The Gateway to Computer Science Excellence
For all GATE CSE Questions
Toggle navigation
Facebook Login
or
Email or Username
Password
Remember
Login
Register

I forgot my password
Activity
Questions
Unanswered
Tags
Subjects
Users
Ask
Prev
Blogs
New Blog
Exams
Recent questions and answers in Discrete Mathematics
+6
votes
8
answers
1
TIFR2018B1
What is the remainder when $4444^{4444}$ is divided by $9?$ $1$ $2$ $5$ $7$ $8$
answered
2 days
ago
in
Combinatory
by
Lakshman Patel RJIT
Veteran
(
58.7k
points)

558
views
tifr2018
modulararithmetic
permutationandcombination
+50
votes
6
answers
2
GATE200625
Let $S = \{1, 2, 3,\ldots, m\}, m >3.$ Let $X_1,\ldots,X_n$ be subsets of $S$ each of size $3.$ Define a function $f$ from $S$ to the set of natural numbers as, $f(i)$ is the number of sets $X_j$ that contain the element $i.$ That is $f(i)=\left  \left\{j \mid i\in X_j \right\} \right$ then $ \sum_{i=1}^{m} f(i)$ is: $3m$ $3n$ $2m+1$ $2n+1$
answered
2 days
ago
in
Set Theory & Algebra
by
Madhab
Loyal
(
5.7k
points)

3k
views
gate2006
settheory&algebra
normal
functions
+33
votes
6
answers
3
GATE2016226
A binary relation $R$ on $\mathbb{N} \times \mathbb{N}$ is defined as follows: $(a, b) R(c, d)$ if $a \leq c$ or $b \leq d$. Consider the following propositions: $P:$ $R$ is reflexive. $Q:$ $R$ is transitive. Which one of the following statements is TRUE? Both $P$ and $Q$ are true. $P$ is true and $Q$ is false. $P$ is false and $Q$ is true. Both $P$ and $Q$ are false.
answered
2 days
ago
in
Set Theory & Algebra
by
arjuno
(
275
points)

4.8k
views
gate20162
settheory&algebra
relations
normal
+31
votes
8
answers
4
GATE2005IT36
Let $P(x)$ and $Q(x)$ ...
answered
3 days
ago
in
Mathematical Logic
by
Madhab
Loyal
(
5.7k
points)

4.5k
views
gate2005it
mathematicallogic
firstorderlogic
normal
+1
vote
1
answer
5
Made Easy Test Series 2019: Combinatory  Permutations And Combinations
in how many ways 6 letters can be placed in 6 envelopes such that at least 4 letters go into their corresponding envelopes ?
answered
4 days
ago
in
Combinatory
by
suvradip das
(
149
points)

199
views
discretemathematics
permutationandcombination
madeeasytestseries2019
madeeasytestseries
+37
votes
2
answers
6
GATE199116,a
Find the number of binary strings $w$ of length $2n$ with an equal number of $1's$ and $0's$ and the property that every prefix of $w$ has at least as many $0's$ as $1's.$
answered
4 days
ago
in
Combinatory
by
Rishiryanemo
(
19
points)

1.6k
views
gate1991
permutationandcombination
normal
descriptive
catalannumber
0
votes
1
answer
7
ugc net 2018 july79
answered
6 days
ago
in
Mathematical Logic
by
mishrapankajs
(
11
points)

249
views
+26
votes
4
answers
8
GATE20012.1
How many $4$digit even numbers have all $4$ digits distinct $2240$ $2296$ $2620$ $4536$
answered
6 days
ago
in
Combinatory
by
Kushagra गुप्ता
Active
(
4k
points)

3.8k
views
gate2001
permutationandcombination
normal
+39
votes
7
answers
9
GATE200544
What is the minimum number of ordered pairs of nonnegative numbers that should be chosen to ensure that there are two pairs $(a,b)$ and $(c,d)$ in the chosen set such that, $a \equiv c\mod 3$ and $b \equiv d \mod 5$ $4$ $6$ $16$ $24$
answered
6 days
ago
in
Combinatory
by
Kushagra गुप्ता
Active
(
4k
points)

