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Recent questions and answers in Engineering Mathematics
+1
vote
1
answer
1
GATE19989
Derive the expressions for the number of operations required to solve a system of linear equations in $n$ unknowns using the Gaussian Elimination Method. Assume that one operation refers to a multiplication followed by an addition.
answered
11 minutes
ago
in
Linear Algebra
by
Arjun
Veteran
(
406k
points)

252
views
gate1998
linearalgebra
systemofequations
gaussianelimination
descriptive
+1
vote
2
answers
2
TIFR2014A18
We are given a collection of real numbers where a real number $a_{i}\neq 0$ occurs $n_{i}$ times. Let the collection be enumerated as $\left\{x_{1}, x_{2},...x_{n}\right\}$ so that $x_{1}=x_{2}=...=x_{n_{1}}=a_{1}$ and so on, and $n=\sum _{i}n_{i}$ is finite. What is ... $\min_{i} a_{i}$ $\min_{i} \left(n_{i}a_{i}\right)$ $\max_{i} a_{i}$ None of the above.
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Calculus
by
Arjun
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406k
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161
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tifr2014
limits
+19
votes
3
answers
3
TIFR2014A5
The rules for the University of Bombay fiveaside cricket competition specify that the members of each team must have birthdays in the same month. What is the minimum number of mathematics students needed to be enrolled in the department to guarantee that they can raise a team of students? $23$ $91$ $60$ $49$ None of the above.
answered
13 hours
ago
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Combinatory
by
Kuldeep Pal
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815
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tifr2014
permutationsandcombinations
discretemathematics
normal
pigeonholeprinciple
+34
votes
7
answers
4
GATE2017247
If the ordinary generating function of a sequence $\big \{a_n\big \}_{n=0}^\infty$ is $\large \frac{1+z}{(1z)^3}$, then $a_3a_0$ is equal to ___________ .
answered
13 hours
ago
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Combinatory
by
mohan123
(
101
points)

5.3k
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gate20172
permutationsandcombinations
generatingfunctions
numericalanswers
normal
+13
votes
8
answers
5
GATE20181
Which one of the following is a closed form expression for the generating function of the sequence $\{a_n\}$, where $a_n = 2n +3 \text{ for all } n=0, 1, 2, \dots$? $\frac{3}{(1x)^2}$ $\frac{3x}{(1x)^2}$ $\frac{2x}{(1x)^2}$ $\frac{3x}{(1x)^2}$
answered
15 hours
ago
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Combinatory
by
Kuldeep Pal
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1.3k
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5.7k
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gate2018
generatingfunctions
normal
+2
votes
1
answer
6
GATE19994
Let $G$ be a finite group and $H$ be a subgroup of $G$. For $a \in G$, define $aH=\left\{ah \mid h \in H\right\}$. Show that $aH = bH.$ Show that for every pair of elements $a, b \in G$, either $aH = bH$ or $aH$ and $bH$ are disjoint. Use the above to argue that the order of $H$ must divide the order of $G.$
answered
1 day
ago
in
Set Theory & Algebra
by
Satbir
Boss
(
12.9k
points)

449
views
gate1999
settheory&algebra
groups
normal
cosets
+8
votes
3
answers
7
TIFR2011B23
Suppose $(S_{1}, S_{2},\ldots,S_{m})$ is a finite collection of nonempty subsets of a universe $U.$ Note that the sets in this collection need not be distinct. Consider the following basic step to be performed on this sequence. While there exist sets $S_{i}$ and ... of a finite universe $U$ and a choice of $S_{i}$ and $S_{j}$ in each step such that the process does not terminate.
answered
1 day
ago
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Set Theory & Algebra
by
Arjun
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406k
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319
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tifr2011
settheory&algebra
sets
+5
votes
2
answers
8
TIFR2015A15
Let $A$ and $B$ be nonempty disjoint sets of real numbers. Suppose that the average of the numbers in the first set is $\mu_{A}$ and the average of the numbers in the second set is $\mu_{B}$; let the corresponding variances be $v_{A}$ and $v_{B}$ ... $p.v_{A}+ (1  p). v_{B} + (\mu_{A} \mu_{B})^{2}$
answered
1 day
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Probability
by
Arjun
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406k
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249
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tifr2015
statistics
probability
+4
votes
2
answers
9
TIFR2018A10
Let $C$ be a biased coin such that the probability of a head turning up is $p.$ Let $p_n$ denote the probability that an odd number of heads occurs after $n$ tosses for $n \in \{0,1,2,\ldots \},$ ... $p_{n}=1 \text{ if } n \text{ is odd and } 0 \text{ otherwise}.$
answered
1 day
ago
in
Probability
by
Arjun
Veteran
(
406k
points)

