivity
numerical-answers
normal
51
votes
17
answers
6
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
19.7k
views
gatecse-2016-set1
combinatory
generating-functions
normal
numerical-answers
76
votes
8
answers
7
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
14.2k
views
gatecse-2016-set2
mathematical-logic
normal
numerical-answers
propositional-logic
93
votes
9
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
20.2k
views
gatecse-2014-set1
graph-theory
numerical-answers
normal
graph-connectivity
38
votes
4
answers
9
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
17.7k
views
gate1996
linear-algebra
system-of-equations
normal
60
votes
7
answers
10
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
17.5k
views
gateit-2005
probability
binomial-distribution
expectation
normal
70
votes
15
answers
11
GATE CSE 2012 | Question: 33
Suppose a fair six-sided die is rolled once. If the value on the die is $1, 2,$ or $3,$ the die is rolled a second time. What is the probability that the sum total of values that turn up is at least $6$ ? $\dfrac{10}{21}$ $\dfrac{5}{12}$ $\dfrac{2}{3}$ $\dfrac{1}{6}$
gatecse
asked
in
Probability
Sep 26, 2014
by
gatecse
16.9k
views
gatecse-2012
probability
conditional-probability
normal
82
votes
8
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
15.9k
views
gatecse-2016-set1
set-theory&algebra
functions
normal
numerical-answers
27
votes
11
answers
13
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
15.9k
views
gatecse-2019
engineering-mathematics
discrete-mathematics
graph-theory
graph-connectivity
17
votes
15
answers
14
GATE CSE 2019 | Question: 21
The value of $3^{51} \text{ mod } 5$ is _____
Arjun
asked
in
Combinatory
Feb 7, 2019
by
Arjun
13.9k
views
gatecse-2019
numerical-answers
combinatory
modular-arithmetic
44
votes
5
answers
15
GATE CSE 2017 Set 1 | Question: 19
Let $X$ be a Gaussian random variable with mean 0 and variance $\sigma ^{2}$. Let $Y$ = $\max\left ( X,0 \right )$ where $\max\left ( a,b \right )$ is the maximum of $a$ and $b$. The median of $Y$ is ______________ .
Arjun
asked
in
Probability
Feb 14, 2017
by
Arjun
16.3k
views
gatecse-2017-set1
probability
numerical-answers
normal-distribution
62
votes
6
answers
16
GATE CSE 2007 | Question: 23
Which of the following graphs has an Eulerian circuit? Any $k$-regular graph where $k$ is an even number. A complete graph on $90$ vertices. The complement of a cycle on $25$ vertices. None of the above
Kathleen
asked
in
Graph Theory
Sep 22, 2014
by
Kathleen
19.3k
views
gatecse-2007
graph-theory
normal
graph-connectivity
25
votes
8
answers
17
GATE CSE 2015 Set 1 | Question: 54
Let G be a connected planar graph with 10 vertices. If the number of edges on each face is three, then the number of edges in G is_______________.
makhdoom ghaya
asked
in
Graph Theory
Feb 14, 2015
by
makhdoom ghaya
19.5k
views
gatecse-2015-set1
graph-theory
graph-connectivity
normal
graph-planarity
numerical-answers
58
votes
5
answers
18
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
19.5k
views
gatecse-2018
linear-algebra
matrix
eigen-value
normal
42
votes
6
answers
19
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
16.2k
views
gatecse-2018
set-theory&algebra
countable-uncountable-set
normal
5
votes
2
answers
20
How many transitive relations are there on a set with n elements if a)n=1 b) n=2 c) n=3
How many transitive relations are there on a set with n elements if a)n=1 b) n=2 c) n=3
Sanjay Sharma
asked
in
Set Theory & Algebra
Mar 7, 2017
by
Sanjay Sharma
28.9k
views
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