4.7k
views
gate2005
settheory&algebra
normal
pigeonholeprinciple
+1
vote
1
answer
10
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 $(A \cup B’) \cap (A \cap B)$ is equal to $\{u,v,w,x\}$ $\{ \ \}$ $\{u,v,w,x,y,z\}$ $\{u,v,w\}$
answered
Jan 13
in
Set Theory & Algebra
by
habedo007
Active
(
2.8k
points)

116
views
isro2020
discretemathematics
settheory&algebra
sets
easy
+1
vote
1
answer
11
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
answered
Jan 13
in
Mathematical Logic
by
chirudeepnamini
Active
(
4.3k
points)

152
views
isro2020
discretemathematics
mathematicallogic
propositionallogic
normal
+2
votes
1
answer
12
GO2019FLT111
Which one of the following best expresses the generating function sequence $\{a_n\}$, for the given closed form representation? $F(x) = \frac{1}{1xx^2}$ $a_n=a_{n1}+3, n>0, a_0=1$ $a_n=a_{n1}+a_{n2}, n>1, a_0=1, a_1=1$ $a_n=2n+3, n>1$ $a_n=2a_{n1}+3, n>1, a_0=1$
answered
Jan 12
in
Set Theory & Algebra
by
blackcloud
(
469
points)

306
views
go2019flt1
generatingfunctions
settheory&algebra
+15
votes
7
answers
13
GATE200550
Let $G(x) = \frac{1}{(1x)^2} = \sum\limits_{i=0}^\infty g(i)x^i$, where $x < 1$. What is $g(i)$? $i$ $i+1$ $2i$ $2^i$
answered
Jan 9
in
Combinatory
by
arjuno
(
275
points)

1.9k
views
gate2005
normal
generatingfunctions
+21
votes
6
answers
14
GATE2005IT34
Let $n =$ $p^{2}q$, where $p$ and $q$ are distinct prime numbers. How many numbers m satisfy $1 ≤ m ≤ n$ and $gcd$ $(m, n) = 1?$ Note that $gcd$ $(m, n)$ is the greatest common divisor of $m$ and $n$. $p(q  1)$ $pq$ $\left ( p^{2}1 \right ) (q  1)$ $p(p  1) (q  1)$
answered
Jan 9
in
Set Theory & Algebra
by
arjuno
(
275
points)

2k
views
gate2005it
settheory&algebra
normal
numbertheory
+28
votes
2
answers
15
GATE20035
$n$ couples are invited to a party with the condition that every husband should be accompanied by his wife. However, a wife need not be accompanied by her husband. The number of different gatherings possible at the party is \(^{2n}\mathrm{C}_n\times 2^n\) \(3^n\) \(\frac{(2n)!}{2^n}\) \(^{2n}\mathrm{C}_n\)
answered
Jan 9
in
Combinatory
by
arjuno
(
275
points)

2.6k
views
gate2003
permutationandcombination
normal
+16
votes
10
answers
16
GATE20181
Which one of the following is a closed form expression for the generating function of the sequence $\{a_n\}$, where $a_n = 2n +3 \text{ for all } n=0, 1, 2, \dots$? $\frac{3}{(1x)^2}$ $\frac{3x}{(1x)^2}$ $\frac{2x}{(1x)^2}$ $\frac{3x}{(1x)^2}$
answered
Jan 6
in
Combinatory
by
Çșȇ ʛấẗẻ
Active
(
1.9k
points)

6.9k
views
gate2018
generatingfunctions
normal
permutationandcombination
+47
votes
5
answers
17
GATE2007IT25
What is the largest integer $m$ such that every simple connected graph with $n$ vertices and $n$ edges contains at least $m$ different spanning trees ? $1$ $2$ $3$ $n$
answered
Jan 6
in
Graph Theory
by
endurance1
(
13
points)

