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Recent questions in Discrete Mathematics
1
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31
#self doubt
In the above figure, how many topological sorts are possible, I tried the following method, if we include 5 _ _ _ _ _ for 5 space 5c3 for (2,3,1) then 2 position is 4,0 so a total of 10 if we do like 4 5 _ _ _ _ then only ... GFG the total possible sorts are 13 can someone why this difference is coming ? https://www.geeksforgeeks.org/all-topological-sorts-of-a-directed-acyclic-graph/
Dknights
asked
in
Graph Theory
Jan 31
by
Dknights
122
views
discrete-mathematics
0
votes
1
answer
32
#self doubt
Can someone please explain the following case of combination I means identical D means different DOIB with boxes being empty and non empty As in this question the given value in question itself i am not able to interpret. https://gateoverflow.in/420251/go-classes-test-series-2024-mock-gate-test-12-question-17
Dknights
asked
in
Combinatory
Jan 28
by
Dknights
186
views
discrete-mathematics
3
votes
1
answer
33
GO Classes Test Series 2024 | Mock GATE | Test 13 | Question: 28
A group $G$ in which $(a b)^2=a^2 b^2$ for all $a, b$ in $G$ is necessarily finite cyclic abelian none of the above
GO Classes
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in
Set Theory & Algebra
Jan 28
by
GO Classes
310
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goclasses2024-mockgate-13
goclasses
set-theory&algebra
group-theory
1-mark
4
votes
1
answer
34
GO Classes Test Series 2024 | Mock GATE | Test 13 | Question: 30
A university's mathematics department has $10$ professors and will offer $20$ different courses next semester. Each professor will be assigned to teach exactly $2$ of the courses, and each course will have exactly one professor assigned to teach it. If any ... $10^{20}-2^{10}$ $\dfrac{20 ! 10 !}{2^{10}}$
GO Classes
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in
Combinatory
Jan 28
by
GO Classes
489
views
goclasses2024-mockgate-13
goclasses
combinatory
counting
1-mark
3
votes
0
answers
35
GO Classes Test Series 2024 | Mock GATE | Test 13 | Question: 61
Let $S$ be the set of all functions $f: \mathbb{R} \rightarrow \mathbb{R}$. Consider the two binary operations + and $\circ$ on $S$ ... law $(g+h) \circ f=(g \circ f)+(h \circ f)$. None III only II and III only I, II, and III
GO Classes
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in
Set Theory & Algebra
Jan 28
by
GO Classes
405
views
goclasses2024-mockgate-13
goclasses
set-theory&algebra
group-theory
2-marks
4
votes
1
answer
36
GO Classes Test Series 2024 | Mock GATE | Test 13 | Question: 62
As a refresher, if $R$ is an equivalence relation over a set $A$ and $x \in A$, then the equivalence class of $\boldsymbol{x}$ in $\boldsymbol{R}$, denoted $[x]_R,$ is the set $ [x]_R=\{y \in A \mid x R y\} $ Let's now introduce some ... $\mathrm{I}(\mathrm{R})=n / 2$ and $\mathrm{W}(\mathrm{R})=n / 2$
GO Classes
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Jan 28
by
GO Classes
456
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goclasses2024-mockgate-13
goclasses
set-theory&algebra
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2-marks
3
votes
1
answer
37
GO Classes Test Series 2024 | Mock GATE | Test 13 | Question: 63
For an undirected graph $G$, let $\overline{G}$ refer to the complement (a graph on the same vertex set as $G$, with $(i, j)$ as an edge in $\overline{G}$ if and only if it is not an edge in $G$ ). Consider the following ... is equivalent to (iii) and (v). (i) is equivalent to (ii) and (iv). (i) is equivalent to (ii) and (v)
GO Classes
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in
Graph Theory
Jan 28
by
GO Classes
405
views
goclasses2024-mockgate-13
goclasses
graph-theory
vertex-cover
2-marks
6
votes
2
answers
38
GO Classes Test Series 2024 | Mock GATE | Test 12 | Question: 17
The number of ways that one can divide $10$ distinguishable objects into $3$ indistinguishable non-empty piles, is: $ \left\{\begin{array}{c} 10 \\ 3 \end{array}\right\}=9330 $ In how many different ways can one do this if the piles are also distinguishable?
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Combinatory
Jan 21
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GO Classes
846
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numerical-answers
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1-mark
5
votes
2
answers
39
GO Classes Test Series 2024 | Mock GATE | Test 12 | Question: 18
The number of ways that one can divide $10$ distinguishable objects in $3$ indistinguishable non-empty piles, is: $ \left\{\begin{array}{c} 10 \\ 3 \end{array}\right\}=9330 $ In how many different ways can one do this if the objects are also indistinguishable?
