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
47
votes
6
answers
321
GATE CSE 2000 | Question: 6
Let $S$ be a set of $n$ elements $\left\{1, 2,\ldots, n\right\}$ and $G$ a graph with $2^{n}$ vertices, each vertex corresponding to a distinct subset of $S$. Two vertices are adjacent iff the symmetric difference of the corresponding sets has ... Every vertex in $G$ has the same degree. What is the degree of a vertex in $G$? How many connected components does $G$ have?
Kathleen
asked
in
Set Theory & Algebra
Sep 14, 2014
by
Kathleen
6.4k
views
gatecse-2000
set-theory&algebra
normal
descriptive
set-theory
33
votes
6
answers
322
GATE CSE 2000 | Question: 5
A multiset is an unordered collection of elements where elements may repeat any number of times. The size of a multiset is the number of elements in it, counting repetitions. What is the number of multisets of size $4$ that can be ... n distinct elements so that at least one element occurs exactly twice? How many multisets can be constructed from n distinct elements?
Kathleen
asked
in
Combinatory
Sep 14, 2014
by
Kathleen
7.8k
views
gatecse-2000
combinatory
normal
descriptive
28
votes
3
answers
323
GATE CSE 2000 | Question: 4
Let $S= \{0, 1, 2, 3, 4, 5, 6, 7\}$ and $⊗$ denote multiplication modulo $8,$ that is, $x ⊗ y= (xy) \mod 8$ Prove that $( \{ 0, 1\}, ⊗)$ is not a group. Write three distinct groups $(G, ⊗)$ where $G ⊂ S$ and $G$ has $2$ elements.
Kathleen
asked
in
Set Theory & Algebra
Sep 14, 2014
by
Kathleen
4.1k
views
gatecse-2000
set-theory&algebra
descriptive
group-theory
8
votes
1
answer
324
GATE CSE 2000 | Question: 3
Consider the following sequence: $s_1 = s_2 = 1$ and $s_i = 1 + \min \left({s_{i-1}, s_{i-2}}\right) \text{ for } i > 2$. Prove by induction on $n$ that $s_n=⌈\frac{n}{2}⌉$.
Kathleen
asked
in
Set Theory & Algebra
Sep 14, 2014
by
Kathleen
1.5k
views
gatecse-2000
set-theory&algebra
mathematical-induction
descriptive
47
votes
7
answers
325
GATE CSE 2000 | Question: 2.7
Let $a, b, c, d$ be propositions. Assume that the equivalence $a ⇔ ( b \vee \neg b)$ and $b ⇔c$ hold. Then the truth-value of the formula $(a ∧ b) → (a ∧ c) ∨ d$ is always True False Same as the truth-value of $b$ Same as the truth-value of $d$
Kathleen
asked
in
Mathematical Logic
Sep 14, 2014
by
Kathleen
12.1k
views
gatecse-2000
mathematical-logic
normal
propositional-logic
60
votes
6
answers
326
GATE CSE 2000 | Question: 2.6
Let $P(S)$ denotes the power set of set $S.$ Which of the following is always true? $P(P(S)) = P(S)$ $P(S) ∩ P(P(S)) = \{ Ø \}$ $P(S) ∩ S = P(S)$ $S ∉ P(S)$
Kathleen
asked
in
Set Theory & Algebra
Sep 14, 2014
by
Kathleen
13.5k
views
gatecse-2000
set-theory&algebra
easy
set-theory
39
votes
5
answers
327
GATE CSE 2000 | Question: 2.5
A relation $R$ is defined on the set of integers as $xRy$ iff $(x + y)$ is even. Which of the following statements is true? $R$ is not an equivalence relation $R$ is an equivalence relation having $1$ equivalence class $R$ is an equivalence relation having $2$ equivalence classes $R$ is an equivalence relation having $3$ equivalence classes
Kathleen
asked
in
Set Theory & Algebra
Sep 14, 2014
by
Kathleen
14.0k
views
gatecse-2000
set-theory&algebra
relations
normal
37
votes
4
answers
328
GATE CSE 2000 | Question: 2.4
A polynomial $p(x)$ satisfies the following: $p(1) = p(3) = p(5) = 1$ $p(2) = p(4) = -1$ The minimum degree of such a polynomial is $1$ $2$ $3$ $4$
Kathleen
asked
in
Set Theory & Algebra
Sep 14, 2014
by
Kathleen
7.7k
views
gatecse-2000
set-theory&algebra
normal
polynomials
39
votes
6
answers
329
GATE CSE 2000 | Question: 1.1
The minimum number of cards to be dealt from an arbitrarily shuffled deck of $52$ cards to guarantee that three cards are from same suit is $3$ $8$ $9$ $12$
Kathleen
asked
in
Combinatory
Sep 14, 2014
by
Kathleen
10.0k
views
gatecse-2000
easy
pigeonhole-principle
combinatory
12
votes
1
answer
330
GATE CSE 1992 | Question: 15.a
Use Modus ponens $(A, A → B |= B)$ or resolution to show that the following set is inconsistent: $Q(x) \rightarrow P (x) \vee \sim R (a)$ $R (a) \vee \sim Q(a)$ $Q(a)$ $\sim P (y)$ where $x$ and $y$ are universally quantified variables, $a$ is a constant and $P, Q, R$ are monadic predicates.
