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Recent questions and answers in Engineering Mathematics
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1
CMI2011B02a
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.
answered
May 21
in
Set Theory & Algebra
by
Kushagra Chatterjee
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cmi2011
descriptive
graphconnectivity
proof
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Sheldon Ross, Chapter #4, Question #13
An airline operates a flight having 50 seats. As they expect some passenger to not show up, they overbook the flight by selling 51 tickets. The probability that an individual passenger will not show up is 0.01, independent of all other ... the airline has to pay a compensation of Rs.1lakh to that passenger. What is the expected revenue of the airline?
asked
May 21
in
Probability
by
Asim Siddiqui 4
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809
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13
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probability
randomvariable
sheldonross
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3
Made Easy Test Series:Lattice
The number of totally ordered set compatible to the given POSET are __________
answered
May 20
in
Set Theory & Algebra
by
Satbir
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7.5k
points)

29
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madeeasytestseries
lattice
0
votes
1
answer
4
ISI2018MMA15
Let $G$ be a finite group of even order. Then which of the following statements is correct? The number of elements of order $2$ in $G$ is even The number of elements of order $2$ in $G$ is odd $G$ has no subgroup of order $2$ None of the above.
answered
May 20
in
Set Theory & Algebra
by
Harsh Kumar
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8
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isi2018
engineeringmathematics
discretemathematics
settheory&algebra
groups
+1
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1
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5
ISI2018PCBA1
Consider a $n \times n$ matrix $A=I_n\alpha\alpha^T$, where $I_n$ is the $n\times n$ identity matrix and $\alpha$ is an $n\times 1$ column vector such that $\alpha^T\alpha=1$.Show that $A^2=A$.
answered
May 20
in
Linear Algebra
by
Kaustubh Vande
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11
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30
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isi2018pcba
engineeringmathematics
linearalgebra
matrices
descriptive
0
votes
1
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6
Discrete mathematics #TEST_BOOK
I Have doubt about the language. Is it asking about the sum of elements if we make the GBL set for the given lattice .
answered
May 20
in
Set Theory & Algebra
by
Arkaprava
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1.1k
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#discrete
#lattice
+1
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1
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7
GateForum Question Bank :Graph Theory
What is the probability that there is an edge in an undirected random graph having 8 vertices? 1 1/8
answered
May 20
in
Graph Theory
by
srestha
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114k
points)

51
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graphtheory
discretemathematics
+1
vote
2
answers
8
CMI2011B01b
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. ... preferred roads differing in at least one road? Substantiate your answers by either proving the assertion or providing a counterexample.
answered
May 19
in
Graph Theory
by
Arjun
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400k
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121
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cmi2011
descriptive
graphtheory
graphconnectivity
0
votes
2
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9
Made Easy Test Series:Discrete MathematicsPoset
Consider the following Posets: $I)\left ( \left \{ 1,2,5,7,10,14,35,70 \right \},\leq \right )$ $II)\left ( \left \{ 1,2,3,6,14,21,42 \right \},/ \right )$ $III)\left ( \left \{ 1,2,3,6,11,22,33,66 \right \},/ \right )$ Which of the above poset are isomorphic to $\left ( P\left ( S \right ),\subseteq \right )$ where $S=\left \{ a,b,c \right \}?$
answered
May 18
in
Set Theory & Algebra
by
Hirak
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2k
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30
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poset
madeeasytestseries
discretemathematics
0
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0
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10
Self Doubt:Mathematical Logic
Represent these two statement in first order logic: $A)$ Only Alligators eat humans $B)$ Every Alligator eats humans Is Every represents $\equiv \exists$ and Only represents $\equiv \forall$ ?? Can we differentiate it with verb ‘eat’ and ‘eats’??
asked
May 18
in
Mathematical Logic
by
srestha
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114k
points)