267
views
tifr2018
probability
+2
votes
1
answer
10
TIFR2013A18
Consider three independent uniformly distributed (taking values between $0$ and $1$) random variables. What is the probability that the middle of the three values (between the lowest and the highest value) lies between $a$ and $b$ where $0 ≤ a < b ≤ 1$? $3 (1  b) a (b  a)$ ... $(1  b) a (b  a)$ $6 ((b^{2} a^{2})/ 2  (b^{3}  a^{3})/3)$.
answered
1 day
ago
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Probability
by
Arjun
Veteran
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406k
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219
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tifr2013
probability
randomvariable
uniformdistribution
+2
votes
1
answer
11
GATE19894viii
Provide short answers to the following questions: $P_{n} (t)$ is the probability of $n$ events occurring during a time interval $t$. How will you express $P_{0} (t + h)$ in terms of $P_{0} (h)$, if $P_{0} (t)$ has stationary independent increments? (Note: $P_{t} (t)$is the probability density function).
answered
2 days
ago
in
Probability
by
Arjun
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406k
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108
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gate1989
descriptive
probability
poissondistribution
+37
votes
3
answers
12
GATE200725
Let A be a $4 \times 4$ matrix with eigen values 5,2,1,4. Which of the following is an eigen value of the matrix$\begin{bmatrix} A & I \\ I & A \end{bmatrix}$, where $I$ is the $4 \times 4$ identity matrix? $5$ $7$ $2$ $1$
answered
2 days
ago
in
Linear Algebra
by
Ashwani Kumar 2
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14.6k
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2.9k
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gate2007
eigenvalue
linearalgebra
difficult
+4
votes
1
answer
13
TIFR2015A12
Consider two independent and identically distributed random variables $X$ and $Y$ uniformly distributed in $[0, 1]$. For $\alpha \in \left[0, 1\right]$, the probability that $\alpha$ max $(X, Y) < XY$ is $1/ (2\alpha)$ exp $(1  \alpha)$ $1  \alpha$ $(1  \alpha)^{2}$ $1  \alpha^{2}$
answered
2 days
ago
in
Probability
by
Arjun
Veteran
(
406k
points)

221
views
tifr2015
probability
randomvariable
uniformdistribution
+16
votes
3
answers
14
GATE199811
Suppose $A = \{a, b, c, d\}$ and $\Pi_1$ is the following partition of A $\Pi_1 = \left\{\left\{a, b, c\right\}\left\{d\right\}\right\}$ List the ordered pairs of the equivalence relations induced by $\Pi_1$. Draw the graph of the above equivalence relation ... $\left\langle\left\{\Pi_1, \Pi_2, \Pi_3, \Pi_4\right\}, \text{ refines } \right\rangle$.
answered
2 days
ago
in
Set Theory & Algebra
by
Satbir
Boss
(
12.9k
points)

1.6k
views
gate1998
settheory&algebra
normal
partialorder
descriptive
0
votes
0
answers
15
Sheldon Ross Chapter2 Question15b
If it is assumed that all $\binom{52}{5}$ poker hands are equally likely, what is the probability of being dealt two pairs? (This occurs when the cards have denominations a, a, b, b, c, where a, b, and c are all distinct.) my approach is: selecting a ... I'm getting answer 0.095 but in the book answer is given 0.0475 where am I going wrong?
asked
3 days
ago
in
Probability
by
aditi19
Active
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3.7k
points)

43
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probability
sheldonross
engineeringmathematics
+7
votes
1
answer
16
TIFR2018B10
For two $n$ bit strings $x,y \in\{0,1\}^{n},$ define $z=x\oplus y$ to be the bitwise XOR of the two strings (that is, if $x_{i},y_{i},z_{i}$ denote the $i^{th}$ bits of $x,y,z$ respectively, then $z_{i}=x_{i}+y_{i} \bmod 2$ ... The number of such linear functions for $n \geq 2$ is: $2^{n}$ $2^{n^{2}}$ $\large2^{\frac{n}{2}}$ $2^{4n}$ $2^{n^{2}+n}$
answered
3 days
ago
in
Set Theory & Algebra
by
Arjun
Veteran
(
406k
points)

224
views
tifr2018
functions
+17
votes
3
answers
17
GATE19992.2
Two girls have picked $10$ roses, $15$ sunflowers and $15$ daffodils. What is the number of ways they can divide the flowers among themselves? $1638$ $2100$ $2640$ None of the above
answered
3 days
ago
in
Combinatory
by
brucebayne
(
21
points)

3.6k
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gate1999
permutationsandcombinations
normal
0
votes
1
answer
18
MadeEasy Test Series: Probability
How to get the idea that we have to use Binomial distribution or Hypergeometric Distribution. I know that if the probability is not changing(i.e with replacement) then we go Binomial otherwise Hypergeometric. But in question, it is not indicating ... So is there any by default approach that we have to use Binomial if nothing is a mention about a replacement.
answered
4 days
ago
in
Mathematical Logic
by
vizzard110
(
29
points)

