Recent questions in Discrete Mathematics

+2 votes

1 answer

1

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

asked Aug 8 in Combinatory by Shaik Masthan Veteran (62k points) | 76 views

+2 votes

2 answers

2

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

asked Jul 2 in Set Theory & Algebra by Arjun Veteran (416k points) | 251 views

+1 vote

2 answers

3

UGCNET-June-2019-II-2
How many ways are there to place $8$ indistinguishable balls into four distinguishable bins? $70$ $165$ $^8C_4$ $^8P_4$

asked Jul 2 in Combinatory by Arjun Veteran (416k points) | 181 views

+1 vote

2 answers

4

UGCNET-June-2019-II-3
How many bit strings of length ten either start with a $1$ bit or end with two bits $00$ ? $320$ $480$ $640$ $768$

asked Jul 2 in Combinatory by Arjun Veteran (416k points) | 116 views

+2 votes

1 answer

5

UGCNET-June-2019-II-4
Suppose that a connected planar graph has six vertices, each of degree four. Into how many regions is the plane divided by a planar representation of this graph? $6$ $8$ $12$ $20$

asked Jul 2 in Graph Theory by Arjun Veteran (416k points) | 93 views

+3 votes

1 answer

6

UGCNET-June-2019-II-5
For which values of $m$ and $n$ does the complete bipartite graph $k_{m,n}$ have a Hamiltonian circuit ? $m\neq n,\ \ m,n \geq 2$ $m\neq n,\ \ m,n \geq 3$ $m=n,\ \ m,n \geq 2$ $m= n,\ \ m,n \geq 3$

asked Jul 2 in Graph Theory by Arjun Veteran (416k points) | 75 views

+2 votes

2 answers

7

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 $ $\rceil p \vee q$ $\rceil p\ \vee \rceil q$

asked Jul 2 in Mathematical Logic by Arjun Veteran (416k points) | 87 views

+1 vote

1 answer

8

UGCNET-June-2019-II-7
How many cards must be selected from a standard deck of $52$ cards to guarantee that at least three hearts are present among them? $9$ $13$ $17$ $42$

asked Jul 2 in Combinatory by Arjun Veteran (416k points) | 90 views

+2 votes

2 answers

9

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)

asked Jul 2 in Mathematical Logic by Arjun Veteran (416k points) | 72 views

+1 vote

2 answers

10

UGCNET-June-2019-II-9
Find the zero-one matrix of the transitive closure of the relation given by the matrix $A$ : $A =\begin{bmatrix} 1 & 0& 1\\ 0 & 1 & 0\\ 1& 1& 0 \end{bmatrix}$ ... $\begin{bmatrix} 1 & 1& 1\\ 0 & 1 & 0\\ 1& 0& 1 \end{bmatrix}$

asked Jul 2 in Set Theory & Algebra by Arjun Veteran (416k points) | 80 views

+1 vote

1 answer

11

UGCNET-June-2019-II-13
How many different Boolean functions of degree $n$ are the $2^{2^n}$ $(2^2)^n$ $2^{2^n} -1$ $2^n$

asked Jul 2 in Set Theory & Algebra by Arjun Veteran (416k points) | 54 views

+2 votes

1 answer

12

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 $\phi(45)$? $3$ $12$ $6$ $24$

asked Jul 2 in Combinatory by Arjun Veteran (416k points) | 39 views

+1 vote

1 answer

13

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 $P_2$

asked Jul 2 in Graph Theory by Arjun Veteran (416k points) | 31 views

0 votes

1 answer

14

GATE1995-25b
Determine the number of positive integers $(\leq 720)$ which are not divisible by any of $2,3$ or $5.$

asked Jun 6 in Set Theory & Algebra by Arjun Veteran (416k points) | 148 views

0 votes

0 answers

15

#ACE ACADEMY BOOKLET QUESTION
The solution of $\sqrt{a_n} – 2\sqrt{a_{n-1}} + \sqrt{a_{n-2}} = 0$ where $a_0 = 1$ and $a_1 = 2$ is ${\Big[\frac{2^{n+1} + (-1)^n}{3}\Big]}^2$ $(n+1)^2$ $(n-1)^3$ $(n-1)^2$

asked Jun 5 in Combinatory by `JEET Active (3.5k points) | 90 views

+1 vote

1 answer

16

Mathematical Logic Ques:Self doubt
“Not every satisfiable logic is valid” Representation of it will be $1)\sim \left ( \forall S(x)\rightarrow V(x) \right )$ or $2)\sim \left ( \forall S(x)\vee V(x) \right )$ Among $1)$ and $2)$, which one is correct? and why?

asked Jun 4 in Mathematical Logic by srestha Veteran (113k points) | 112 views

0 votes

0 answers

17

Doubt on a math question
Chk this question https://gateoverflow.in/100202/test-series-counting $1)$Can someone verify this ans?? See if $\left ( _{0}^{6}\textrm{C} \right )$ in one set, other set will contain $\left ( _{6}^{6}\textrm{C} \right )$ elements. right?? Now why do we again need $2^{n}$ ... meaning of it?? $2)$ How $\sum_{I=0}^{n}\left ( _{i}^{n}\textrm{C} \right ).2^{n-i}=3^{n}$??

