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Recent questions in Engineering Mathematics
20
votes
4
answers
7681
CMI2014-A-01
For the inter-hostel six-a-side football tournament, a team of $6$ players is to be chosen from $11$ players consisting of $5$ forwards, $4$ defenders and $2$ goalkeepers. The team must include at least $2$ forwards, at least $2$ defenders and at least $1$ goalkeeper. Find the number of different ways in which the team can be chosen. $260$ $340$ $720$ $440$
go_editor
asked
in
Combinatory
May 27, 2016
by
go_editor
2.3k
views
cmi2014
combinatory
discrete-mathematics
normal
0
votes
2
answers
7682
Bipartite Graph
Consider the graph given below: The two distinct sets of vertices, which make the graph bipartite are: (A) (v1, v4, v6); (v2, v3, v5, v7, v8) (B) (v1, v7, v8); (v2, v3, v5, v6) (C) (v1, v4, v6, v7); (v2, v3, v5, v8) (D) (v1, v4, v6, v7, v8); (v2, v3, v5)
im.raj
asked
in
Graph Theory
May 26, 2016
by
im.raj
3.0k
views
0
votes
1
answer
7683
Which of the following is/are not true?
(a) The set of negative integers is countable. (b) The set of integers that are multiples of 7 is countable. (c) The set of even integers is countable. (d) The set of real numbers between 0 and 1/2 is countable.
im.raj
asked
in
Set Theory & Algebra
May 26, 2016
by
im.raj
1.6k
views
countable-uncountable-set
0
votes
2
answers
7684
DM/ Set Problem
S1: There exists infinite sets A, B, C such that A ∩ (B ∪ C) is finite. S2: There exists two irrational numbers x and y such that (x+y) is rational. Which of the following is true about S1 and S2? (A) Only S1 is correct and S2 is incorrect (B) Only S2 ... and S1 is not correct (C) S1 and S2 both are correct (D) S1 and S2 both are not correct (E) If you think any other options.
cse23
asked
in
Set Theory & Algebra
May 25, 2016
by
cse23
492
views
set-theory&algebra
finite-infinite-set
closure-property
3
votes
2
answers
7685
Kenneth Rosen Edition 6th Exercise 1.2 Question 30 (Page No. 29)
Show that (p ∨ q) ∧ (¬p ∨ r) → (q ∨ r) is a tautology. Prove it without Truth tables.
Shyam Singh 1
asked
in
Mathematical Logic
May 23, 2016
by
Shyam Singh 1
856
views
kenneth-rosen
discrete-mathematics
mathematical-logic
0
votes
4
answers
7686
Find the total number of ways in which the vowels in the word ' PERMUTATION ' appears in alphabetical order .
pC
asked
in
Combinatory
May 23, 2016
by
pC
2.4k
views
combinatory
1
vote
4
answers
7687
CMI2013-B-03
A simple graph is one in which there are no self loops and each pair of distinct vertices is connected by at most one edge. Show that any finite simple graph has at least two vertices with the same degree.
go_editor
asked
in
Graph Theory
May 23, 2016
by
go_editor
1.0k
views
cmi2013
descriptive
graph-theory
graph-connectivity
14
votes
3
answers
7688
CMI2013-B-02
A complete graph on $n$ vertices is an undirected graph in which every pair of distinct vertices is connected by an edge. A simple path in a graph is one in which no vertex is repeated. Let $G$ be a complete graph on $10$ vertices. Let $u$, $v$, $ w$ be three distinct vertices in $G$. How many simple paths are there from $u$ to $v$ going through $w$?
go_editor
asked
in
Graph Theory
May 23, 2016
by
go_editor
3.1k
views
cmi2013
descriptive
graph-theory
graph-connectivity
17
votes
5
answers
7689
CMI2013-A-07
Consider the following two statements. There are infinitely many interesting whole numbers. There are finitely many uninteresting whole numbers. Which of the following is true? Statements $1$ and $2$ are equivalent. Statement $1$ implies statement $2$. Statement $2$ implies statement $1$. None of the above.
