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Recent questions and answers in Discrete Mathematics
+19
votes
4
answers
1
GATE20005
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 constructed from n distinct elements so that at least one element occurs exactly twice? How many multisets can be constructed from n distinct elements?
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Combinatory
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gate2000
permutationandcombination
normal
descriptive
+4
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7
answers
2
TIFR2018B1
What is the remainder when $4444^{4444}$ is divided by $9?$ $1$ $2$ $5$ $7$ $8$
answered
15 hours
ago
in
Combinatory
by
Verma Ashish
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377
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tifr2018
modulararithmetic
permutationandcombination
+2
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6
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3
GATE201921
The value of $3^{51} \text{ mod } 5$ is _____
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16 hours
ago
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Combinatory
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Verma Ashish
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2.7k
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gate2019
numericalanswers
permutationandcombination
modulararithmetic
+22
votes
3
answers
4
GATE20002.5
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
answered
20 hours
ago
in
Set Theory & Algebra
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MRINMOY_HALDER
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2.7k
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gate2000
settheory&algebra
relations
normal
+26
votes
6
answers
5
GATE2014251
A cycle on $n$ vertices is isomorphic to its complement. The value of $n$ is _____.
answered
1 day
ago
in
Graph Theory
by
King Suleiman
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629
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3.6k
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gate20142
graphtheory
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normal
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nongate
+1
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1
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6
set theory
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2 days
ago
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Set Theory & Algebra
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Debadrita Talapatra
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11
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48
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settheory&algebra
discretemathematics
engineeringmathematics
sets
+25
votes
3
answers
7
GATE201431
Consider the following statements: P: Good mobile phones are not cheap Q: Cheap mobile phones are not good L: P implies Q M: Q implies P N: P is equivalent to Q Which one of the following about L, M, and N is CORRECT? Only L is TRUE. Only M is TRUE. Only N is TRUE. L, M and N are TRUE.
answered
6 days
ago
in
Mathematical Logic
by
sohailkhan
(
47
points)

2.4k
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gate20143
mathematicallogic
easy
propositionallogic
+34
votes
5
answers
8
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
JashanArora
(
63
points)

3.9k
views
gate2005
settheory&algebra
normal
pigeonholeprinciple
+25
votes
4
answers
9
GATE200922
For the composition table of a cyclic group shown below: ... $a,b$ are generators $b,c$ are generators $c,d$ are generators $d,a$ are generators
answered
Aug 9
in
Set Theory & Algebra
by
spike500
(
29
points)

1.8k
views
gate2009
settheory&algebra
normal
groups
0
votes
1
answer
10
recurrence relation
Which recurrence relation satisfy the sequence: 2, 3, 4, . . ., for n ≥ 1. A ) T(N) = 2 T(N1)  T(N2) B)T(N) = T(N1) + T(N2) C)T(N) = N+1 D) None of these
answered
Aug 8
in
Mathematical Logic
by
Rohit Suryanarayan
(
15
points)

439
views
recurrence
+2
votes
1
answer
11
ISI MTECH CS 2019 INTERVIEW question
As due to rain, the match between the teams in ICC world cup got canceled , So lets the total team be 10, exclude semi finals and finals , consider only league match, What is the total number of matches that played between the teams ... many ways those n matches can be conducted ? Source : https://gateoverflow.in/blog/8548/isimtechcs2019interviewexperience
answered
Aug 8
in
Combinatory
by
Shaik Masthan
Veteran
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61.9k
points)

74
views
permutationandcombination
+52
votes
4
answers
12
GATE200333
Consider the following formula and its two interpretations \(I_1\) and \(I_2\). \(\alpha: (\forall x)\left[P_x \Leftrightarrow (\forall y)\left[Q_{xy} \Leftrightarrow \neg Q_{yy} \right]\right] \Rightarrow (\forall x)\left[\neg P_x\right]\) \(I_1\) : Domain: the set of ... , \(I_1\) does not Neither \(I_1\) nor \(I_2\) satisfies \(\alpha\) Both \(I_1\) and \(I_2\) satisfies \(\alpha\)
answered
Aug 6
in
Mathematical Logic
by
MRINMOY_HALDER
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1.7k
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4k
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gate2003
mathematicallogic
difficult
firstorderlogic
+1
vote
2
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13
Graph Connectivity
Consider the given statements S1: In a simple graph G with 6 vertices, if degree of each vertex is 2, then Euler circuit exists in G. S2:In a simple graph G, if degree of each vertex is 3 then the graph G is connected. Which of the following is/are true?
answered
Aug 5
in
Graph Theory
by
IamDRD
(
11
points)