26
views
madeeasytestseries
probability
binomialdistribution
+1
vote
1
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19
Doubt
How many distinct unlabeled graphs are there with 4 vertices and 3 edges?
answered
4 days
ago
in
Graph Theory
by
Gyanu
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1.5k
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64
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0
votes
1
answer
20
Zeal Test Series 2019: Graph Theory  Graph Connectivity
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Graph Theory
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Gyanu
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1.5k
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zeal
graphtheory
graphconnectivity
zeal2019
+2
votes
3
answers
21
Degree of vertices
Consider an undirected graph with $n$ vertices, vertex $1$ has degree $1$,while each vertex $2,3,.............,n1$ has degree $4$.The degree of vertex $n$ is unknown. Which of the following statement must be true? Vertex $n$ has degree $1$ Graph is connected There is a path from vertex $1$ to vertex $n$ Spanning tree will include edge connecting vertex $1$ and vertex $n$
answered
5 days
ago
in
Graph Theory
by
Sainath Mandavilli
(
15
points)

97
views
discretemathematics
graphtheory
+1
vote
1
answer
22
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?
answered
5 days
ago
in
Probability
by
Debdeep1998
Junior
(
849
points)

45
views
probability
randomvariable
sheldonross
+1
vote
1
answer
23
Sheldon Ross, Chapter# 4 RANDOM VARIABLES, Q.51 (9th edition page#167)
If a student copies his assignments from his friend he would get 80 marks. If he had done the assignments independently he would have scored 50 marks out of 100 and if the teacher finds he is cheating he ... , what is the probability that he will lose more marks with copying than by doing his independent work independently?
answered
5 days
ago
in
Probability
by
Debdeep1998
Junior
(
849
points)

67
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probability
sheldonross
randomvariable
0
votes
2
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24
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
5 days
ago
in
Graph Theory
by
Akanksha Agrawal
(
33
points)

59
views
graphtheory
0
votes
1
answer
25
Sheldon Ross Example5n
Compute the probability that if 10 married couples are seated at random at a round table, then no wife sits next to her husband 1 wife sits next to her husband. pick one of the 10 couples=$\binom{10}{1}$. These couples can interchange their position such that ... sits together=$\frac{N}{19!}$ so probability that no couple sits together=$1\frac{N}{19!}$ is this correct?
answered
6 days
ago
in
Probability
by
Satbir
Boss
(
12.9k
points)

88
views
permutationsandcombinations
probability
discretemathematics
sheldonross
0
votes
0
answers
26
total number of spanning tree
[closed]
asked
Jun 10
in
Mathematical Logic
by
Sanjay Sharma
Boss
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47.1k
points)

41
views
+3
votes
3
answers
27
ISI2017MMA27
A box contains $5$ fair and $5$ biased coins. Each biased coin has a probability of head $\frac{4}{5}$. A coin is drawn at random from the box and tossed. Then the second coin is drawn at random from the box ( without replacing the first one). Given that the first coin has shown head ... the second coin is fair is $\frac{20}{39}\\$ $\frac{20}{37}\\$ $\frac{1}{2}\\$ $\frac{7}{13}$
answered
Jun 9
in
Probability
by
ankitrazzagmail.com
(
55
points)

307
views
isi2017
engineeringmathematics
probability
0
votes
2
answers
28
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??
answered
Jun 9
in
Combinatory
by
Koushik Sinha 2
(
253
points)

58
views
discretemathematics
permutationsandcombinations
+2
votes
2
answers
29
TIFR2019A13
Consider the integral $\int^{1}_{0} \frac{x^{300}}{1+x^2+x^3} dx$ What is the value of this integral correct up to two decimal places? $0.00$ $0.02$ $0.10$ $0.33$ $1.00$
answered
Jun 9
in
Calculus
by
Arjun
Veteran
(
406k
points)

205
views
tifr2019
engineeringmathematics
calculus
integration
+2
votes
2
answers
30
GATE198816i
Assume that the matrix $A$ given below, has factorization of the form $LU=PA$, where $L$ is lowertriangular with all diagonal elements equal to 1, $U$ is uppertriangular, and $P$ is a permutation matrix. For $A = \begin{bmatrix} 2 & 5 & 9 \\ 4 & 6 & 5 \\ 8 & 2 & 3 \end{bmatrix}$ Compute $L, U,$ and $P$ using Gaussian elimination with partial pivoting.
answered
Jun 8
in
Linear Algebra
by
ankitgupta.1729
Boss
(
13.2k
points)

