Recent questions and answers in Discrete Mathematics

+19 votes

4 answers

1

GATE2000-5
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 constructed from n distinct elements so that at least one element occurs exactly twice? How many multisets can be constructed from n distinct elements?

answered 10 hours ago in Combinatory by Verma Ashish Loyal (9.1k points) | 1.4k views

+4 votes

7 answers

2

TIFR2018-B-1
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 Loyal (9.1k points) | 377 views

+2 votes

6 answers

3

GATE2019-21
The value of $3^{51} \text{ mod } 5$ is _____

answered 16 hours ago in Combinatory by Verma Ashish Loyal (9.1k points) | 2.7k views

+22 votes

3 answers

4

GATE2000-2.5
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

answered 20 hours ago in Set Theory & Algebra by MRINMOY_HALDER Active (1.7k points) | 2.7k views

+26 votes

6 answers

5

GATE2014-2-51
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 Junior (629 points) | 3.6k views

+1 vote

1 answer

6

set theory

answered 2 days ago in Set Theory & Algebra by Debadrita Talapatra (11 points) | 48 views

+25 votes

3 answers

7

GATE2014-3-1
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 views

+34 votes

5 answers

8

GATE2005-44
What is the minimum number of ordered pairs of non-negative 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

+25 votes

4 answers

9

GATE2009-22
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

0 votes

1 answer

10

recurrence relation
Which recurrence relation satisfy the sequence: 2, 3, 4, . . ., for n ≥ 1. A ) T(N) = 2 T(N-1) - T(N-2) B)T(N) = T(N-1) + T(N-2) C)T(N) = N+1 D) None of these

answered Aug 8 in Mathematical Logic by Rohit Suryanarayan (15 points) | 439 views

+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/isi-mtech-cs-2019-interview-experience

answered Aug 8 in Combinatory by Shaik Masthan Veteran (61.9k points) | 74 views

+52 votes

4 answers

12

GATE2003-33
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 Active (1.7k points) | 4k views

+1 vote

2 answers

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

+1 vote

2 answers

14

#ACE_ACADEMY_DISCRETE_MATHS_BOOKLET.
Which of the following is not true? (a) Number of edge-disjoint 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 (333 points) | 65 views

+1 vote

3 answers

15

UGCNET-June2015-II-5
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 (n-1)(n-2)+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

+1 vote

1 answer

16

UGCNET-June-2019-II-69
Consider the following properties with respect to a flow network $G=(V,E)$ in which a flow is a real-valued 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

+2 votes

3 answers

17

ACE ACADEMY BOOKLET QUESTION
Let $G$ $=$ $(V, E)$ be a simple non-empty connected undirected graph, in which every vertex has degree 4. For any partition $V$ into two non-empty and non-overlapping 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

UGCNET-June-2019-II-3
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

+13 votes

4 answers

20

GATE2007-IT-76
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 non-empty, open interval $(a, b)$ such that for all $x_0$ satisfying $a < x_0 < b$, the sequence converges ... sequence converges to the value? $\frac{1+\sqrt{1+8c}}{2c}$ $\frac{1-\sqrt{1+8c}}{2c}$ $2$ $\frac{2}{2c-1}$

answered Jul 20 in Combinatory by ankitgupta.1729 Boss (14k points) | 1.2k views

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

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 it-self is one-to-one. Give an example of an decreasing function from $R$ to itself that is not one-to-one

answered Jul 17 in Set Theory & Algebra by chirudeepnamini (217 points) | 11 views

+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

+36 votes

7 answers

24

GATE2003-40
A graph $G=(V,E)$ satisfies $\mid E \mid \leq 3 \mid V \mid - 6$. The min-degree of $G$ is defined as $\min_{v\in V}\left\{ \text{degree }(v)\right \}$. Therefore, min-degree of $G$ cannot be $3$ $4$ $5$ $6$

answered Jul 14 in Graph Theory by PRANAV M (143 points) | 3.5k views

+1 vote

2 answers

25

UGCNET-June-2019-II-2
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

+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 (45.1k points) | 14 views

+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 (45.1k points) | 8 views

+1 vote

1 answer

29

Kenneth Rosen Edition 7th Exercise 2.2 Question 36 (Page No. 137)
Show that $A \oplus B = (A-B) \cup (B-A).$

answered Jul 12 in Set Theory & Algebra by Lakshman Patel RJIT Boss (45.1k points) | 6 views

+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 (45.1k points) | 37 views

+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

+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

+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

+2 votes

2 answers

34

UGCNET-June-2019-II-1
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

+2 votes

2 answers

35

UGCNET-June-2019-II-8
Match List-I with List-II: ... ) - (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

+10 votes

6 answers

36

TIFR2015-A-7
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

+2 votes

2 answers

37

UGCNET-June-2019-II-6
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

+2 votes

1 answer

38

UGCNET-June-2019-II-63
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

+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

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

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