Login
Register
@
Dark Mode
Profile
Edit my Profile
Messages
My favorites
Register
Activity
Q&A
Questions
Unanswered
Tags
Subjects
Users
Ask
Previous Years
Blogs
New Blog
Exams
Dark Mode
Filter
Recent
Hot!
Most votes
Most answers
Most views
Previous GATE
Featured
Previous GATE Questions in Discrete Mathematics
2
votes
3
answers
1
GATE CSE 2024 | Set 2 | Question: 2
Let $p$ and $q$ be the following propositions: $p$ : Fail grade can be given. $q$ : Student scores more than $50 \%$ marks. Consider the statement: "Fail grade cannot be given when student scores more than $50 \%$ marks." ... above statement in propositional logic? $q \rightarrow \neg p$ $q \rightarrow p$ $p \rightarrow q$ $\neg p \rightarrow q$
Arjun
asked
in
Mathematical Logic
Feb 16
by
Arjun
3.0k
views
gatecse2024-set2
mathematical-logic
2
votes
2
answers
2
GATE CSE 2024 | Set 2 | Question: 7
Let $\text{A}$ be the adjacency matrix of a simple undirected graph $\text{G}$. Suppose $\text{A}$ is its own inverse. Which one of the following statements is always TRUE? $\text{G}$ is a cycle $\text{G}$ is a perfect matching $\text{G}$ is a complete graph There is no such graph $\text{G}$
Arjun
asked
in
Graph Theory
Feb 16
by
Arjun
2.5k
views
gatecse2024-set2
graph-theory
1
vote
2
answers
3
GATE CSE 2024 | Set 2 | Question: 24
Let $\text{P}$ be the partial order defined on the set $\{1,2,3,4\}$ as follows \[ P=\{(x, x) \mid x \in\{1,2,3,4\}\} \cup\{(1,2),(3,2),(3,4)\} \] The number of total orders on $\{1,2,3,4\}$ that contain $\text{P}$ is __________.
Arjun
asked
in
Set Theory & Algebra
Feb 16
by
Arjun
1.8k
views
gatecse2024-set2
numerical-answers
set-theory&algebra
partial-order
1
vote
2
answers
4
GATE CSE 2024 | Set 2 | Question: 50
The chromatic number of a graph is the minimum number of colours used in a proper colouring of the graph. The chromatic number of the following graph is __________.
Arjun
asked
in
Graph Theory
Feb 16
by
Arjun
1.6k
views
gatecse2024-set2
graph-theory
numerical-answers
2
votes
2
answers
5
GATE CSE 2024 | Set 2 | Question: 53
Let $Z_{n}$ be the group of integers $\{0,1,2, \ldots, n-1\}$ with addition modulo $n$ as the group operation. The number of elements in the group $Z_{2} \times Z_{3} \times Z_{4}$ that are their own inverses is ___________.
Arjun
asked
in
Set Theory & Algebra
Feb 16
by
Arjun
1.8k
views
gatecse2024-set2
numerical-answers
set-theory&algebra
group-theory
0
votes
1
answer
6
GATE CSE 2024 | Set 1 | Question: 22
Let $A$ and $B$ be non-empty finite sets such that there exist one-to-one and onto functions $\text{(i)}$ from $A$ to $B$ and $\text{(ii)}$ from $A \times A$ to $A \cup B$. The number of possible values of $\text{|A|}$ is ___________.
Arjun
asked
in
Set Theory & Algebra
Feb 16
by
Arjun
1.6k
views
gatecse2024-set1
numerical-answers
set-theory&algebra
0
votes
1
answer
7
GATE CSE 2024 | Set 1 | Question: 41
The chromatic number of a graph is the minimum number of colours used in a proper colouring of the graph. Let $G$ be any graph with $n$ vertices and chromatic number $k$. Which of the following statements is/are always TRUE? $G$ contains a complete subgraph with ... $n/k$ $G$ contains at least $k(k-1) / 2$ edges $G$ contains a vertex of degree at least $k$
Arjun
asked
in
Graph Theory
Feb 16
by
Arjun
1.8k
views
gatecse2024-set1
multiple-selects
graph-theory
1
vote
1
answer
8
GATE CSE 2024 | Set 1 | Question: 42
Consider the operators $\diamond$ and $\square$ defined by $a \diamond b=a+2 b, a \square b=a b$, for positive integers. Which of the following statements is/are TRUE? Operator $\diamond$ ... $\square$ obeys the distributive law Operator $\square$ over the operator $\diamond$ obeys the distributive law
Arjun
asked
in
Set Theory & Algebra
Feb 16
by
Arjun
1.6k
views
gatecse2024-set1
multiple-selects
set-theory&algebra
7
votes
4
answers
9
GATE CSE 2023 | Question: 5
The Lucas sequence $L_{n}$ is defined by the recurrence relation: \[ L_{n}=L_{n-1}+L_{n-2}, \quad \text { for } \quad n \geq 3, \] with $L_{1}=1$ and $L_{2}=3$ ... $L_{n}=\left(\frac{1+\sqrt{5}}{2}\right)^{n}-\left(\frac{1-\sqrt{5}}{2}\right)^{n}$
admin
asked
in
Combinatory
Feb 15, 2023
by