252
views
gate1988
normal
descriptive
linearalgebra
matrices
+19
votes
3
answers
31
GATE201416
Let the function ... There exists $\theta \in (\frac{\pi}{6},\frac{\pi}{3})$ such that $f'(\theta)\neq 0$ I only II only Both I and II Neither I Nor II
answered
Jun 8
in
Calculus
by
97apoorva singh
(
77
points)

3.5k
views
gate20141
calculus
differentiability
normal
+3
votes
5
answers
32
TIFR2019B13
A row of $10$ houses has to be painted using the colours red, blue, and green so that each house is a single colour, and any house that is immediately to the right of a red or a blue house must be green. How many ways are there to paint the houses? $199$ $683$ $1365$ $3^{10}2^{10}$ $3^{10}$
answered
Jun 8
in
Combinatory
by
shaktisingh
(
67
points)

268
views
tifr2019
engineeringmathematics
discretemathematics
permutationsandcombinations
+1
vote
2
answers
33
GATE199017c
Show that the elements of the lattice $(N, \leq)$, where $N$ is the set of positive intergers and $a \leq b$ if and only if $a$ divides $b$, satisfy the distributive property.
answered
Jun 8
in
Set Theory & Algebra
by
Arjun
Veteran
(
406k
points)

239
views
gate1990
descriptive
settheory&algebra
lattice
+3
votes
1
answer
34
TIFR2017B6
Consider the First Order Logic (FOL) with equality and suitable function and relation symbols. Which of the following is FALSE? Partial orders cannot be axiomatized in FOL FOL has a complete proof system Natural numbers cannot be axiomatized in FOL Real numbers cannot be axiomatized in FOL Relational numbers cannot be axiomatized in FOL
answered
Jun 8
in
Mathematical Logic
by
Arjun
Veteran
(
406k
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174
views
tifr2017
firstorderlogic
normal
0
votes
1
answer
35
TIFR2019B12
Let $G=(V,E)$ be a directed graph with $n(\geq 2)$ vertices, including a special vertex $r$. Each edge $e \in E$ has a strictly positive edge weight $w(e)$. An arborescence in $G$ rooted at $r$ is a subgraph $H$ of $G$ in which every ... $w^*$ is less than the weight of the minimum weight directed Hamiltonian cycle in $G$, when $G$ has a directed Hamiltonian cycle
answered
Jun 8
in
Graph Theory
by
Arjun
Veteran
(
406k
points)

230
views
tifr2019
engineeringmathematics
discretemathematics
graphtheory
difficult
0
votes
1
answer
36
UGCNETJuly2018II76
Consider the following statements: False $\models$ True If $\alpha \models (\beta \wedge \gamma \text{ then } \alpha \models \gamma$ Which of the following is correct with respect to above statements? Both statement a and statement b are false Statement a is true and statement b is false Statement a is false and statement b is true Both statement a and statement b are true
answered
Jun 8
in
Discrete Mathematics
by
Irfanshaan
(
11
points)

370
views
ugcnetjuly2018ii
discretemathematics
propositionallogic
0
votes
1
answer
37
Differentiability
$\varphi \left ( x \right )=x^{2}\cos \frac{1}{x}$ when $x\neq 0$ $=0$ when $x=0$ Is it differentiable at $x=0$? Is it continuous ?
answered
Jun 7
in
Calculus
by
ankitgupta.1729
Boss
(
13.2k
points)

49
views
calculus
discretemathematics
0
votes
1
answer
38
Linear Algebra (Self Doubt)
Let $A$ be a $n \times n$ square matrix whose all columns are independent. Is $Ax = b$ always solvable? Actually, I know that $Ax= b$ is solvable if $b$ is in the column space of $A$. However, I am not sure if it is solvable for all values of $b$.
answered
Jun 7
in
Linear Algebra
by
Sourajit25
Junior
(
953
points)

55
views
linearalgebra
+7
votes
1
answer
39
GATE19879e
How many true inclusion relations are there of the from $A \subseteq B$, where $A$ and $B$ are subsets of a set $S$ with $n$ elements?
answered
Jun 7
in
Set Theory & Algebra
by
Arjun
Veteran
(
406k
points)

434
views
gate1987
settheory&algebra
relations
0
votes
1
answer
40
ISI2017MMA26
Let $n$ be the number of ways in which 5 men and 7 women can stand in a queue such that all the women stand consecutively. Let $m$ be the number of ways in which the same 12 persons can stand in a queue such that exactly 6 women stand consecutively. Then the value of $\frac{m}{n}$ is $5$ $7$ $5/7$ $7/5$
answered
Jun 7
in
Combinatory
by
venkatesh pagadala
(
491
points)

25
views
isi2017
engineeringmathematics
discretemathematics
permutationsandcombinations
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