go_editor
asked
in
Mathematical Logic
May 23, 2016
by
go_editor
2.3k
views
cmi2013
mathematical-logic
logical-reasoning
19
votes
6
answers
7690
CMI2013-A-06
A simple graph is one in which there are no self-loops and each pair of distinct vertices is connected by at most one edge. Let $G$ be a simple graph on $8$ vertices such that there is a vertex of degree $1$, a vertex of degree $2$, a vertex of degree $3$, a vertex ... degree $6$ and a vertex of degree $7$. Which of the following can be the degree of the last vertex? $3$ $0$ $5$ $4$
go_editor
asked
in
Graph Theory
May 23, 2016
by
go_editor
5.2k
views
cmi2013
graph-theory
normal
degree-of-graph
13
votes
5
answers
7691
CMI2013-A-02
$10\%$ of all email you receive is spam. Your spam filter is $90\%$ reliable: that is, $90\%$ of the mails it marks as spam are indeed spam and $90\%$ of spam mails are correctly labeled as spam. If you see a mail marked spam by your filter, what is the probability that it really is spam? $10\%$ $50\%$ $70\%$ $90\%$
go_editor
asked
in
Probability
May 23, 2016
by
go_editor
7.8k
views
cmi2013
probability
conditional-probability
11
votes
1
answer
7692
CMI2012-B-01
Let $G=(V, E)$ be a graph where $\mid V \mid =n$ and the degree of each vertex is strictly greater than $\frac{n}{2}$. Prove that $G$ has a Hamiltonian path. (Hint: Consider a path of maximum length in $G$.)
go_editor
asked
in
Graph Theory
May 23, 2016
by
go_editor
964
views
cmi2012
descriptive
graph-theory
graph-connectivity
8
votes
5
answers
7693
CMI2012-A-07
A man has three cats. At least one is male. What is the probability that all three are male? $\frac{1}{2}$ $\frac{1}{7}$ $\frac{1}{8}$ $\frac{3}{8}$
go_editor
asked
in
Probability
May 22, 2016
by
go_editor
2.0k
views
cmi2012
probability
4
votes
2
answers
7694
CMI2012-A-02
Let $T$ be a tree on 100 vertices. Let $n_i$ be the number of vertices in $T$ which have exactly $i$ neighbors. Let $s= \Sigma_{i=1}^{100} i . n_i$ Which of the following is true? $s=99$ $s=198$ $99 \: < \: s \: < \: 198$ None of the above
go_editor
asked
in
Graph Theory
May 22, 2016
by
go_editor
844
views
cmi2012
graph-theory
tree
0
votes
1
answer
7695
power set
Sourabh Kumar
asked
in
Mathematical Logic
May 20, 2016
by
Sourabh Kumar
912
views
set-theory
3
votes
1
answer
7696
CMI2011-B-02a
Let $G$ be a connected graph. For a vertex $x$ of $G$ we denote by $G−x$ the graph formed by removing $x$ and all edges incident on $x$ from $G$. $G$ is said to be good if there are at least two distinct vertices $x, y$ in $G$ such that both $G − x$ and $G − y$ are connected. Show that for any subgraph $H$ of $G$, $H$ is good if and only if $G$ is good.
go_editor
asked
in
Set Theory & Algebra
May 19, 2016
by
go_editor
551
views
cmi2011
descriptive
graph-connectivity
proof
1
vote
2
answers
7697
CMI2011-B-01a
A multinational company is developing an industrial area with many buildings. They want to connect the buildings with a set of roads so that: Each road connects exactly two buildings. Any two buildings are connected via a sequence of roads. Omitting any road ... it always possible to colour each building with either red or blue so that every road connects a red and blue building?
go_editor
asked
in
Graph Theory
May 19, 2016
by
go_editor
683
views
cmi2011
descriptive
graph-coloring
24
votes
4
answers
7698
CMI2011-A-07
Let $G=(V, E)$ be a graph. Define $\overline{G}$ to be $(V, \overline{E})$, where for all $u, \: v \: \in V \: , (u, v) \in \overline{E}$ if and only if $(u, v) \notin E$. Then which of the following is true? $\overline{G}$ is always ... $G$ is not connected. At least one of $G$ and $\overline{G}$ connected. $G$ is not connected or $\overline{G}$ is not connected
go_editor
asked
in
Graph Theory
May 19, 2016
by
go_editor
1.8k
views
cmi2011
graph-theory
graph-connectivity
2
votes
2
answers
7699
CMI2011-A-05
A $\text{3-ary}$ boolean function is a function that takes three boolean arguments and produces a boolean output. Let $f$ and $g$ be $\text{3-ary}$ boolean functions. We say that $f$ and $g$ are neighbours if $f$ and $g$ agree on at least one input and disagree on at ... $\text{3-ary}$ boolean function $h$. How many neighbours does $h$ have? $128$ $132$ $254$ $256$
go_editor
asked
in
Set Theory & Algebra
May 19, 2016
by
go_editor
1.0k
views
cmi2011
functions
2
votes
1
answer
7700
Probability IITB (RA) 2016
This question was asked in IITB (RA) 2016 admissions. Three person A, B and C each have a bag of five different coloured balls. All three bags have balls from same five colours. A grabs B and C's bag and took two balls without ... took two balls and put them in his bag without looking. What is the probability that all three bags have different coloured balls?
Utk
asked
in
Probability
May 19, 2016
by
Utk
990
views
probability
gate-2016-admission
admissions
iit-bombay
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