162
views
graphtheory
eulergraph
graphconnectivity
+1
vote
2
answers
14
#ACE_ACADEMY_DISCRETE_MATHS_BOOKLET.
Which of the following is not true? (a) Number of edgedisjoint Hamiltonian cycles in $K_7$ is $3$ (b) If $G$ is a simple graph with $6$ vertices and the degree of each vertex is at least $3$, then the Hamiltonian cycle exists in ... simple graph with $5$ vertices and $7$ edges, then the Hamiltonian cycle exists in $G$ Please help me understand all the options.
answered
Aug 1
in
Graph Theory
by
Raghava45
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333
points)

65
views
discretemathematics
graphtheory
+1
vote
3
answers
15
UGCNETJune2015II5
Consider a Hamiltonian Graph(G) with no loops and parallel edges. Which of the following is true with respect to this graph (G)? deg (v) $\geq$ n/2 for each vertex of G $\mid E(G) \mid \geq $1/2 (n1)(n2)+2 edges deg(v) + deg(w) $\geq$ n fr every v and $\omega$ not connected by an edge a and b b and c a and c a, b, and c
answered
Aug 1
in
Graph Theory
by
tripu
(
11
points)

1.9k
views
ugcnetjune2015ii
discretemathematics
graphtheory
+1
vote
1
answer
16
UGCNETJune2019II69
Consider the following properties with respect to a flow network $G=(V,E)$ in which a flow is a realvalued function $f:V \times V \rightarrow R$: $P_1$: For all $u, v, \in V, \: f(u,v)=f(v,u)$ $P_2$: $\underset{v \in V}{\Sigma} f(u,v)=0$ for all $u \in V$ Which one of the following is/are correct? Only $P_1$ Only $P_2$ Both $P_1$ and $P_2$ Neither $P_1$ nor $P_2$
answered
Jul 29
in
Graph Theory
by
abhinav kumar
(
17
points)

31
views
ugcnetjune2019ii
flownetwork
+2
votes
3
answers
17
ACE ACADEMY BOOKLET QUESTION
Let $G$ $=$ $(V, E)$ be a simple nonempty connected undirected graph, in which every vertex has degree 4. For any partition $V$ into two nonempty and nonoverlapping subsets $S$ and $T$. Which of the following is true? There are at least two edges that ... $S$ and one end point in $T$ There are exactly one edge that have one end point in $S$ and one end point in $T$
answered
Jul 26
in
Graph Theory
by
gvjha3
(
11
points)

95
views
+1
vote
1
answer
18
graph theory(basic doubt)
Q.1)How many nonisomorphic simple graph are there with 6 vertices and 4 edges??
answered
Jul 24
in
Graph Theory
by
gorya506
(
163
points)

56
views
+1
vote
2
answers
19
UGCNETJune2019II3
How many bit strings of length ten either start with a $1$ bit or end with two bits $00$ ? $320$ $480$ $640$ $768$
answered
Jul 23
in
Combinatory
by
Lakshman Patel RJIT
Boss
(
45.1k
points)

115
views
ugcnetjune2019ii
permutationandcombination
inclusionexclusion
+13
votes
4
answers
20
GATE2007IT76
Consider the sequence $\langle x_n \rangle , \: n \geq 0$ defined by the recurrence relation $x_{n+1} = c . x^2_n 2$, where $c > 0$. Suppose there exists a nonempty, open interval $(a, b)$ such that for all $x_0$ satisfying $a < x_0 < b$, the sequence converges ... sequence converges to the value? $\frac{1+\sqrt{1+8c}}{2c}$ $\frac{1\sqrt{1+8c}}{2c}$ $2$ $\frac{2}{2c1}$
answered
Jul 20
in
Combinatory
by
ankitgupta.1729
Boss
(
14k
points)

