Recent questions and answers in Discrete Mathematics

+1 vote

2 answers

1

PGEE 2018
p: n is a prime number q: n mod 30 is prime number 1) p implies q 2) q implies p 3) p implies q or q implies p 4) If p implies q then q implies p

answered 2 hours ago in Mathematical Logic by Kushagra Chatterjee Junior (827 points) | 64 views

+1 vote

2 answers

2

PGEE 2018
Two trucks are 150 KM apart on the main road, Truck one start and go 25km straight then 15 km right 25 km left and finally turn towards the main road however due to breakage truck two only go 35 km straight what is the total distance between them now? A) 150 KM B) 50 Km C) 65 Km D) 85 Km

answered 4 hours ago in Mathematical Logic by Kushagra Chatterjee Junior (827 points) | 36 views

+1 vote

1 answer

3

PGEE 2018
If root of equation f(x) is 0 ar x= -3 and X= 3 then root of equation f(x+3) will be at ? A) X= 0 and X=6 B) X=-3 and X=3 C) X=-6 and X=0; D) X=-6 and X= 6

answered 6 hours ago in Set Theory & Algebra by Akhilesh Singla Active (3.1k points) | 25 views

+1 vote

1 answer

4

PGEE 2018
Which of the following tell us which day is on 14th of a particular month I) 17th is on 3rd Saturday II) the last date of the month is on Wednesday A) Only 1 is sufficient B) Only 2 is sufficient C) Both are required D) Both are insufficient

answered 6 hours ago in Mathematical Logic by Akhilesh Singla Active (3.1k points) | 27 views

+1 vote

2 answers

5

PGEE 2018
One one evening sita and gita were sitting in a park with there back facing each other sita was able to see her shadow on left at what direction was gita sitting ? A) North-East B) North C) West D) South

answered 7 hours ago in Mathematical Logic by Vipin Rai (21 points) | 42 views

+1 vote

1 answer

6

PGEE 2018
Which of the statement is sufficient to determine children of x 1) Q and U are brothers of T 2) P is the sister of U and S 3) P and T are daughters of X A) 1 and 2 B) 1,2 and 3 C) 2 and 3 D) data insufficient

answered 7 hours ago in Mathematical Logic by Mk Utkarsh Boss (11.9k points) | 22 views

0 votes

2 answers

7

PGEE 2018
Maximal Independence Number is the cardinality of maximal independence set ( Independence set V of graph G is set in which no vertex of the set have a direct edge between them). 1) Maximal Independence Number of a complete graph is n-1 2) Maximal Independence ... Maximal Independence Number of a complete graph is 1 4) Maximal Independence Number of complete graph is $\geq \frac{n}{2}$

answered 8 hours ago in Graph Theory by abhishekmehta4u Loyal (9.7k points) | 24 views

+1 vote

1 answer

8

PGEE 2018
Consider Undirected Graph G having vertex V {A,B,C,D,E} and edge pair as E {AB BD BE AC CE CD} A) Given graph is disconnected B) Given graph is complete C) Given graph has vertex connectivity 2 D) Given graph has edge connectivity 1

answered 8 hours ago in Graph Theory by abhishekmehta4u Loyal (9.7k points) | 19 views

0 votes

1 answer

9

PGEE 2018
Consider function f: N $\rightarrow$ N, where N is a natural number, which of the following function is not one to one but onto A) f(1)=f(2)=1 f(n)=n-1 B) 2n C) $n^{2}$

answered 8 hours ago in Set Theory & Algebra by abhishekmehta4u Loyal (9.7k points) | 29 views

0 votes

1 answer

10

PGEE 2018
Which of the following statement is true? 1) Exactly one of the statement is false 2) Exactly two statements are false 3) Exactly three statements are false 4) Exactly four statements are false A) II B) !V C) III D) I

answered 9 hours ago in Mathematical Logic by Akhilesh Singla Active (3.1k points) | 13 views

0 votes

2 answers

11

Number theory
Why does a perfect square number have odd number of factors?

answered 1 day ago in Mathematical Logic by pankaj_vir Loyal (6.3k points) | 16 views

+4 votes

2 answers

12

ISRO-DEC2017-9
The function $f:[0,3]\rightarrow [1,29]$ defined by $f(x)=2x^{3}-15x^{2}+36x+1$ is injective and surjective surjective but not injective injective but not surjective neither injective nor surjective

answered 1 day ago in Set Theory & Algebra by abhishekmehta4u Loyal (9.7k points) | 916 views

