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Recent questions in Engineering Mathematics

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141

combinatorics problem-2
How many ways are there to distribute 5 distinct toys among 3 children such that every child gets at least 1 toy? answer given is 150. but I'm getting 9. My approach go as follows: step-1 : give 1 toy to all 3 children, now, I am left with (5-3) = ... to either of first or second or third child. thus, toy1 has 3 choices and so do toy2. Therefore, my answer would be 3*3 = 9.

Roshakaw asked in Combinatory Aug 25, 2022

214 views

1 vote

2 answers

142

Combinatorics
How many ways are there to distribute 10 identical candies among 3 children such that the first child receives at least 2 candies, the second child receives atmost 6 candies and the third child receives atmost 3 candies.

Roshakaw asked in Combinatory Aug 25, 2022

236 views

0 votes

1 answer

143

Engineering Mathematics
Does the given solution is correct: When S is symmetric and transitive, if S contain (3,1),(1,3) then (3,3) should also be present form transitivity. Please verify the solution.

Overflow04 asked in Set Theory & Algebra Aug 23, 2022

177 views

5 votes

0 answers

144

Combinatorics : Distinct objects and Distinct boxes
How many ways are there to Distribute 7 distinct objects to 3 Distinct boxes and No box should be Empty Any box can be Empty

[ Jiren ] asked in Combinatory Aug 22, 2022

209 views

0 votes

1 answer

145

Engineering Mathematics
why 4^10 is done. solution: Please explain the last portion why 4^ 10 is done.

Overflow04 asked in Set Theory & Algebra Aug 22, 2022

122 views

1 vote

0 answers

146

Engineering Mathematics
Please verify the solution(the differentiation part ),

Overflow04 asked in Calculus Aug 21, 2022

158 views

1 vote

2 answers

147

maths probability
A dice is tossed seven times. What is the probability that all six faces appear at least once?

jugnu1337 asked in Probability Aug 15, 2022

252 views

0 votes

1 answer

148

maths igate test series
Which of the relations below can also be characterized as a function defined on the set I = { 1, 2, 3, 4, 5 } { (x, y) | x, y ∈ I, x < y } B{ (x, y) | x, y ∈ I, x = 1 } C{ (x, y) | x, y ∈ I, x! = y } None of these

jugnu1337 asked in Set Theory & Algebra Aug 15, 2022

167 views

0 votes

1 answer

149

NPTEL Assignment
In how many ways can the word ‘DOCUMENTATION’ be arranged so that all the consonants come together.

simi2426 asked in Combinatory Aug 9, 2022

293 views

0 votes

1 answer

150

ISI 2020 | PCB Mathematics | Question: 3
Suppose $A$ is an $(n \times n)$ matrix over $\mathbb{R}$ such that $A^{p}=0$ for some positive integer $p$. Prove that $I+A$ is an invertible matrix, where $I$ is the $(n \times n)$ identity matrix. Find the characteristic polynomial of $A$.

Lakshman Patel RJIT asked in Linear Algebra Aug 8, 2022

by Lakshman Patel RJIT

72 views

4 votes

1 answer

151

GO Classes Scholarship 2023 | Test | Question: 1
A relation $\text{R}$ on a set $\text{A}$ is said to be Total Relation iff $a\text{R}b$ Or $b\text{R}a$ Or both, for all $a,b \in \mathrm{A}$. Which of the following options is/are false? Every Total relation is ... total and transitive, then $\mathrm{S}$ is an equivalence relation. The number of total relations on a set of $5$ elements is $1024.$

GO Classes asked in Set Theory & Algebra Aug 7, 2022

575 views

2 votes

3 answers

152

GO Classes Scholarship 2023 | Test | Question: 2
Let $\text{S}$ be the set of all bit-strings of length $7 .$ We define a relation $\mathrm{R}$ on the set $\mathrm{S}$ by the rule that $x\mathrm{R}y$ iff $x$ and $y$ ... such that $\forall j \neq i, x_{j}=y_{j}$ and $x_{i} \neq y_{i}$. What is the cardinality of relation $\mathrm{R}$?