13
views
discretemathematics
mathematicallogic
firstorderlogic
+1
vote
2
answers
11
GATE19894vii
Provide short answers to the following questions: In the graph shown above, the depthfirst spanning tree edges are marked with a 'T'. Identify the forward, backward and cross edges.
answered
May 18
in
Graph Theory
by
Arjun
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400k
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258
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gate1989
descriptive
graphtheory
spanningtree
0
votes
1
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12
ACE Workbook:
ACE Workbook: Q) Let G be a simple graph(connected) with minimum number of edges. If G has n vertices with degree1,2 vertices of degree 2, 4 vertices of degree 3 and 3 vertices of degree4, then value of n is ? Can anyone give the answer and how to approach these problems. Thanks in advance.
answered
May 17
in
Graph Theory
by
pdeshal
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11
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37
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graphtheory
+3
votes
1
answer
13
Limits
answered
May 16
in
Calculus
by
Satbir
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7.5k
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87
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limits
engineeringmathematics
calculus
+2
votes
1
answer
14
madeEasy Test Series 2018: Calculas  Limits
The value of $\lim_{x\rightarrow \infty }\left ( \frac{4^{x+2} + 3^{x}}{4^{x2}} \right )$ is
answered
May 16
in
Calculus
by
Satbir
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104
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engineeringmathematics
calculus
limits
madeeasytestseries
+12
votes
4
answers
15
GATE201514
$\lim_{x\rightarrow \infty } x^{ \tfrac{1}{x}}$ is $\infty $ 0 1 Not defined
answered
May 16
in
Calculus
by
Satbir
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7.5k
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2k
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gate20151
calculus
limits
normal
0
votes
2
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16
ISI2019MMA22
A coin with probability $p (0 < p < 1)$ of getting head, is tossed until a head appears for the first time. If the probability that the number of tosses required is even is $2/5$, then the value of $p$ is $2/7$ $1/3$ $5/7$ $2/3$
answered
May 16
in
Probability
by
noob_coder
(
251
points)

100
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isi2019
probability
0
votes
1
answer
17
ISI2018MMA18
Let $A_1 = (0, 0), A_2 = (1, 0), A_3 = (1, 1)\ $and$\ A_4 = (0, 1)$ be the four vertices of a square. A particle starts from the point $A_1$ at time $0$ and moves either to $A_2$ or to $A_4$ with equal probability. Similarly, in each of the subsequent ... $T$ be the minimum number of steps required to cover all four vertices. The probability $P(T = 4)$ is $0$ $1/16$ $1/8$ $1/4$
answered
May 16
in
Probability
by
radadiyamohit
(
11
points)

18
views
isi2018
engineeringmathematics
probability
0
votes
0
answers
18
Discrete Mathematics by Kenneth Rosen,section2.4,recursive functions
$C_{a}^{k}:\mathbb{N}^{k}\rightarrow \mathbb{N}$ I am studying discrete math from beginnings and came across this term in primitive recursive function.I don't know what $C_{a}^{k}$ means and does $\mathbb{N}$ means set of natural numbers?Someone please help me out.
asked
May 15
in
Set Theory & Algebra
by
souren
(
21
points)

31
views
discretemathematics
settheory&algebra
kennethrosen
0
votes
2
answers
19
Ace Test Series: Probability  Uniform Distribution
answered
May 15
in
Probability
by
noob_coder
(
251
points)

101
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randomvariable
probability
expectation
uniformdistribution
acetestseries
0
votes
2
answers
20
UGCNETDec2012III25
The number of distinct bracelets of five beads made up of red, blue and green beads (two bracelets are indistinguishable if the rotation of one yield another) is, 243 81 51 47
answered
May 15
in
Combinatory
by
Kuljeet Shan
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1.3k
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1.5k
views
ugcnetdec2012iii
0
votes
1
answer
21
#GATE 2014 IN
answered
May 14
in
Linear Algebra
by
Satbir
Loyal
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7.5k
points)

22
views
0
votes
1
answer
22
Recurrence Relation SelfDoubt
What will be solution of recurrence relation if roots are like this: r1=2, r2=2, r3=2, r4=2 is this the case of repetitive roots?
answered
May 14
in
Combinatory
by
Raghava45
(
321
points)

28
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relations
recurrence
recurrenceeqation
discretemathematics
combinational
0
votes
1
answer
23
GATE 2015 SET2 Q 29
Let the random variable X represent the number of times a fair coin needs to be tossed till two consecutive heads appear for the first time. The expectation of X is _______.
answered
May 14
in
Probability
by
Alakhator
(
89
points)

142
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probability
usergate2015
usermod
expectation
0
votes
2
answers
24
Recurrence Relation
Let $T(n) = T(n1) + \frac{1}{n} , T(1) = 1 ;$ then $T(n) = ? $ $O(n^{2})$ $O(logn)$ $O(nlogn)$ $O(n^{2}logn)$
answered
May 14
in
Combinatory
by
Raghava45
(
321
points)