5.4k
views
gate2007it
graphtheory
spanningtree
normal
+1
vote
3
answers
18
ISI2019MMA27
A general election is to be scheduled on $5$ days in May such that it is not scheduled on two consecutive days. In how many ways can the $5$ days be chosen to hold the election? $\begin{pmatrix} 26 \\ 5 \end{pmatrix}$ $\begin{pmatrix} 27 \\ 5 \end{pmatrix}$ $\begin{pmatrix} 30 \\ 5 \end{pmatrix}$ $\begin{pmatrix} 31 \\ 5 \end{pmatrix}$
answered
Jan 6
in
Combinatory
by
Navneet Singh Tomar
Junior
(
735
points)

2.8k
views
isi2019mma
engineeringmathematics
discretemathematics
permutationandcombination
0
votes
1
answer
19
Kenneth Rosen Edition 7th Exercise 1.7 Question 7 (Page No. 91)
Use a direct proof to show that every odd integer is the difference of two squares.
answered
Jan 5
in
Mathematical Logic
by
vedantbonde19
(
29
points)

23
views
kennethrosen
discretemathematics
mathematicallogic
propositionallogic
0
votes
1
answer
20
Kenneth Rosen Edition 7th Exercise 1.7 Question 15 (Page No. 91)
Use a proof by contraposition to show that if $x+y≥2$,where $x$ and $y$ are real numbers, then $x≥1$ or $y≥1$.
answered
Jan 5
in
Mathematical Logic
by
vedantbonde19
(
29
points)

13
views
kennethrosen
discretemathematics
mathematicallogic
propositionallogic
+1
vote
1
answer
21
Kenneth Rosen Edition 7th Exercise 1.7 Question 11 (Page No. 91)
Prove or disprove that the product of two irrational numbers is irrational.
answered
Jan 5
in
Mathematical Logic
by
vedantbonde19
(
29
points)

20
views
kennethrosen
discretemathematics
mathematicallogic
propositionallogic
+1
vote
1
answer
22
Kenneth Rosen Edition 7th Exercise 1.7 Question 10 (Page No. 91)
Use a direct proof to show that the product of two rational numbers is rational.
answered
Jan 5
in
Mathematical Logic
by
vedantbonde19
(
29
points)

9
views
kennethrosen
discretemathematics
mathematicallogic
propositionallogic
+29
votes
4
answers
23
GATE2015254
Let $X$ and $Y$ denote the sets containing 2 and 20 distinct objects respectively and $F$ denote the set of all possible functions defined from $X$ to $Y$. Let $f$ be randomly chosen from $F$. The probability of $f$ being onetoone is ______.
answered
Jan 4
in
Set Theory & Algebra
by
shivam001
Junior
(
963
points)

2.7k
views
gate20152
settheory&algebra
functions
normal
numericalanswers
+24
votes
3
answers
24
GATE19962.1
Let $R$ denote the set of real numbers. Let $f:R\times R \rightarrow R \times R$ be a bijective function defined by $f(x,y) = (x+y, xy)$. The inverse function of $f$ is given by $f^{1} (x,y) = \left( \frac {1}{x+y}, \frac{1}{xy}\right)$ ... $f^{1}(x,y)=\left [ 2\left(xy\right),2\left(x+y\right) \right ]$
answered
Jan 4
in
Set Theory & Algebra
by
shivam001
Junior
(
963
points)

2.6k
views
gate1996
settheory&algebra
functions
normal
+70
votes
8
answers
25
GATE201238
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 $15$ $30$ $90$ $360$
answered
Jan 3
in
Graph Theory
by
JashanArora
Loyal
(
6.2k
points)

