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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
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Aug 8
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Combinatory
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Shaik Masthan
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permutationandcombination
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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
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Jul 2
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Set Theory & Algebra
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Arjun
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251
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ugcnetjune2019ii
poset
settheory&algebra
+1
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2
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3
UGCNETJune2019II2
How many ways are there to place $8$ indistinguishable balls into four distinguishable bins? $70$ $165$ $^8C_4$ $^8P_4$
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Jul 2
in
Combinatory
by
Arjun
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416k
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181
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ugcnetjune2019ii
permutationandcombination
+1
vote
2
answers
4
UGCNETJune2019II3
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
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416k
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116
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ugcnetjune2019ii
permutationandcombination
inclusionexclusion
+2
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1
answer
5
UGCNETJune2019II4
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
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416k
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93
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ugcnetjune2019ii
graphplanarity
handshakingtheorem
+3
votes
1
answer
6
UGCNETJune2019II5
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
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Arjun
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416k
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75
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ugcnetjune2019ii
graphtheory
+2
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2
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7
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 $ $\rceil p \vee q$ $\rceil p\ \vee \rceil q$
asked
Jul 2
in
Mathematical Logic
by
Arjun
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416k
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87
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ugcnetjune2019ii
propositionallogic
+1
vote
1
answer
8
UGCNETJune2019II7
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
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416k
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90
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ugcnetjune2019ii
permutationandcombination
pigeonholeprinciple
+2
votes
2
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9
UGCNETJune2019II8
Match ListI with ListII: ... )  (iv); (b)  (i); (c)  (iii); (d)  (ii) (a)  (iv); (b)  (iii); (c)  (i); (d)  (ii)
asked
Jul 2
in
Mathematical Logic
by
Arjun
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416k
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72
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ugcnetjune2019ii
propositionallogic
+1
vote
2
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10
UGCNETJune2019II9
Find the zeroone 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
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80
views
ugcnetjune2019ii
settheory&algebra
+1
vote
1
answer
11
UGCNETJune2019II13
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
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416k
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54
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ugcnetjune2019ii
boolean
function
+2
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1
answer
12
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 $\phi(45)$? $3$ $12$ $6$ $24$
asked
Jul 2
in
Combinatory
by
Arjun
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416k
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39
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ugcnetjune2019ii
eulerphifunction
+1
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1
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13
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 $P_2$
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Jul 2
in
Graph Theory
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Arjun
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31
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ugcnetjune2019ii
flownetwork
0
votes
1
answer
14
GATE199525b
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
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416k
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148
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gate1995
settheory&algebra
numericalanswers
sets
0
votes
0
answers
15
#ACE ACADEMY BOOKLET QUESTION
The solution of $\sqrt{a_n} – 2\sqrt{a_{n1}} + \sqrt{a_{n2}} = 0$ where $a_0 = 1$ and $a_1 = 2$ is ${\Big[\frac{2^{n+1} + (1)^n}{3}\Big]}^2$ $(n+1)^2$ $(n1)^3$ $(n1)^2$
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Jun 5
in
Combinatory
by
`JEET
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90
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discretemathematics
permutationandcombination
recurrence
#recurrencerelations
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1
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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?
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Jun 4
in
Mathematical Logic
by
srestha
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113k
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112
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discretemathematics
mathematicallogic
0
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17
Doubt on a math question
Chk this question https://gateoverflow.in/100202/testseriescounting $1)$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 $\sum_{I=0}^{n}\left ( _{i}^{n}\textrm{C} \right ).2^{ni}=3^{n}$??
asked
Jun 4
in
Set Theory & Algebra
by
srestha
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113k
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28
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discretemathematics
settheory&algebra
+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
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113k
points)

47
views
discretemathematics
mathematicallogic
0
votes
0
answers
19
#Rosen exercise1 ,question71 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
counting
+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
mathematicallogic
discretemathematics
+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
probability
acebooklet
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
mathematicallogic
propositionallogic
discretemathematics
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 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 $T$
asked
May 26
in
Graph Theory
by
`JEET
Active
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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
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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
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(
3.5k
points)

49
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graphtheory
discretemathematics
+1
vote
2
answers
27
#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.
asked
May 26
in
Graph Theory
by
`JEET
Active
(
3.5k
points)

70
views
discretemathematics
graphtheory
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 DoubtLA
In a nonhomogeneous 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
linearalgebra
systemofequations
0
votes
3
answers
30
Self DoubtCombinatory
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
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86
views
discretemathematics
permutationandcombination
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