123
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discretemathematics
recurrence
relations
recurrenceeqation
0
votes
0
answers
25
Rosen 7e Exercise 8.2 Questionno26 page no525 Recurrence Relation
What is the general form of the particular solution guaranteed to exist of the linear nonhomogeneous recurrence relation $a_n$=$6a_{n1}$$12a_{n2}$+$8a_{n3}$+F(n) if F(n)=$n^2$ F(n)=$2^n$ F(n)=$n2^n$ F(n)=$(2)^n$ F(n)=$n^22^n$ F(n)=$n^3(2)^n$ F(n)=3
asked
May 14
in
Combinatory
by
aditi19
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24
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kennethrosen
discretemathematics
#recurrencerelations
recurrence
0
votes
0
answers
26
Rosen 7e Exercise8.2 Question no23 page no525 Recurrence Relation
Consider the nonhomogeneous linear recurrence relation $a_n$=$3a_{n1}$+$2^n$ in the book solution is given $a_n$=$2^{n+1}$ but I’m getting $a_n$=$3^{n+1}2^{n+1}$
asked
May 13
in
Combinatory
by
aditi19
Active
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3.5k
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17
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kennethrosen
discretemathematics
#recurrencerelations
recurrence
0
votes
1
answer
27
ISI2018MMA10
A new flag of ISI club is to be designed with $5$ vertical strips using some or all of the four colors: green, maroon, red and yellow. In how many ways this can be done so that no two adjacent strips have the same color? $120$ $324$ $424$ $576$
answered
May 13
in
Combinatory
by
Sayan Bose
Loyal
(
6.9k
points)

20
views
isi2018
engineeringmathematics
discretemathematics
permutationsandcombinations
+1
vote
6
answers
28
GATE201913
Compute $\lim_{x \rightarrow 3} \frac{x^481}{2x^25x3}$ $1$ $53/12$ $108/7$ Limit does not exist
answered
May 13
in
Calculus
by
Bikki_gupta
(
59
points)

1.6k
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gate2019
engineeringmathematics
calculus
limits
0
votes
1
answer
29
ISI2019MMA21
A function $f:\mathbb{R^2} \rightarrow \mathbb{R}$ is called degenerate on $x_i$, if $f(x_1,x_2)$ remains constant when $x_i$ varies $(i=1,2)$. Define $f(x_1,x_2) = \mid 2^{\pi _i/x_1} \mid ^{x_2} \text{ for } x_1 \neq 0$, where $i = \sqrt {1}$. ... $x_1$ but not on $x_2$ $f$ is degenerate on $x_2$ but not on $x_1$ $f$ is neither degenerate on $x_1$ nor on $x_2$
answered
May 13
in
Calculus
by
pratekag
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372
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isi2019
engineeringmathematics
calculus
0
votes
2
answers
30
#probability(self doubt)
An automobile showroom has 10 cars, 2 of which are defective. If you are going to buy the 6th car sold that day at random, then the probability of selecting a defective car is??
answered
May 13
in
Combinatory
by
srestha
Veteran
(
114k
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30
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#probability
self
doubt
0
votes
1
answer
31
ISI2018MMA20
Consider the set of all functions from $\{1, 2, . . . ,m\}$ to $\{1, 2, . . . , n\}$,where $n > m$. If a function is chosen from this set at random, the probability that it will be strictly increasing is $\binom{n}{m}/n^m\\$ $\binom{n}{m}/m^n\\$ $\binom{m+n1}{m1}/n^m\\$ $\binom{m+n1}{m}/m^n$
answered
May 12
in
Probability
by
Arkaprava
Active
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1.1k
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22
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isi2018
engineeringmathematics
probability
0
votes
1
answer
32
ISI2018PCBB3
An $n$variable Boolean function $f:\{0,1\}^n \rightarrow \{0,1\} $ is called symmetric if its value depends only on the number of $1’s$ in the input. Let $\sigma_n $ denote the number of such functions. Calculate the value of $\sigma_4$. Derive an expression for $\sigma_n$ in terms of $n$.
answered
May 12
in
Set Theory & Algebra
by
Arkaprava
Active
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1.1k
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10
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isi2018pcbb
engineeringmathematics
discretemathematics
settheory&algebra
functions
descriptive
0
votes
1
answer
33
ISI2018PCBA4
Let $A$ and $B$ are two nonempty finite subsets of $\mathbb{Z}$, the set of all integers. Define $A+B=\{a+b:a\in A,b\in B\}$.Prove that $A+B\geq A +B 1 $, where $S$ denotes the cardinality of finite set $S$.
answered
May 12
in
Set Theory & Algebra
by
Arkaprava
Active
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1.1k
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16
views
isi2018pcba
engineeringmathematics
discretemathematics
settheory&algebra
descriptive
0
votes
1
answer
34
ISI2018MMA17
There are eight coins, seven of which have the same weight and the other one weighs more. In order to find the coin having more weight, a person randomly chooses two coins and puts one coin on each side of a common balance. If these two coins are found to have the same ... as before. The probability that the coin will be identified at the second draw is $1/2$ $1/3$ $1/4$ $1/6$
answered
May 12
in
Probability
by
bholebaba
(
11
points)