1.2k
views
gate2007it
permutationandcombination
normal
recurrence
0
votes
1
answer
21
Probability
Prabha is working in a software company. Her manager is running a dinner for those employees having atleast one son. If Prabha is invited to the dinner and everyone knows she has two children. What is the probability that they are both boys?
answered
Jul 20
in
Mathematical Logic
by
bankeshk
(
27
points)

36
views
probability
engineeringmathematics
conditionalprobability
0
votes
1
answer
22
Kenneth Rosen Edition 7th Exercise 2.3 Question 27 (Page No. 153)
Prove that a strictly decreasing function from $R$ to itself is onetoone. Give an example of an decreasing function from $R$ to itself that is not onetoone
answered
Jul 17
in
Set Theory & Algebra
by
chirudeepnamini
(
217
points)

11
views
kennethrosen
discretemathematics
settheory&algebra
+8
votes
8
answers
23
Kenneth Rosen Edition 6 Question 45 (Page No. 346)
How many bit strings of length eight contain either three consecutive 0s or four consecutive 1s?
answered
Jul 14
in
Combinatory
by
srestha
Veteran
(
113k
points)

2.2k
views
permutationandcombination
counting
+36
votes
7
answers
24
GATE200340
A graph $G=(V,E)$ satisfies $\mid E \mid \leq 3 \mid V \mid  6$. The mindegree of $G$ is defined as $\min_{v\in V}\left\{ \text{degree }(v)\right \}$. Therefore, mindegree of $G$ cannot be $3$ $4$ $5$ $6$
answered
Jul 14
in
Graph Theory
by
PRANAV M
(
143
points)

3.5k
views
gate2003
graphtheory
normal
degreeofgraph
+1
vote
2
answers
25
UGCNETJune2019II2
How many ways are there to place $8$ indistinguishable balls into four distinguishable bins? $70$ $165$ $^8C_4$ $^8P_4$
answered
Jul 13
in
Combinatory
by
Lakshman Patel RJIT
Boss
(
45.1k
points)

180
views
ugcnetjune2019ii
permutationandcombination
+1
vote
1
answer
26
relation
A binary relation R on Z × Z is defined as follows: (a, b) R (c, d) iff a = c or b = d Consider the following propositions: 1. R is reflexive. 2. R is symmetric. 3. R is antisymmetric. Which one of the following statements is True? A Both 1 and 2 are true B 1 is true and 2 is false C 1 is false and 3 is true D Both 2 and 3 are true
answered
Jul 12
in
Mathematical Logic
by
mohan123
Junior
(
663
points)

64
views
+1
vote
1
answer
27
Kenneth Rosen Edition 7th Exercise 2.2 Question 32 (Page No. 137)
Find the symmetric difference of $\left \{ 1,3,5 \right \}$ and $\left \{ 1,2,3 \right \}.$
answered
Jul 12
in
Set Theory & Algebra
by
Lakshman Patel RJIT
Boss
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45.1k
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14
views
kennethrosen
discretemathematics
settheory&algebra
+1
vote
1
answer
28
Kenneth Rosen Edition 7th Exercise 2.2 Question 35 (Page No. 137)
Show that $A\oplus B = (A \cup B) – (A \cap B).$
answered
Jul 12
in
Set Theory & Algebra
by
Lakshman Patel RJIT
Boss
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45.1k
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8
views
kennethrosen
discretemathematics
settheory&algebra
+1
vote
1
answer
29
Kenneth Rosen Edition 7th Exercise 2.2 Question 36 (Page No. 137)
Show that $A \oplus B = (AB) \cup (BA).$
answered
Jul 12
in
Set Theory & Algebra
by
Lakshman Patel RJIT
Boss
(
45.1k
points)

6
views
kennethrosen
discretemathematics
settheory&algebra
+1
vote
2
answers
30
Kenneth Rosen Edition 7th Exercise 2.2 Question 37 (Page No. 137)
Show that if $A$ is a subset of a universal set $U$, then $A \oplus A = \phi.$ $A \oplus \phi = A.$ $A \oplus U = \sim A.$ $A \oplus \sim A= U.$
answered
Jul 11
in
Set Theory & Algebra
by
Lakshman Patel RJIT
Boss
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45.1k
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37
views
kennethrosen
discretemathematics
settheory&algebra
+1
vote
2
answers
31
Kenneth Rosen Edition 7th Exercise 2.3 Question 69 (Page No. 155)
Find the inverse function of $f(x) = x^3 +1.$
answered
Jul 11
in
Set Theory & Algebra
by
Lakshman Patel RJIT
Boss
(
45.1k
points)