11.3k
views
gate2012
graphtheory
normal
markstoall
counting
+46
votes
4
answers
26
GATE200479
How many graphs on $n$ labeled vertices exist which have at least $\frac{(n^2  3n)}{ 2}$ edges ? $^{\left(\frac{n^2n}{2}\right)}C_{\left(\frac{n^23n} {2}\right)}$ $^{{\large\sum\limits_{k=0}^{\left (\frac{n^23n}{2} \right )}}.\left(n^2n\right)}C_k\\$ $^{\left(\frac{n^2n}{2}\right)}C_n\\$ $^{{\large\sum\limits_{k=0}^n}.\left(\frac{n^2n}{2}\right)}C_k$
answered
Jan 3
in
Graph Theory
by
JashanArora
Loyal
(
6.2k
points)

4.8k
views
gate2004
graphtheory
permutationandcombination
normal
counting
+1
vote
1
answer
27
ME FLT
Consider the following statements with respect to POSETs. I. Every non empty, finite POSET has at least one maximal and at least one minimal element. II. Every POSET has at most one greatest element and at most one least element. Which of the above statement(s) is/are true?
answered
Jan 1
in
Mathematical Logic
by
Veenit
Active
(
1.6k
points)

44
views
discretemathematics
+24
votes
4
answers
28
GATE19981.5
What is the converse of the following assertion? I stay only if you go I stay if you go If I stay then you go If you do not go then I do not stay If I do not stay then you go
answered
Dec 31, 2019
in
Mathematical Logic
by
JashanArora
Loyal
(
6.2k
points)

3.5k
views
gate1998
mathematicallogic
easy
propositionallogic
+2
votes
1
answer
29
ISI 2004 MIII
Let $X$ be a nonempty set and let $\mathcal{P}(X)$ denote the collection of all subsets of $X.$ Define $\textit{f}:\textit{X$\times$ $\mathcal{P}$(X)}\rightarrow \mathbb{R}$ by $f(x,A) = \begin{cases} 1 \text{ if } x \in A & \\ 0 \text{ if } x \notin A & \end{cases}$ ... $f(x,A)+f(x,B)  f(x,A) \cdot f(x,B)$ $f(x,A)+ \mid f(x,A)  f(x,B) \mid$
answered
Dec 31, 2019
in
Set Theory & Algebra
by
ankitgupta.1729
Boss
(
17k
points)

150
views
isi2004
functions
0
votes
1
answer
30
$\textbf{NTA NET DEC 2019 (group)}$
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 $\mathrm {a^n=e}$ for some integer $\mathrm {m \le n}$ then $\mathbf m$ must divide $\mathbf n$ ... $(3)\;\;\;\text{Niether}\; \mathrm{S_1}\;\text{nor}\;\mathrm{S_2}$
answered
Dec 30, 2019
in
Set Theory & Algebra
by
`JEET
Boss
(
18.9k
points)

95
views
ugcnetdec2019ii
grouptheory
+2
votes
1
answer
31
GATE19879f
Give the composition tables (Cayley Tables) of the two non isomorphic groups of order 4 with elements $e, a, b, c$ where $c$ is the identity element. Use the order $e, a, b, c$ for the rows and columns.
answered
Dec 30, 2019
in
Set Theory & Algebra
by
ankitgupta.1729
Boss
(
17k
points)

216
views
gate1987
groupisomorphism
settheory&algebra
nongate
+58
votes
10
answers
32
GATE2015139
Consider the operations $\textit{f (X, Y, Z) = X'YZ + XY' + Y'Z'}$ and $\textit{g (X, Y, Z) = X'YZ + X'YZ' + XY}$ Which one of the following is correct? Both $\left\{\textit{f} \right\}$ and $\left\{ \textit{g}\right\}$ are ... Only $\left\{ \textit{g}\right\}$ is functionally complete Neither $\left\{ \textit{f}\right\}$ nor $\left\{\textit{g}\right\}$ is functionally complete
answered
Dec 29, 2019
in
Set Theory & Algebra
by
pranshu27
(
21
points)

8.2k
views
gate20151
settheory&algebra
functions
difficult
0
votes
3
answers
33
Express the statement in logical expression
Express the statement "Everyone has exactly one best friend" as a logical expression involving predicates,quantifiers with a domain consisting of all people,and logical connectives without using uniqueness quantifier. I am confused pleased explain it
answered
Dec 28, 2019
in
Mathematical Logic
by
rohithk
(
11
points)