asked Jun 4 in Set Theory & Algebra by srestha Veteran (113k points) | 28 views

+1 vote

1 answer

18

Doubt on GATE Question
Read the statements: All women are entrepreneurs. Some women are doctors. Which of the following conclusions can be logically inferred from the above statements? All women are doctors All doctors are entrepreneurs All entrepreneurs are women Some entrepreneurs are doctors ... Is it because , if we make set of doctor as 0, then All doctors are entrepreneurs is meaningless.

asked Jun 1 in Mathematical Logic by srestha Veteran (113k points) | 47 views

0 votes

0 answers

19

#Rosen exercise-1 ,question-71 counting
use mathematical induction to prove the sum rule for m tasks from the sum rule for two tasks.

asked May 31 in Combinatory by sandeep singh gaur (251 points) | 30 views

+1 vote

1 answer

20

Mathematical Logic: Doubt on meaning of statement
The notation $\exists ! x P(x)$ denotes the proposition there exists a unique $x$ such that $P(x)$ ... What will be answer here?? Is the assumption only for left hand side and not right hand side??

asked May 31 in Mathematical Logic by srestha Veteran (113k points) | 74 views

+1 vote

0 answers

21

Descrete Mathematic ACE Text Book Practice Question #16
A women's health clinic has four doctors and each patient is assigned to one of them. If a patient givs birth btween 8 am and 4 pm, then her chance of being attended by her assigned doctor is 3/4, otherwise it is 1/4. What is the probability that ... is attended by the assigned doctor when she gives birth? (A) 25/144 (B) 5/12 (C) 7/12 (D) 1/12 [closed]

asked May 30 in Mathematical Logic by JAYKISHAN (89 points) | 65 views

0 votes

1 answer

22

Proposition Logic Question
Are these propositions? 1.This sentence is true 2.This sentence is false Aren’t these liar paradox?

asked May 30 in Mathematical Logic by Reshu $ingh (253 points) | 110 views

0 votes

0 answers

23

Ace booklet functions page:152 q.no 44
Let A, B, C are k element sets and let S be an n element set where k<=n. How many triples of functions f:A->S, g:B->S, h:C->S are there such that f, g and h are all injective and f(A) =g(B) =h(C) =?

asked May 27 in Set Theory & Algebra by chandan2teja (127 points) | 22 views

+2 votes

3 answers

24

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 $T$

asked May 26 in Graph Theory by `JEET Active (3.5k points) | 96 views

+2 votes

3 answers

25

Ace academy booklet #graph theory
Which of the following is $\textbf{not}$ TRUE? (a) In a complete graph $K_n$ ($n$ $\geq$ $3$), Euler circuit exists $\Leftrightarrow$ $n$ is odd. (b) In a complete bipartite graph $K_{m,n}$ (m $\geq$ 2 and n $\geq$2), Euler circuit exists ... Euler circuit exits for all $n$ (d) In a wheel graph $W_n$ ($n \geq 4$), Euler circuit exits $\Leftrightarrow$ $n$ is even.

asked May 26 in Graph Theory by `JEET Active (3.5k points) | 51 views

+1 vote

1 answer

26

ACE ACADEMY BOOKLET
Which of the following is $\textbf{not}$ TRUE? (a) In a complete graph $K_n$ ($n$ $\geq$ $3$), Hamiltonian cycle exists for all n. (b) In a complete bipartite graph $K_{m,n}$ (m $\geq$ 2 and n $\geq$2), Hamiltonian cycle exists $\Leftrightarrow$ ... Hamiltonian cycle exits for all $n$ (d) In a wheel graph $W_n$ ($n \geq 4$), Hamiltonian cycle exits $\Leftrightarrow$ $n$ is even.

asked May 26 in Graph Theory by `JEET Active (3.5k points) | 49 views

+1 vote

2 answers

27

#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.

asked May 26 in Graph Theory by `JEET Active (3.5k points) | 70 views

0 votes

0 answers

28

Ace workbook lattice concept
If X is minimum element of S then X is related to y for all y belongs to S. Let [S;R] be a poset. If every non empty subset of S has a minimum element then a) S is Totally ordered set b) S is bounded set. C) S is complemented ... then 1 will be part of every non empty subset of S. Is this correct way of interpreting the question. If not can you please elaborate it

asked May 26 in Set Theory & Algebra by chandan2teja (127 points) | 22 views

0 votes

0 answers

29

Self Doubt-LA
In a non-homogeneous equation Ax = b, x has a unique solution when $A^{-1}$ exists i.e x = $A^{-1}$b but when det(A) = 0 then we have infinite solution or many solution. please give a mathematical explanation of how the 2nd statement occurs?

asked May 26 in Mathematical Logic by MRINMOY_HALDER Active (1.7k points) | 34 views

0 votes

3 answers

30

Self Doubt-Combinatory
In how many ways we can put $n$ distinct balls in $k$ dintinct bins?? Will it be $n^{k}$ or $k^{n}$?? Taking example will be easy way to remove this doubt or some other ways possible??

asked May 25 in Combinatory by srestha Veteran (113k points) | 86 views

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