39
views
kennethrosen
discretemathematics
settheory&algebra
+2
votes
2
answers
32
MADEEASY
Consider a set S={1000,1001,1002........,9999}. The numbers in set S having atleast one digit as 2 and atleast one digit as 5 are?
answered
Jul 11
in
Combinatory
by
srestha
Veteran
(
113k
points)

246
views
counting
+9
votes
4
answers
33
ISI 2004 MIII
The number of permutation of $\{1,2,3,4,5\}$ that keep at least one integer fixed is. $81$ $76$ $120$ $60$
answered
Jul 9
in
Combinatory
by
Debargha Bhattacharj
Junior
(
515
points)

629
views
permutationandcombination
isi2004
discretemathematics
normal
+2
votes
2
answers
34
UGCNETJune2019II1
Consider the poset $( \{3,5,9,15,24,45 \}, \mid).$ Which of the following is correct for the given poset ? There exist a greatest element and a least element There exist a greatest element but not a least element There exist a least element but not a greatest element There does not exist a greatest element and a least element
answered
Jul 8
in
Set Theory & Algebra
by
Arnabh Gangwar
(
115
points)

243
views
ugcnetjune2019ii
poset
settheory&algebra
+2
votes
2
answers
35
UGCNETJune2019II8
Match ListI with ListII: ... )  (iv); (b)  (i); (c)  (iii); (d)  (ii) (a)  (iv); (b)  (iii); (c)  (i); (d)  (ii)
answered
Jul 7
in
Mathematical Logic
by
Lakshmikanta
(
27
points)

68
views
ugcnetjune2019ii
propositionallogic
+10
votes
6
answers
36
TIFR2015A7
A $1 \times 1$ chessboard has one square, a $2 \times 2$ chessboard has five squares. Continuing along this fashion, what is the number of squares on the regular $8 \times 8$ chessboard? $64$ $65$ $204$ $144$ $256$
answered
Jul 7
in
Combinatory
by
Bishal1997
(
11
points)

721
views
tifr2015
permutationandcombination
+2
votes
2
answers
37
UGCNETJune2019II6
Which of the following is principal conjunctive normal form for $[(p\vee q)\wedge\ \rceil p \rightarrow \rceil q ]$ ? $p\ \vee \rceil q$ $p \vee q $ $\rceil p \vee q$ $\rceil p\ \vee \rceil q$
answered
Jul 7
in
Mathematical Logic
by
Satbir
Boss
(
17.2k
points)

83
views
ugcnetjune2019ii
propositionallogic
+2
votes
1
answer
38
UGCNETJune2019II63
Consider the Euler’s phi function given by $\phi(n) = n \underset{p/n}{\Pi } \bigg( 1 – \frac{1}{p} \bigg)$ where $p$ runs over all the primes dividing $n$. What is the value of $\phi(45)$? $3$ $12$ $6$ $24$
answered
Jul 6
in
Combinatory
by
Ram Swaroop
Active
(
3.9k
points)

39
views
ugcnetjune2019ii
eulerphifunction
+1
vote
3
answers
39
Model Question IISc CDS CS Written Test Sample question
Anand is preparing a pizza with 8 slices, and he has 10 toppings to put on the pizza. He can put only one topping on each slice but can use the same topping on zero or more slices. In how many unique ways can he prepare the slices so that the same topping is not used in adjacent slices?
answered
Jul 6
in
Combinatory
by
venkatesh pagadala
Junior
(
555
points)

292
views
iisc
cds
0
votes
1
answer
40
Kenneth Rosen Edition 6th Exercise 7.5 Question 3 e (Page No. 507)
Which of these relations on the set of all functions from Z to Z are equivalence relations? Determine the properties of an equivalence relation that the others lack. {(f, g)  f(0) = g(1) and f(1) = g(0)} In many ... made to check the reflexive property. Why can't we check f(0)=f(0) to confirm the reflexive property. Please help.
answered
Jul 5
in
Set Theory & Algebra
by
srestha
Veteran
(
113k
points)

71
views
discretemathematics
kennethrosen
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