22
views
isi2018
engineeringmathematics
probability
0
votes
1
answer
35
ISI2018MMA13
If $A =\begin{bmatrix} 2 &i \\ i & 0 \end{bmatrix}$ , the trace of $A^{10}$ is $2$ $2(1+i)$ $0$ $2^{10}$
answered
May 12
in
Linear Algebra
by
Sayan Bose
Loyal
(
6.9k
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27
views
isi2018
engineeringmathematics
linearalgebra
determinant
+1
vote
1
answer
36
ISI2018MMA26
Let $C_i(i=0,1,2...n)$ be the coefficient of $x^i$ in $(1+x)^n$.Then $\frac{C_0}{2} – \frac{C_1}{3}+\frac{C_2}{4}\dots +(1)^n \frac{C_n}{n+2}$ is equal to $\frac{1}{n+1}\\$ $\frac{1}{n+2}\\$ $\frac{1}{n(n+1)}\\$ $\frac{1}{(n+1)(n+2)}$
answered
May 11
in
Combinatory
by
srestha
Veteran
(
114k
points)

99
views
isi2018
engineeringmathematics
discretemathematics
generatingfunctions
0
votes
0
answers
37
ISI2018MMA28
Consider the following functions $f(x)=\left\{\begin{matrix} 1 &, if\ x \leq 1 \\ 0 & ,if\ x>1 \end{matrix}\right.$ ... at $ 1$ $h_2$ is continuous everywhere and $h_1$ has discontinuity at $ 2$ $h_1$ has discontinuity at $ 2$ and $h_2$ has discontinuity at $ 1$.
asked
May 11
in
Calculus
by
akash.dinkar12
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40.5k
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19
views
isi2018
engineeringmathematics
calculus
continuity
0
votes
0
answers
38
ISI2018MMA30
Consider the function $f(x)=\bigg(1+x+\frac{x^2}{2!}+\frac{x^3}{3!}+\dots+\frac{x^n}{n!}\bigg)e^{x}$, where $n\geq4$ is a positive integer. Which of the following statements is correct? $f$ has no local maximum For every $n$, $f$ has a local maximum at $x = 0$ ... at $x = 0$ when $n$ is even $f$ has no local extremum if $n$ is even and has a local maximum at $x = 0$ when $n$ is odd.
asked
May 11
in
Calculus
by
akash.dinkar12
Boss
(
40.5k
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26
views
isi2018
engineeringmathematics
calculus
maximaminima
0
votes
0
answers
39
ISI2018MMA29
Let $f$ be a continuous function with $f(1) = 1$. Define $F(t)=\int_{t}^{t^2}f(x)dx$. The value of $F’(1)$ is $2$ $1$ $1$ $2$
asked
May 11
in
Calculus
by
akash.dinkar12
Boss
(
40.5k
points)

33
views
isi2018
engineeringmathematics
calculus
integration
0
votes
1
answer
40
ISI2018MMA19
Let $X_1,X_2, . . . ,X_n$ be independent and identically distributed with $P(X_i = 1) = P(X_i = −1) = p\ $and$ P(X_i = 0) = 1 − 2p$ for all $i = 1, 2, . . . , n.$ ... $a_n \rightarrow p, b_n \rightarrow p,c_n \rightarrow 12p$ $a_n \rightarrow1/2, b_n \rightarrow1/2,c_n \rightarrow0$ $a_n \rightarrow0, b_n \rightarrow0,c_n \rightarrow1$
answered
May 11
in
Calculus
by
srestha
Veteran
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114k
points)

23
views
isi2018
engineeringmathematics
calculus
limits
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