470
views
propositionallogic
0
votes
2
answers
34
ISI2016MMA13
Which one of the following statements is correct regarding the elements and subsets of the set $\{1, 2, \{1, 2, 3\}\}$? $\{1, 2\} \in \{1, 2, \{1, 2, 3\} \}$ $\{1, 2\} \subseteq \{1, 2, \{1, 2, 3\} \}$ $\{1, 2, 3\} \subseteq \{1, 2, \{1, 2, 3\} \}$ $3 \in \{1, 2, \{1, 2, 3\} \}$
answered
Dec 26, 2019
in
Set Theory & Algebra
by
smsubham
Boss
(
11.5k
points)

23
views
isi2016mmamma
sets
subsets
0
votes
2
answers
35
Hasse Doubt
what is the least upper bound of {a, b, c}?
answered
Dec 26, 2019
in
Set Theory & Algebra
by
spike500
(
41
points)

131
views
hassediagram
settheory&algebra
lattice
partialorder
+1
vote
1
answer
36
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
answered
Dec 26, 2019
in
Graph Theory
by
`JEET
Boss
(
18.9k
points)

67
views
+1
vote
3
answers
37
PGEE 2018
let 5,8,11,14,17,20.. be series then 320 will be which term of this series A) 104 B) 106 C) 962 D) 87
answered
Dec 26, 2019
in
Set Theory & Algebra
by
Yash4444
Junior
(
833
points)

331
views
iiithpgee
+18
votes
4
answers
38
GATE2015154
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_______________.
answered
Dec 24, 2019
in
Graph Theory
by
scholaraniket
(
479
points)

5.6k
views
gate20151
graphtheory
graphconnectivity
normal
graphplanarity
outofsyllabusnow
numericalanswers
+2
votes
2
answers
39
Euler Path
Which of the following Graph has Euler Path but is not an Euler Graph? A. K1,1 B.K2,10 C.K2,11 D.K10,11.
answered
Dec 24, 2019
in
Graph Theory
by
Nirmal Gaur
Active
(
2.3k
points)

430
views
graphtheory
eulergraph
eulerpath
+1
vote
1
answer
40
ISI2017DCG11
The coefficient of $x^6y^3$ in the expression $(x+2y)^9$ is $84$ $672$ $8$ none of these
answered
Dec 24, 2019
in
Combinatory
by
swatiraoo45#
(
21
points)

20
views
isi2017dcg
permutationandcombination
binomialtheorem
To see more, click for all the
questions in this category
.
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
ISRO CSE 2020 PAPER ANALYSE
BARC OCES/DGFS 2020
ISI CMI PDF by GATE Overflow
Management Trainee Recruitment COAL INDIA 2020
ECIL Interview Experience
All categories
General Aptitude
1.9k
Engineering Mathematics
7.5k
Discrete Mathematics
5.2k
Mathematical Logic
2.1k
Set Theory & Algebra
1.4k
Combinatory
916
Graph Theory
824
Probability
1k
Linear Algebra
723
Calculus
592
Digital Logic
2.9k
Programming and DS
4.9k
Algorithms
4.4k
Theory of Computation
6.2k
Compiler Design
2.1k
Operating System
4.5k
Databases
4.1k
CO and Architecture
3.4k
Computer Networks
4.2k
Non GATE
1.4k
Others
1.4k
Admissions
595
Exam Queries
573
Tier 1 Placement Questions
23
Job Queries
72
Projects
18
Follow @csegate
Recent questions and answers in Discrete Mathematics
Recent Blog Comments
@Swaraj Right.. In Little Endian  Big endian...
Q42 C option is correct for C set as it is an...
@ smsubham The SQL query question No...
Are SQL query and that case 1, case 2 answer in...
@ Debapaul Correct answer should be...
50,737
questions
57,271
answers
198,137
comments
104,779
users