admin
7.8k
views
gatecse-2023
combinatory
recurrence-relation
1-mark
23
votes
5
answers
10
GATE CSE 2023 | Question: 16
Geetha has a conjecture about integers, which is of the form \[ \forall x(P(x) \Longrightarrow \exists y Q(x, y)), \] where $P$ is a statement about integers, and $Q$ is a statement about pairs of integers. Which of the following (one or more) option(s) would imply ... $\exists y \forall x(P(x) \Longrightarrow Q(x, y))$ $\exists x(P(x) \wedge \exists y Q(x, y))$
admin
asked
in
Mathematical Logic
Feb 15, 2023
by
admin
11.0k
views
gatecse-2023
mathematical-logic
first-order-logic
multiple-selects
1-mark
14
votes
3
answers
11
GATE CSE 2023 | Question: 38
Let $U=\{1,2, \ldots, n\},$ where $n$ is a large positive integer greater than $1000.$ Let $k$ be a positive integer less than $n$. Let $A, B$ be subsets of $U$ with $|A|=|B|=k$ and $A \cap B=\emptyset$. We say that a permutation of $U$ separates $A$ from $B$ if ... $2\left(\begin{array}{c}n \\ 2 k\end{array}\right)(n-2 k) !(k !)^{2}$
admin
asked
in
Combinatory
Feb 15, 2023
by
admin
6.3k
views
gatecse-2023
combinatory
counting
2-marks
11
votes
2
answers
12
GATE CSE 2023 | Question: 39
Let $f: A \rightarrow B$ be an onto (or surjective) function, where $A$ and $B$ are nonempty sets. Define an equivalence relation $\sim$ on the set $A$ as \[ a_{1} \sim a_{2} \text { if } f\left(a_{1}\right)=f\left(a_{2}\right), \] ... is NOT well-defined. $F$ is an onto (or surjective) function. $F$ is a one-to-one (or injective) function. $F$ is a bijective function.
admin
asked
in
Set Theory & Algebra
Feb 15, 2023
by
admin
5.7k
views
gatecse-2023
set-theory&algebra
equivalence-class
multiple-selects
2-marks
10
votes
1
answer
13
GATE CSE 2023 | Question: 41
Let $X$ be a set and $2^{X}$ denote the powerset of $X$. Define a binary operation $\Delta$ on $2^{X}$ as follows: \[ A \Delta B=(A-B) \cup(B-A) \text {. } \] Let $H=\left(2^{X}, \Delta\right)$. Which of the following statements about $H$ is/are correct? ... $A \in 2^{X},$ the inverse of $A$ is the complement of $A$. For every $A \in 2^{X},$ the inverse of $A$ is $A$.
admin
asked
in
Set Theory & Algebra
Feb 15, 2023
by
admin
5.5k
views
gatecse-2023
set-theory&algebra
group-theory
multiple-selects
2-marks
7
votes
3
answers
14
GATE CSE 2023 | Question: 45
Let $G$ be a simple, finite, undirected graph with vertex set $\left\{v_{1}, \ldots, v_{n}\right\}$. Let $\Delta(G)$ denote the maximum degree of $G$ and let $\mathbb{N}=\{1,2, \ldots\}$ denote the set of all possible colors. Color the vertices ... $\Delta(G)$. The number of colors used is equal to the chromatic number of $G$.
admin
asked
in
Graph Theory
Feb 15, 2023
by
admin
8.1k
views
gatecse-2023
graph-theory
graph-coloring
multiple-selects
2-marks
0
votes
1
answer
15
GATE CSE 2023 | Memory Based Question: 15
The Lucas sequence $L_n$ is defined by the recurrence relation: $L_n=L_{n-1}+L_{n-2}$, for $n \geq 3$ with $L_1=1$ and $L_2=3$. Which one of the options given is TRUE? $L_n=\left(\frac{1+\sqrt{5}}{2}\right)^n+\left(\frac{1-\sqrt{5}}{3}\right)^n$ ... $L_n=\left(\frac{1+\sqrt{5}}{2}\right)^n+\left(\frac{1-\sqrt{5}}{2}\right)^n$
closed
GO Classes
asked
in
Combinatory
Feb 5, 2023
by
GO Classes
1.5k
views
memorybased-gatecse2023
goclasses
combinatory
recurrence-relation
1
vote
1
answer
16
GATE CSE 2023 | Memory Based Question: 16
How many permutations of $U$ separate $A$ from $B?$ $2\left(\begin{array}{c}n \\ 2 k\end{array}\right)(n-2 k) !(k!)^2$ $\left(\begin{array}{c}n \\ 2 k\end{array}\right)(n-2 k)!(n!)$ $n!$ $\left(\begin{array}{c}n \\ 2 k\end{array}\right)(n-2 k) !(k !)^2$
closed
GO Classes
asked
in
Combinatory
Feb 5, 2023
by
GO Classes
1.0k
views
memorybased-gatecse2023
goclasses
combinatory
counting
1
vote
2
answers
17
GATE CSE 2023 | Memory Based Question: 17
Let $x$ be a set, $2^x=$ power $2 \mathrm{k}$ set of $\mathrm{X}$. define A binary operation $\Delta$ on $2^x$ as $A \Delta B=(A-B) \cup(B-A)$. Let $H=\left(2^x, \Delta\right)$, then for every $A \in 2^x$; inverse of $A$ ... $\mathrm{H}$ is a group. $\mathrm{H}$ satisfies inverse prop, but not a group for every $A \in 2^x$; the inverse of $A$ is $A$.