Kathleen
asked
in
Mathematical Logic
Sep 13, 2014
by
Kathleen
3.3k
views
gate1992
normal
mathematical-logic
propositional-logic
descriptive
40
votes
4
answers
331
GATE CSE 1992 | Question: 14a
If $G$ is a group of even order, then show that there exists an element $a≠e$, the identity in $G$, such that $a^2 = e$.
Kathleen
asked
in
Set Theory & Algebra
Sep 13, 2014
by
Kathleen
7.2k
views
gate1992
set-theory&algebra
group-theory
normal
descriptive
proof
33
votes
3
answers
332
GATE CSE 1992 | Question: 03,iii
How many edges can there be in a forest with $p$ components having $n$ vertices in all?
Kathleen
asked
in
Graph Theory
Sep 13, 2014
by
Kathleen
6.4k
views
gate1992
graph-theory
graph-connectivity
descriptive
24
votes
4
answers
333
GATE CSE 1992 | Question: 02,xvi
Which of the following is/are a tautology? $a \vee b \to b \wedge c$ $a \wedge b \to b \vee c$ $a \vee b \to \left(b \to c \right)$ $a \to b \to \left(b \to c \right)$
Kathleen
asked
in
Mathematical Logic
Sep 13, 2014
by
Kathleen
9.7k
views
gate1992
mathematical-logic
easy
propositional-logic
multiple-selects
9
votes
4
answers
334
GATE CSE 1992 | Question: 02,viii
A non-planar graph with minimum number of vertices has $9$ edges, $6$ vertices $6$ edges, $4$ vertices $10$ edges, $5$ vertices $9$ edges, $5$ vertices
Kathleen
asked
in
Graph Theory
Sep 12, 2014
by
Kathleen
3.2k
views
gate1992
graph-theory
normal
graph-planarity
10
votes
1
answer
335
GATE CSE 1992 | Question: 01,x
Maximum number of edges in a planar graph with $n$ vertices is _____
Kathleen
asked
in
Graph Theory
Sep 12, 2014
by
Kathleen
5.5k
views
gate1992
graph-theory
graph-planarity
easy
fill-in-the-blanks
52
votes
2
answers
336
GATE CSE 1991 | Question: 16,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 $1's.$
Kathleen
asked
in
Combinatory
Sep 12, 2014
by
Kathleen
6.5k
views
gate1991
combinatory
normal
descriptive
catalan-number
39
votes
9
answers
337
GATE CSE 1991 | Question: 03,xii
If $F_1$, $F_2$ and $F_3$ are propositional formulae such that $F_1 \land F_2 \rightarrow F_3$ and $F_1 \land F_2 \rightarrow \sim F_3$ are both tautologies, then which of the following is true: Both $F_1$ and $F_2$ are tautologies The conjunction $F_1 \land F_2$ is not satisfiable Neither is tautologous Neither is satisfiable None of the above
Kathleen
asked
in
Mathematical Logic
Sep 12, 2014
by
Kathleen
8.8k
views
gate1991
mathematical-logic
normal
propositional-logic
multiple-selects
43
votes
4
answers
338
GATE CSE 1991 | Question: 02-iv
Match the pairs in the following questions by writing the corresponding letters only. ...
Kathleen
asked
in
Combinatory
Sep 12, 2014
by
Kathleen
4.9k
views
gate1991
combinatory
normal
match-the-following
51
votes
4
answers
339
GATE CSE 1991 | Question: 01,xv
The maximum number of possible edges in an undirected graph with $n$ vertices and $k$ components is ______.
Kathleen
asked
in
Graph Theory
Sep 12, 2014
by
Kathleen
11.5k
views
gate1991
graph-theory
graph-connectivity
normal
fill-in-the-blanks
19
votes
3
answers
340
GATE CSE 1991 | Question: 01,xiv
If the longest chain in a partial order is of length $n$, then the partial order can be written as a _____ of $n$ antichains.
Kathleen
asked
in
Set Theory & Algebra
Sep 12, 2014
by
Kathleen
5.8k
views
gate1991
set-theory&algebra
partial-order
normal
fill-in-the-blanks
Page:
« prev
1
...
12
13
14
15
16
17
18
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