Recent questions and answers in Engineering Mathematics

+1 vote

1 answer

1

GATE1998-9
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

+1 vote

2 answers

2

TIFR2014-A-18
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.

answered 40 minutes ago in Calculus by Arjun Veteran (406k points) | 161 views

+19 votes

3 answers

3

TIFR2014-A-5
The rules for the University of Bombay five-a-side 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 in Combinatory by Kuldeep Pal Active (1.3k points) | 815 views

+34 votes

7 answers

4

GATE2017-2-47
If the ordinary generating function of a sequence $\big \{a_n\big \}_{n=0}^\infty$ is $\large \frac{1+z}{(1-z)^3}$, then $a_3-a_0$ is equal to ___________ .

answered 13 hours ago in Combinatory by mohan123 (101 points) | 5.3k views

+13 votes

8 answers

5

GATE2018-1
Which one of the following is a closed form expression for the generating function of the sequence $\{a_n\}$, where $a_n = 2n +3 \text{ for all } n=0, 1, 2, \dots$? $\frac{3}{(1-x)^2}$ $\frac{3x}{(1-x)^2}$ $\frac{2-x}{(1-x)^2}$ $\frac{3-x}{(1-x)^2}$

answered 15 hours ago in Combinatory by Kuldeep Pal Active (1.3k points) | 5.7k views

+2 votes

1 answer

6

GATE1999-4
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

+8 votes

3 answers

7

TIFR2011-B-23
Suppose $(S_{1}, S_{2},\ldots,S_{m})$ is a finite collection of non-empty 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 in Set Theory & Algebra by Arjun Veteran (406k points) | 319 views

+5 votes

2 answers

8

TIFR2015-A-15
Let $A$ and $B$ be non-empty 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 ago in Probability by Arjun Veteran (406k points) | 249 views

+4 votes

2 answers

9

TIFR2018-A-10
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

+2 votes

1 answer

10

TIFR2013-A-18
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 in Probability by Arjun Veteran (406k points) | 219 views

+2 votes

1 answer

11

GATE1989-4-viii
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 Veteran (406k points) | 108 views

+37 votes

3 answers

12

GATE2007-25
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 Boss (14.6k points) | 2.9k views

+4 votes

1 answer

13

TIFR2015-A-12
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

+16 votes

3 answers

14

GATE1998-11
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

0 votes

0 answers

15

Sheldon Ross Chapter-2 Question-15b
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 (3.7k points) | 43 views

+7 votes

1 answer

16

TIFR2018-B-10
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

+17 votes

3 answers

17

GATE1999-2.2
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 bruce-bayne (21 points) | 3.6k views

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

+1 vote

1 answer

19

Doubt
How many distinct unlabeled graphs are there with 4 vertices and 3 edges?

answered 4 days ago in Graph Theory by Gyanu Active (1.5k points) | 64 views

0 votes

1 answer

20

Zeal Test Series 2019: Graph Theory - Graph Connectivity

answered 5 days ago in Graph Theory by Gyanu Active (1.5k points) | 68 views

+2 votes

3 answers

21

Degree of vertices
Consider an undirected graph with $n$ vertices, vertex $1$ has degree $1$,while each vertex $2,3,.............,n-1$ 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

+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

+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 views

0 votes

2 answers

24

ACE Workbook:
ACE Workbook: Q) Let G be a simple graph(connected) with minimum number of edges. If G has n vertices with degree-1,2 vertices of degree 2, 4 vertices of degree 3 and 3 vertices of degree-4, 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

0 votes

1 answer

25

Sheldon Ross Example-5n
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

0 votes

0 answers

26

total number of spanning tree
[closed]

asked Jun 10 in Mathematical Logic by Sanjay Sharma Boss (47.1k points) | 41 views

+3 votes

3 answers

27

ISI2017-MMA-27
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

0 votes

2 answers

28

Self Doubt-Combinatory
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

+2 votes

2 answers

29

TIFR2019-A-13
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

+2 votes

2 answers

30

GATE1988-16i
Assume that the matrix $A$ given below, has factorization of the form $LU=PA$, where $L$ is lower-triangular with all diagonal elements equal to 1, $U$ is upper-triangular, 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

+19 votes

3 answers

31

GATE2014-1-6
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

+3 votes

5 answers

32

TIFR2019-B-13
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

+1 vote

2 answers

33

GATE1990-17c
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

+3 votes

1 answer

34

TIFR2017-B-6
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 points) | 174 views

0 votes

1 answer

35

TIFR2019-B-12
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

0 votes

1 answer

36

UGCNET-July-2018-II-76
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

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

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

+7 votes

1 answer

39

GATE1987-9e
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

0 votes

1 answer

40

ISI2017-MMA-26
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

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