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Recent questions in Engineering Mathematics
4
votes
2
answers
7701
Conditional Probability IITB (RA) 2016
This question was asked in IITB (RA) admissions 2016. I have two blue dice, with which I play a game. If I throw a double six (i.e. if I get two six on both the dices) then I win the game. I separately throw a red dice. If I get ... rolled the three die. I turn around to you and said, "I won!". What is the probability that I actually won the game?
Utk
asked
in
Probability
May 19, 2016
by
Utk
999
views
probability
conditional-probability
gate-2016-admission
admissions
interview
1
vote
3
answers
7702
CMI2011-A-03
You have a bag with $347$ black balls and $278$ white balls. Without looking, you pick up two balls from the bag and apply the following rule. If both balls are of the same colour, you throw them both away. Otherwise, you throw away the black ... are possible, but the probability of it being white is greater. Both colours are possible, but the probability of it being black is greater.
go_editor
asked
in
Probability
May 19, 2016
by
go_editor
1.1k
views
cmi2011
probability
1
vote
1
answer
7703
CMI2011-A-02
You have two six-sided cubic dice but they are numbered in a strange manner. On the first die, two opposite faces are numbered $1$, two opposite faces are numbered $3$ and the last pair of opposite faces are numbered $6$. On the second die, the three pairs of ... than $7$. The probability that the sum is a multiple of $5$ is the same as the probability that the sum is a prime number.
go_editor
asked
in
Probability
May 19, 2016
by
go_editor
582
views
cmi2011
probability
1
vote
0
answers
7704
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 vertices ... some constant $c < 1$. There are no graphs with each vertex connected to at most $38$ other vertices. None of the above
go_editor
asked
in
Graph Theory
May 19, 2016
by
go_editor
949
views
cmi2010
graph-theory
graph-connectivity
1
vote
1
answer
7705
CMI2010-A-05
You have two normal, fair, dice, with faces labelled $1,2, \dots 6$. If you throw both dice, which of the following is true about the total value shown by the dice? The probability that the total is $6$ is less than the probability that the total is $9$. ... total is $9$. The probability that the total is $6$ is greater than the probability that the total is $9$. None of the above.
go_editor
asked
in
Probability
May 19, 2016
by
go_editor
449
views
cmi2010
probability
4
votes
2
answers
7706
CMI2010-A-04
Let $m$ and $n$ range over natural numbers and let $\text{Prime}(n)$ be true if $n$ is a prime number. Which of the following formulas expresses the fact that the set of prime numbers is infinite? $(\forall m) (\exists n) (n > m) \text{ implies Prime}(n)$ ... $(\exists n) (\forall m) (n > m) \wedge \text{Prime}(n)$
go_editor
asked
in
Mathematical Logic
May 19, 2016
by
go_editor
853
views
cmi2010
first-order-logic
19
votes
3
answers
7707
CMI2010-A-02
We need to choose a team of $11$ from a pool of $15$ players and also select a captain. The number of different ways this can be done is $ \begin{pmatrix} 15 \\ 11 \end{pmatrix}$ $11$ . $ \begin{pmatrix} 15 \\ 11 \end{pmatrix}$ $15 . 14 . 13 . 12 . 11 .10 . 9 . 8 . 7 . 6 . 5$ $(15 . 14 . 13 . 12 . 11 .10 . 9 . 8 . 7 . 6 . 5) . 11$
go_editor
asked
in
Combinatory
May 19, 2016
by
go_editor
2.3k
views
cmi2010
combinatory
normal
discrete-mathematics
3
votes
1
answer
7708
CMI2010-B-01a
An international cellphone company provides service on $7$ different frequencies. They wish to set up business in TamilNadu and have fixed the locations of $100$ towers for their new service. The company has to ensure that two towers broadcasting on the same frequency are at least $100$ km apart, so that there is no interference of signals. Model this problems using graphs.
go_editor
asked
in
Graph Theory
May 19, 2016
by
go_editor
963
views
cmi2010
descriptive
graph-theory
graph-connectivity
2
votes
2
answers
7709
CMI2010-B-02
Let $G$ be a graph in which each vertex has degree at least $k$. Show that there is a path of length $k$ in $G$—that is, a sequence of $k+1$ distinct vertices $v_0, v_1, \dots , v_k$ such that for $0 \leq i < k,$ $v_i$ is connected to $v_{i+1}$ in $G$.
go_editor
asked
in
Graph Theory
May 19, 2016
by
go_editor
625
views
cmi2010
descriptive
graph-theory
graph-connectivity
4
votes
1
answer
7710
CMI2010-B-05
Sales have slumped at the Siruseri noodle factory and the management may need to terminate the contracts of some employees. Every employee has one immediate boss. The seniormost person in the company is the president, who has no boss. For legal reasons, if an employee's contract is not terminated, then his boss's contract ...