+1 vote

1 answer

13

UGC NET NOV 2017 PAPER II Q-9
9. Negation of the proposition › x H(x) is : (1) › x ¬ H(x) (2) ∀ x ¬ H(x) (3) ∀ x H(x) (4) ¬ x H(x)

answered 2 days ago in Mathematical Logic by Pradip Tilala (43 points) | 103 views

0 votes

3 answers

14

ISRO-DEC2017-6
The proposition $(P\Rightarrow Q)\wedge (Q\Rightarrow P)$ is a Tautology Contradiction Contingency Absurdity

answered 2 days ago in Mathematical Logic by abhishekmehta4u Loyal (9.7k points) | 709 views

+1 vote

1 answer

15

Set system and linear algebra
We have $m$ sets $A_1,A_2,A_3 \text{ to } A_m$. All $A_i \subseteq [n]$ where $ [n] = \{1,2,3, \dots n \}.$ Given that $|A_i| = \text{odd number}$ and $|A_i \cap A_j| = \text{even number }\forall i \neq j$. Show that $m \leq n$.

answered 2 days ago in Set Theory & Algebra by Sachin Mittal 1 Boss (15.5k points) | 134 views

0 votes

0 answers

16

Probability
murder takes place in an isolated village with 500 inhabitants. The police believe that red polyester fibers will have been transferred on to the murderer's clothes during the assault. Forensic experiments reveal that a probability of 0.9 can be assigned to such a transfer while the ... (a) P(guilt| fibers present) (b) P(fibres|guilt) (c) P(fibers) (d) P(guilt and fibers present). [closed]

asked 3 days ago in Mathematical Logic by Abhi Girin (419 points) | 58 views

0 votes

1 answer

17

Partial ordering
Is partial ordering and hasse diagram stuffs present in GATE 2019 Syllabus. Because topological order is already there in algorithems. Can anybody plz provide topic wise GATE 2019 Syllabus i am not getting it topic wise. Thanku in advance

answered 3 days ago in Mathematical Logic by sonveer tomar 1 Junior (891 points) | 20 views

0 votes

1 answer

18

IIT Kanpur Sample Test Paper
Given an undirected graph with vertices as your friends and edges between people who do not talk to each other. Your task is to invite as many guests to your party such that there are no two friends at the party who have problem talking to each ... instance of: A. Maximum vertex cover. B. Maximum cut. C. Maximum eigenvalue of adjacency matrix. D. None of the above.

answered 4 days ago in Graph Theory by Mk Utkarsh Boss (11.9k points) | 54 views

+1 vote

1 answer

19

CMI2010-A-06
A simple graph is one with no self-loops or multiple edges. Among the simple graphs with n vertices and at most 20n − 3 edges: There is always a graph with all vertices connected to at least 42 other vertices. For all such graphs the number of ... for some constant $c < 1$. There are no graphs with each vertex connected to at most 38 other vertices. None of the above

answered 4 days ago in Graph Theory by Mk Utkarsh Boss (11.9k points) | 86 views

0 votes

0 answers

20

#Pigeonhole Principle Doubt
How many positive integers not exceeding 1000 are divisible by 7? So, the doubt here is why we are taking floor function while calculating this .

asked 4 days ago in Combinatory by Abhinavg (127 points) | 37 views

0 votes

0 answers

21

ISI-2004-30

asked 4 days ago in Mathematical Logic by jjayantamahata Active (1.1k points) | 30 views

0 votes

0 answers

22

ISI-2004-30

asked 4 days ago in Mathematical Logic by jjayantamahata Active (1.1k points) | 37 views

0 votes

2 answers

23

CMI2017-B-5
An undirected graph is connected if, for any two vertices {u, v} of the graph, there is a path in the graph starting at u and ending at v. A tree is a connected, undirected graph that contains no cycle. (a) A leaf in a tree is a vertex that has degree 1. Prove that ... -that is, u ∈ V1 and v ∈ V2 or vice versa. Prove that if G is a tree with at least two vertices, then G is bipartite.

answered 5 days ago in Graph Theory by Mk Utkarsh Boss (11.9k points) | 85 views

0 votes

1 answer

24

ISI-2004-16

answered 5 days ago in Mathematical Logic by Kushagra Chatterjee Junior (827 points) | 15 views