closed
GO Classes
asked
in
Set Theory & Algebra
Feb 5, 2023
by
GO Classes
868
views
memorybased-gatecse2023
goclasses
set-theory&algebra
group-theory
multiple-selects
14
votes
2
answers
18
GATE CSE 2022 | Question: 17
Which of the following statements is/are $\text{TRUE}$ for a group $\textit{G}?$ If for all $x,y \in \textit{G}, \; (xy)^{2} = x^{2} y^{2},$ then $\textit{G}$ is commutative. If for all $x \in \textit{G}, \; x^{2} = 1,$ then ... $2,$ then $\textit{G}$ is commutative. If $\textit{G}$ is commutative, then a subgroup of $\textit{G}$ need not be commutative.
Arjun
asked
in
Set Theory & Algebra
Feb 15, 2022
by
Arjun
7.4k
views
gatecse-2022
set-theory&algebra
group-theory
multiple-selects
1-mark
19
votes
5
answers
19
GATE CSE 2022 | Question: 20
Consider a simple undirected graph of $10$ vertices. If the graph is disconnected, then the maximum number of edges it can have is _______________ .
Arjun
asked
in
Graph Theory
Feb 15, 2022
by
Arjun
8.6k
views
gatecse-2022
numerical-answers
graph-theory
graph-connectivity
1-mark
17
votes
3
answers
20
GATE CSE 2022 | Question: 22
The number of arrangements of six identical balls in three identical bins is _____________ .
Arjun
asked
in
Combinatory
Feb 15, 2022
by
Arjun
10.2k
views
gatecse-2022
numerical-answers
combinatory
balls-in-bins
1-mark
Page:
1
2
3
4
5
6
...
19
next »
Subscribe to GATE CSE 2024 Test Series
Subscribe to GO Classes for GATE CSE 2024
Quick search syntax
tags
tag:apple
author
user:martin
title
title:apple
content
content:apple
exclude
-tag:apple
force match
+apple
views
views:100
score
score:10
answers
answers:2
is accepted
isaccepted:true
is closed
isclosed:true
Recent Posts
Post GATE 2024 Guidance [Counseling tips and resources]
GATE CSE 2024 Result Responses
[Project Contest] Pytorch backend support for MLCommons Cpp Inference implementation
Participating in MLCommons Inference v4.0 submission (deadline is February 23 12pm IST)
IIITH PGEE 2024 Test Series by GO Classes
Subjects
All categories
General Aptitude
(3.5k)
Engineering Mathematics
(10.4k)
Discrete Mathematics
(7.1k)
Mathematical Logic
(2.5k)
Set Theory & Algebra
(1.9k)
Combinatory
(1.6k)
Graph Theory
(1.1k)
Probability
(1.4k)
Linear Algebra
(1.1k)
Calculus
(792)
Optimization
(0)
Digital Logic
(3.6k)
Programming and DS
(6.2k)
Algorithms
(4.8k)
Theory of Computation
(6.9k)
Compiler Design
(2.5k)
Operating System
(5.2k)
Databases
(4.8k)
CO and Architecture
(4.0k)
Computer Networks
(4.9k)
Artificial Intelligence
(79)
Machine Learning
(48)
Data Mining and Warehousing
(25)
Non GATE
(1.4k)
Others
(2.7k)
Admissions
(684)
Exam Queries
(1.6k)
Tier 1 Placement Questions
(17)
Job Queries
(80)
Projects
(11)
Unknown Category
(870)
64.3k
questions
77.9k
answers
244k
comments
80.0k
users
Previous GATE Questions in Discrete Mathematics
Recent Blog Comments
category ?
Hi @Arjun sir, I have obtained a score of 591 in ...
download here
Can you please tell about IIT-H mtech CSE self...
Please add your admission queries here:...
Network Sites
GO Mechanical
GO Electrical
GO Electronics
GO Civil
CSE Doubts
Aptitude Overflow