go_editor
asked
in
Combinatory
May 19, 2016
by
go_editor
615
views
cmi2010
descriptive
combinatory
1
vote
1
answer
7711
Logic basic
Express the quantification ∃!xP(x) using Universal , Existential Quantification and Logical Connectives
Dexter
asked
in
Mathematical Logic
May 17, 2016
by
Dexter
398
views
mathematical-logic
1
vote
1
answer
7712
logic basic
Express each of these statements using qunatifers .Then form the negation of the statement so that no negation is to left of a quantifier , Next Express the negation is in Simple English (Do not simplify the words "it is the not case that ") ... ) Some students have solved every excercise in this book 5) No student has solved atleast one exercise in every section of this book
Dexter
asked
in
Mathematical Logic
May 17, 2016
by
Dexter
811
views
mathematical-logic
1
vote
1
answer
7713
Logic basic
Express each of the sentences using predicates , quantifier logical connectives and mathematical operations where the domain consists of all integers 1) The product of 2 negative number is positive 2) The average of 2 positive integers is positive 3) The difference ... negative 4) The absolute value of the sum of integers does not exceed The sum of the absolute values of these integers
Dexter
asked
in
Mathematical Logic
May 17, 2016
by
Dexter
1.3k
views
mathematical-logic
0
votes
1
answer
7714
Logic basic
Express each of these system specification using predicates , quantifier and logical connectives if necessary 1) At least one console must be accessible during every fault condition 2) The email address of every user can be retrived whenever the archieve contain ... the network 5) No one knows the password of every user on the system except system administrator who knows all passwords
Dexter
asked
in
Mathematical Logic
May 17, 2016
by
Dexter
2.3k
views
mathematical-logic
1
vote
1
answer
7715
logic basic
Let I (X) be the statement such as "X has an internet correction " and C(x,y) be the statemenet such as x and y have chatted over the internet where the domain x and y consists for all students in your class. Express each statement using ... with everyone in your class over the Internet 13) there are atleast 2 student in your class who have not chatted with th same student
Dexter
asked
in
Mathematical Logic
May 17, 2016
by
Dexter
919
views
mathematical-logic
2
votes
1
answer
7716
Logic basic
Let F (x,y) be the statement such as x can fool y .where the domain consists of all people in world . Express following statement using quantifiers Express following statement using quantifiers 1) Everybody can fool fred 2) Evelyn can fool everybody 3)Everybody ... 9) non one can fool himself or herself 10 ) There is someone who can fool exactly one person beside himself or herself
Dexter
asked
in
Mathematical Logic
May 17, 2016
by
Dexter
4.2k
views
mathematical-logic
1
vote
1
answer
7717
Logic basic
Let Q(x,y) be the statement "Student x has been a contestant on quiz show y " Express each of these statement in terms of Q(x,y) , quantifiers and logical connectives 1)There is a student at your school who has been a contestant on ... your school who has been a contestant on jeopardy and Wheel of fortune 4)Atleast 2 studnet from your school have been contestant on Jeopardy
Dexter
asked
in
Mathematical Logic
May 16, 2016
by
Dexter
1.3k
views
mathematical-logic
0
votes
1
answer
7718
Logic basic
Let T (x,y) mean that student x like cuisine y where the domain for x consists off all students at your school and domain for y consists of all cuisines. Express the following in English statement ∀x∀y∃y((x!=z)-----> ∼(T(x,y) ⋀ T(z,y)))
Dexter
asked
in
Mathematical Logic
May 16, 2016
by
Dexter
383
views
mathematical-logic
1
vote
1
answer
7719
Logic Basic
How will you translate following expression into English statement Let C(x,y) mean that student x is enrolled in class y where the domain x consists of all students in your class and domain y consists of all class beign given at your school ∃x∃y∀z((x!=y) ⋀ (C(x,z)-->C(y,z)))
Dexter
asked
in
Mathematical Logic
May 16, 2016
by
Dexter
401
views
mathematical-logic
1
vote
2
answers
7720
logic basic
Let P(x) , Q(x) and R(x) be the statements "x is a clear explantion " , "x is satisfactory " and "x is an excuse " resp Suppose that the domain x consists of all English text Express each of these using ... All clear explanation are satisfactory 2) Some excuses are unsatisfactory 3) Some excuses are not clear explanation 4) does 3 follow from 1and 2
Dexter
asked
in
Mathematical Logic
May 16, 2016
by
Dexter
505
views
mathematical-logic
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