0 votes

1 answer

25

Propositional logic
Sagar will marry Sheela only if She is a graduate and a good cook. Which is True ? 1.Sheela is a good cook but not a graduate hence Sagar will not marry sheela. 2.Sagar will marry sheela since she is a good cook though she is not a graduate. 3 ... and a good cook implies Sagar will marry Sheela 4.Sagar did not marry Sheela implies that she is neither a graduate nor a good cook.

answered 5 days ago in Mathematical Logic by Deepakk Poonia (Dee) Active (2.9k points) | 46 views

+1 vote

1 answer

26

Narsingh Deo Problem 2-28

answered 5 days ago in Graph Theory by Kushagra Chatterjee Junior (827 points) | 46 views

0 votes

1 answer

27

ISI-2004-23

answered 5 days ago in Mathematical Logic by Kushagra Chatterjee Junior (827 points) | 22 views

+9 votes

2 answers

28

TIFR2018-A-9
How many ways are there to assign colours from range $\left\{1,2,...,r\right\}$ to vertices of the following graph so that adjacent vertices receive distinct colours? $r^{4}$ $r^{4} - 4r^{3}$ $r^{4}-5r^{3}+8r^{2}-4r$ $r^{4}-4r^{3}+9r^{2}-3r$ $r^{4}-5r^{3}+10r^{2}-15r$

answered 6 days ago in Graph Theory by Sourav Basu Active (1.4k points) | 278 views

0 votes

1 answer

29

ISI-2004-14

answered 6 days ago in Mathematical Logic by jjayantamahata Active (1.1k points) | 9 views

0 votes

1 answer

30

PGEE Sample paper
More than one option can be correct [closed]

answered 6 days ago in Mathematical Logic by Kushagra Chatterjee Junior (827 points) | 77 views

+14 votes

6 answers

31

TIFR2015-B-5
Suppose $\begin{pmatrix} 0&1 &0&0&0&1 \\ 1&0&1&0&0&0 \\ 0&1&0&1&0&1 \\ 0&0&1&0&1&0 \\ 0&0&0&1&0&1 \\ 1&0&1&0&1&0 \end{pmatrix}$ is the adjacency matrix of an ... below has the above adjacency matrix? Only $(i)$ Only $(ii)$ Only $(iii)$ Only $(iv)$ $(i)$ and $(ii)$

answered 6 days ago in Graph Theory by Hitesh (369 points) | 572 views

0 votes

0 answers

32

PGEE Sample paper
More than one option can be correct [closed]

asked 6 days ago in Mathematical Logic by Akhilesh Singla Active (3.1k points) | 97 views

0 votes

1 answer

33

Show that the two graphs are isomorphic (Narsingh Deo)

answered 6 days ago in Graph Theory by Hitesh (369 points) | 16 views

+1 vote

1 answer

34

What are the relevant chapters for GATE from the Graph Theory book by Narsingh Deo?

answered 6 days ago in Graph Theory by Mk Utkarsh Boss (11.9k points) | 107 views

0 votes

2 answers

35

GATE question
Q. 6 Xs has to be placed in the figure below such that each row contains at least one X. In how many ways can this be done? a) 160 b) 180 c) 170 d) 26

answered 6 days ago in Combinatory by Soumya29 Loyal (5.2k points) | 66 views

+1 vote

1 answer

36

Graph Theory
Let G be a simple graph in which every vertex has degree 3. Prove that G decomposes into claws iff G is bipartite.

answered 6 days ago in Graph Theory by Kushagra Chatterjee Junior (827 points) | 13 views

0 votes

0 answers

37

Combinations with 3 Jugs
You are given 3 jugs A,B and C of capacities 8, 5 and 3 liters, respectively. A is filled and B and C are empty. Total amount of water is 8 liters. How many different combinations are possible with at least one of the jug being empty or at-least one of them being full. For example $(8,0,0)$ , $(4,4,0)$ , $(5,3,0)$ [closed]

asked 6 days ago in Combinatory by Mk Utkarsh Boss (11.9k points) | 56 views

0 votes

1 answer

38

ISI-2004-11

answered 6 days ago in Mathematical Logic by Prateek Raghuvanshi Junior (899 points) | 30 views

0 votes

1 answer

39

ISI-2004-10

answered 6 days ago in Mathematical Logic by jjayantamahata Active (1.1k points) | 15 views

0 votes

1 answer

40

ISII-2004-8

answered Apr 15 in Mathematical Logic by sonveer tomar 1 Junior (891 points) | 14 views

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