GO Classes
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Combinatory
Jan 21
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GO Classes
833
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goclasses2024-mockgate-12
goclasses
numerical-answers
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counting
1-mark
2
votes
1
answer
40
GO Classes Test Series 2024 | Mock GATE | Test 12 | Question: 19
Let $\ast $ be the binary operation on the rational numbers given by $a \ast b=a+b+2 a b$. Which of the following are true? $\ast $ is commutative There is a rational number that is a $\ast \;-$ identity. Every rational number has a $\ast \;-$ inverse. I only I and II only I and III only I, II, and III
GO Classes
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in
Set Theory & Algebra
Jan 21
by
GO Classes
431
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goclasses2024-mockgate-12
goclasses
set-theory&algebra
group-theory
1-mark
10
votes
1
answer
41
GO Classes Test Series 2024 | Mock GATE | Test 12 | Question: 45
Below is a drawing(graph representation) of a binary relation $\text{R}$ over a set $\text{P}$ of elements $\{ \text{A, B, C, D, E, F}\}:$ Which of the following first-order logic statements about $\mathrm{R}$ ... $\forall x \in P . \exists y \in P . x R y$
GO Classes
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Mathematical Logic
Jan 21
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GO Classes
560
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goclasses2024-mockgate-12
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2-marks
4
votes
1
answer
42
GO Classes Test Series 2024 | Mock GATE | Test 12 | Question: 46
Assume the following graph is a labeled graph i.e. every vertex has a unique label. In how many ways can we color the following labeled graph $\mathrm{G}$ with six colors $\{R, G, B, W, Y, M\}$ such that no two adjacent vertices are assigned the same color?
GO Classes
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Jan 21
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GO Classes
568
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goclasses2024-mockgate-12
goclasses
numerical-answers
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2-marks
6
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1
answer
43
GO Classes Test Series 2024 | Mock GATE | Test 12 | Question: 47
An involution is a function $f: A \rightarrow A$ where $f(f(x))=x$. A fixed point of any function $f: A \rightarrow A$ is an element $x \in A$ for which $f(x)$ $=x$. Which of the following statement(s) ... $f: \mathrm{A} \rightarrow \mathrm{A}$ is a bijective function.
GO Classes
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in
Set Theory & Algebra
Jan 21
by
GO Classes
412
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goclasses2024-mockgate-12
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2-marks
0
votes
0
answers
44
Madeeasy test 45, question 48
Can anyone please explain the statements II and III?
VinayBhojwani
asked
in
Mathematical Logic
Jan 15
by
VinayBhojwani
139
views
2-marks
engineering-mathematics
made-easy-test-series
0
votes
1
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45
Made easy mock test questions from Functions
Can you explain the procedure and if possible can you share some links to any youtube playlist from where I can study this particular subject(Functions).
Rohit Chakraborty
asked
in
Set Theory & Algebra
Jan 15
by
Rohit Chakraborty
139
views
test-series
functions
discrete-mathematics
gate-preparation
made-easy-test-series
3
votes
1
answer
46
GO Classes Test Series 2024 | Mock GATE | Test 11 | Question: 11
The figure above shows an undirected graph with six vertices. Enough edges are to be deleted from the graph in order to leave a spanning tree, which is a connected subgraph having the same six vertices and no cycles. How many edges must be deleted?
GO Classes
asked
in
Graph Theory
Jan 13
by
GO Classes
408
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goclasses2024-mockgate-11
goclasses
numerical-answers
graph-theory
1-mark
8
votes
1
answer
47
GO Classes Test Series 2024 | Mock GATE | Test 11 | Question: 12
Let $A-B$ denote $\{x \in A: x \notin B\}$. If $(A-B) \cup B=A$, which of the following must be true? $B$ is empty $A \subseteq B$ $B \subseteq A$ $(B-A) \cup A=B$
GO Classes
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in
Set Theory & Algebra
Jan 13
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GO Classes
594
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goclasses2024-mockgate-11
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set-theory&algebra
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1-mark
5
votes
1
answer
48
GO Classes Test Series 2024 | Mock GATE | Test 11 | Question: 18
If $F$ is a function such that, for all positive integers $x$ and $y, F(x, 1)=x+1, F(1, y)=2 y$, and $F(x+1, y+1)=F(F(x, y+1), y)$, then $F(2,3)=$
GO Classes
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in
Set Theory & Algebra
Jan 13
by
GO Classes
477
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goclasses2024-mockgate-11
goclasses
numerical-answers
set-theory&algebra
functions
1-mark
2
votes
1
answer
49
GO Classes Test Series 2024 | Mock GATE | Test 11 | Question: 37
If $b$ and $c$ are elements in a group $G$, and if $b^5=c^3=e$, where $e$ is the unit element of $G$, then the inverse of $b^2 c b^4 c^2$ must be $b^4 c^2 b^2 c$ $c^2 b^4 c b^2$ $c b^2 c^2 b^4$ $c b c^2 b^3$
GO Classes
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in
Set Theory & Algebra
Jan 13
by
GO Classes
387
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goclasses2024-mockgate-11
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set-theory&algebra
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2-marks
8
votes
1
answer
50
GO Classes Test Series 2024 | Mock GATE | Test 11 | Question: 38
A binary relation $\mathrm{R}$ over a set $\mathrm{A}$ is called a "GO Relation" if for all $\mathrm{x}, \mathrm{y}, \mathrm{z}$ $\in A$, if $x R y$ and $x R z$, then $y R z$. Which of the following ... is transitive. If $R$ is a GO relation then $R$ is reflexive. If $R$ is an equivalence relation then $R$ is a GO relation.
GO Classes
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Set Theory & Algebra
Jan 13
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GO Classes
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