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Most answered questions in Discrete Mathematics
32
votes
5
answers
181
GATE CSE 2018 | Question: 18
The chromatic number of the following graph is _____
gatecse
asked
in
Graph Theory
Feb 14, 2018
by
gatecse
12.1k
views
graph-theory
graph-coloring
numerical-answers
gatecse-2018
1-mark
5
votes
5
answers
182
Kenneth Rosen Edition 6th Exercise 5.5 Question 15 (Page No. 380)
How many solutions are there to the equation x1 + x2 + x3 + x4 + x5 = 21, where xi , i = 1, 2, 3, 4, 5, is a nonnegative integer such that: 0$\leq$ x1$\leq$10 ?
Nirmal Gaur
asked
in
Combinatory
Apr 14, 2017
by
Nirmal Gaur
9.8k
views
discrete-mathematics
kenneth-rosen
combinatory
19
votes
5
answers
183
ISI 2004 MIII
In how many ways can three person, each throwing a single die once, make a score of $11$ $22$ $27$ $24$ $38$
Tesla!
asked
in
Combinatory
Apr 3, 2017
by
Tesla!
2.8k
views
combinatory
isi2004
14
votes
5
answers
184
ISI 2004 MIII
The number of permutation of $\{1,2,3,4,5\}$ that keep at least one integer fixed is. $81$ $76$ $120$ $60$
Tesla!
asked
in
Combinatory
Apr 3, 2017
by
Tesla!
3.1k
views
combinatory
isi2004
discrete-mathematics
normal
39
votes
5
answers
185
GATE CSE 2017 Set 2 | Question: 24
Consider the quadratic equation $x^2-13x+36=0$ with coefficients in a base $b$. The solutions of this equation in the same base $b$ are $x=5$ and $x=6$. Then $b=$ _____
khushtak
asked
in
Set Theory & Algebra
Feb 14, 2017
by
khushtak
14.3k
views
gatecse-2017-set2
polynomials
numerical-answers
set-theory&algebra
3
votes
5
answers
186
Probability
2 friends Alice and Bob have found an unfair coin,It has 72% chance of coming up heads.Alice and Bob plays a game with this coin.If coin comes up head then tails,Alice wins.If it's reverse(tails,then heas),Bob wins.And if neither of those two things happens,the game restarts and continues untill there is a winner What is Bob's probability of winning?
Prajwal Bhat
asked
in
Mathematical Logic
Jan 12, 2017
by
Prajwal Bhat
1.9k
views
probability
engineering-mathematics
13
votes
5
answers
187
TIFR CSE 2016 | Part B | Question: 1
A Boolean formula is said to be a $tautology$ if it evaluates to TRUE for all assignments to its variables. Which one of the following is NOT a tautology? $(( p \vee q) \wedge (r \vee s)) \Rightarrow (( p \wedge r) \vee q \vee s)$ ... $(( p \vee q ) \wedge ( r \vee s)) \Rightarrow ( p \vee q)$
go_editor
asked
in
Mathematical Logic
Dec 28, 2016
by
go_editor
2.1k
views
tifr2016
mathematical-logic
propositional-logic
34
votes
5
answers
188
TIFR CSE 2016 | Part A | Question: 15
In a tournament with $7$ teams, each team plays one match with every other team. For each match, the team earns two points if it wins, one point if it ties, and no points if it loses. At the end of all matches, the teams are ordered in the descending ... of points a team must earn in order to be guaranteed a place in the next round? $13$ $12$ $11$ $10$ $9$
go_editor
asked
in
Combinatory
Dec 28, 2016
by
go_editor
5.8k
views
tifr2016
combinatory
pigeonhole-principle
normal
20
votes
5
answers
189
TIFR CSE 2016 | Part A | Question: 8
Let $A$ and $B$ be finite sets such that $A \subseteq B$. Then, what is the value of the expression: $ \sum \limits_{C:A \subseteq C \subseteq B} (-1)^{\mid C \setminus A \mid,}$ Where $C \setminus A=\{x \in C : x \notin A \}$? Always $0$ Always $1$ $0$ if $A=B$ and $1$ otherwise $1$ if $A=B$ and $0$ otherwise Depends on the size of the universe
go_editor
asked
in
Set Theory & Algebra
Dec 27, 2016
by
go_editor
2.7k
views
tifr2016
set-theory&algebra
set-theory
8
votes
5
answers
190
TIFR CSE 2016 | Part A | Question: 2
Consider the graph shown below: The following experiment is performed using this graph. First, an edge $e =\{i,j\}$ of the graph is chosen uniformly at random from the set of $9$ possibilities. Next, a common neighbour $k$ of $i$ and $j$ is chosen, again uniformly from the set of ... $\frac{1}{6}$ $\frac{1}{4}$ $\frac{1}{3}$ $\frac{2}{3}$ $\frac{5}{6}$
go_editor
asked
in
Graph Theory
Dec 26, 2016
by
go_editor
1.1k
views
tifr2016
graph-theory
graph-connectivity
probability
37
votes
5
answers
191
GATE CSE 1989 | Question: 4-i
How many substrings (of all lengths inclusive) can be formed from a character string of length $n$? Assume all characters to be distinct, prove your answer.