GO Classes asked in Set Theory & Algebra Aug 7, 2022

492 views

4 votes

1 answer

153

GO Classes Scholarship 2023 | Test | Question: 3
Let $\text{A, B}$ be two disjoint non-empty sets. Let $\text{M}$ be the universal set and $\text{A} \cup \text{B}$ is a proper subset of $\mathrm{M}$. For any set $\mathrm{S}$, let $\mathrm{S}^{\prime}$ be the set of those elements ...

GO Classes asked in Set Theory & Algebra Aug 7, 2022

282 views

5 votes

2 answers

154

GO Classes Scholarship 2023 | Test | Question: 4
Consider a $3 \times 11$ rectangular grid as depicted in Figure $1,$ formed by $33$ tiles of area $1\text{m}^2.$ A staircase walk is a path in the grid which moves only right or up. How many staircase walks are there from $\text{A}$ to $\text{B}$ which start by going to the right two times?

GO Classes asked in Combinatory Aug 7, 2022

308 views

4 votes

1 answer

155

GO Classes Scholarship 2023 | Test | Question: 5
Consider $5$ cards, each has a distinct value from the set $\{2,3,4,5,6\},$ so there are $5$ different values, and we put them face down on the table. There are $5$ players and each player is given a number from $2$ ... with the value that player has. If no player loses, then the dealer loses. How many ways are there so that the dealer loses?

GO Classes asked in Combinatory Aug 7, 2022

246 views

4 votes

1 answer

156

GO Classes Scholarship 2023 | Test | Question: 6
Consider three boxes and $12$ balls of the same size. We have $3$ indistinguishable red balls and $9$ distinguishable blue balls. The first box can fit at most three balls, the second box can fit at most four balls and the third box can fit ... all the red balls go into the same box. What is the total number of ways to put all the balls in the boxes?

GO Classes asked in Combinatory Aug 7, 2022

288 views

3 votes

1 answer

157

GO Classes Scholarship 2023 | Test | Question: 7
Define the generating functions $\text{B}(x)=\displaystyle{} \sum_{n=0}^{\infty} 2^{n} x^{n}$ and $F(x)=\displaystyle{} \sum_{n=0}^{\infty} f_{n} x^{n}$ where $f_{n}$ ... $x^{5}$ is $\mathrm{G}(x)?$

GO Classes asked in Combinatory Aug 7, 2022

317 views

3 votes

1 answer

158

GO Classes Scholarship 2023 | Test | Question: 8
In a directed graph $\mathrm{G}=(\mathrm{V}, \mathrm{E})$, two nodes $u$ and $v$ are strongly connected if and only if they are mutually reachable i.e. there is a path from u to $v$ and a path from $v$ to $u$. ... connected components $\dots?$ can not increase can not decrease by more than $1$ can not decrease by more than $2$ may remain unchanged

GO Classes asked in Graph Theory Aug 7, 2022

350 views

4 votes

2 answers

159

GO Classes Scholarship 2023 | Test | Question: 9
Consider the following graph $\text{G:}$ Let $\text{M, C, I, S, B, E}$ be the Matching number, chromatic number, independence number, Clique number, Vertex cover number, and edge cover number, respectively of $\text{G}.$ What is $\text{M+C+I+S+B+E}?$

GO Classes asked in Graph Theory Aug 7, 2022

363 views

3 votes

1 answer

160

GO Classes Scholarship 2023 | Test | Question: 10
For which of the following does there exist a graph satisfying the specified conditions? A tree with six vertices and six edges. A tree with three or more vertices, two vertices of degree one, and all the other vertices with degree three or ... with $10$ vertices and $8$ edges. A disconnected graph with $12$ vertices and $11$ edges and no cycle.

GO Classes asked in Graph Theory Aug 7, 2022

248 views

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