makhdoom ghaya
asked
in
Combinatory
Nov 29, 2016
by
makhdoom ghaya
6.8k
views
gate1989
descriptive
combinatory
normal
proof
3
votes
5
answers
192
UGC NET CSE | December 2015 | Part 3 | Question: 44
In propositional logic, given $P$ and $P \rightarrow Q$, we can infer ________ $\sim Q$ $Q$ $P \wedge Q$ $\sim P \wedge Q$
go_editor
asked
in
Mathematical Logic
Aug 11, 2016
by
go_editor
3.3k
views
ugcnetcse-dec2015-paper3
propositional-logic
mathematical-logic
3
votes
5
answers
193
UGC NET CSE | December 2015 | Part 2 | Question: 6
Which of the following arguments are not valid? "If Gora gets the job and works hard, then he will be promoted. if Gora gets promotion, then he will be happy. He will not be happy, therefore, either he will not get the job or he will not work hard. ... $n^2 > 1$, then $n>1$. i and iii ii and iii i,ii, and iii i and ii
Anu
asked
in
Mathematical Logic
Jul 5, 2016
by
Anu
6.2k
views
ugcnetcse-dec2015-paper2
discrete-mathematics
mathematical-logic
17
votes
5
answers
194
CMI2013-A-07
Consider the following two statements. There are infinitely many interesting whole numbers. There are finitely many uninteresting whole numbers. Which of the following is true? Statements $1$ and $2$ are equivalent. Statement $1$ implies statement $2$. Statement $2$ implies statement $1$. None of the above.
go_editor
asked
in
Mathematical Logic
May 23, 2016
by
go_editor
2.3k
views
cmi2013
mathematical-logic
logical-reasoning
36
votes
5
answers
195
GATE CSE 2007 | Question: 85
Suppose that a robot is placed on the Cartesian plane. At each step it is allowed to move either one unit up or one unit right, i.e., if it is at $(i,j)$ then it can move to either $(i + 1, j)$ or $(i,j + 1)$. Suppose that the robot is not allowed to traverse the ... $^{20}\mathrm{C}_{10} - ^{8}\mathrm{C}_{4}\times ^{11}\mathrm{C}_{5}$
go_editor
asked
in
Combinatory
Apr 23, 2016
by
go_editor
9.5k
views
gatecse-2007
combinatory
normal
discrete-mathematics
1
vote
5
answers
196
Kenneth Rosen Edition 6th Exercise 1.1 Question 43 (Page No. 20)
Fuzzy logic is used in artificial intelligence. In fuzzy logic, a proposition has a truth value that is a number between 0 and 1, inclusive.A proposition with a truth value of 0 is false and one with a truth value of 1 ... least n of the statements in this list are false. Answer part (b) assuming that the list contains 99 statements
go_editor
asked
in
Mathematical Logic
Apr 16, 2016
by
go_editor
3.6k
views
kenneth-rosen
mathematical-logic
descriptive
difficult
discrete-mathematics
17
votes
5
answers
197
TIFR CSE 2014 | Part B | Question: 16
Consider the ordering relation $x\mid y \subseteq N \times N$ over natural numbers $N$ such that $x \mid y$ if there exists $z \in N$ such that $x ∙ z = y$. A set is called lattice if every finite subset has a least upper bound and greatest lower ... $(N, \mid)$ is a complete lattice. $(N, \mid)$ is a lattice but not a complete lattice.
makhdoom ghaya
asked
in
Set Theory & Algebra
Nov 20, 2015
by
makhdoom ghaya
5.2k
views
tifr2014
set-theory&algebra
partial-order
lattice
27
votes
5
answers
198
TIFR CSE 2014 | Part A | Question: 8
All that glitters is gold. No gold is silver. Claims: No silver glitters. Some gold glitters. Then, which of the following is TRUE? Only claim $1$ follows. Only claim $2$ follows. Either claim $1$ or claim $2$ follows but not both. Neither claim $1$ nor claim $2$ follows. Both claim $1$ and claim $2$ follow.
makhdoom ghaya
asked
in
Mathematical Logic
Nov 9, 2015
by
makhdoom ghaya
3.5k
views
tifr2014
mathematical-logic
first-order-logic
17
votes
5
answers
199
TIFR CSE 2013 | Part B | Question: 4
A set $S$ together with partial order $\ll$ is called a well order if it has no infinite descending chains, i.e. there is no infinite sequence $x_1, x_2,\ldots$ of elements from $S$ such that $x_{i+1} \ll x_i$ and $x_{i+1} \neq x_i$ for all $i$. ... $2^{24}$ words. $W$ is not a partial order. $W$ is a partial order but not a well order. $W$ is a well order.
makhdoom ghaya
asked
in
Set Theory & Algebra
Nov 6, 2015
by
makhdoom ghaya
3.1k
views
tifr2013
set-theory&algebra
partial-order
22
votes
5
answers
200
TIFR CSE 2013 | Part A | Question: 9
There are $n$ kingdoms and $2n$ champions. Each kingdom gets $2$ champions. The number of ways in which this can be done is: $\frac{\left ( 2n \right )!}{2^{n}}$ $\frac{\left ( 2n \right )!}{n!}$ $\frac{\left ( 2n \right )!}{2^{n} . n!}$ $\frac{n!}{2}$ None of the above
makhdoom ghaya
asked
in
Combinatory
Nov 4, 2015
by
makhdoom ghaya
3.3k
views
tifr2013
combinatory
discrete-mathematics
normal
balls-in-bins
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