Recent questions in Discrete Mathematics / GATE Overflow for GATE CSE

4 votes

1 answer

31

GO Classes Test Series 2024 | Mock GATE | Test 14 | Question: 39
For sets $A$ and $B$, let $f: A \rightarrow B$ and $g: B \rightarrow A$ be functions such that $f(g(x))=x$ for each $x \in B$. Which among the following statements is/are correct? The function $f$ must be one-to-one. The function $f$ must be onto. The function g must be one-to-one. The function $g$ must be onto.

For sets $A$ and $B$, let $f: A \rightarrow B$ and $g: B \rightarrow A$ be functions such that $f(g(x))=x$ for each $x \in B$. Which among the following statements is/are...

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524 views

GO Classes asked Feb 5

6 votes

2 answers

32

GO Classes Test Series 2024 | Mock GATE | Test 14 | Question: 56
The coefficient of $x^6$ in the expansion of $A(x)$ is, where $ A(x)=\frac{x(1+x)}{(1-x)^3} $

The coefficient of $x^6$ in the expansion of $A(x)$ is, where$$A(x)=\frac{x(1+x)}{(1-x)^3}$$

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560 views

GO Classes asked Feb 5

6 votes

1 answer

33

GO Classes Test Series 2024 | Mock GATE | Test 14 | Question: 57
A strongly connected component $(\mathrm{SCC})$ of a directed graph $\mathrm{G}=(\mathrm{V}, \mathrm{E})$ ... ; edges in its associated directed acyclic graph $G^{\prime}$ be $A, B$ respectively, then what is $A+B?$

A strongly connected component $(\mathrm{SCC})$ of a directed graph $\mathrm{G}=(\mathrm{V}, \mathrm{E})$ is a maximal set of vertices such that any two vertices in the s...

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553 views

GO Classes asked Feb 5

12 votes

3 answers

34

GO Classes Test Series 2024 | Mock GATE | Test 14 | Question: 58
Let $\mathrm{F}$ and $\mathrm{G}$ be two propositional formulae. Which of the following is/are True? If $F \vee G$ is a tautology then at least one of $F, G$ is a tautology. If $F \wedge G$ is a contradiction then at ... $G$ is a tautology. If $F \rightarrow G$ is a contradiction then $F$ is a tautology and $G$ is a contradiction.

Let $\mathrm{F}$ and $\mathrm{G}$ be two propositional formulae.Which of the following is/are True?If $F \vee G$ is a tautology then at least one of $F, G$ is a tautology...

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837 views

GO Classes asked Feb 5

2 votes

2 answers

35

Memory Based GATE DA 2024 | Question: 33
Which of the following are tautologies? $x \land \neg y \Rightarrow y \rightarrow x$ $\neg x \land y \Rightarrow \neg x \rightarrow y$ $x \land \neg y \Rightarrow \neg x \rightarrow y$ $\neg x \land y \Rightarrow y \rightarrow x$

Which of the following are tautologies? $x \land \neg y \Rightarrow y \rightarrow x$$\neg x \land y \Rightarrow \neg x \rightarrow y$\(x \land \neg y \Rightarrow \ne...

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243 views

GO Classes asked Feb 4

0 votes

0 answers

36

Memory Based GATE DA 2024 | Question: 57
First-order logic question: All balls are round except rugby balls.

First-order logic question: All balls are round except rugby balls.

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109 views

GO Classes asked Feb 4

1 votes

0 answers

37

Memory Based GATE DA 2024 | Question: 64
Minimum Number of colors in concentric circles.

Minimum Number of colors in concentric circles.

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136 views

GO Classes asked Feb 4

0 votes

0 answers

38

madeeasy
plz explain option c

plz explain option c

nihal_chourasiya

93 views

nihal_chourasiya asked Feb 1

1 votes

1 answer

39

#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/

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 ...

Dknights

145 views

Dknights asked Jan 31

0 votes

1 answer

40

#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

Can someone please explain the following case of combinationI means identicalD means different DOIB with boxes being empty and non emptyAs in this question the given valu...

Dknights

217 views

Dknights asked Jan 28

3 votes

1 answer

41

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

A group $G$ in which $(a b)^2=a^2 b^2$ for all $a, b$ in $G$ is necessarilyfinitecyclicabeliannone of the above

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358 views

GO Classes asked Jan 28

4 votes

1 answer

42

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 ... $10^{20}-2^{10}$ $\dfrac{20 ! 10 !}{2^{10}}$

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...

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611 views

GO Classes asked Jan 28

3 votes

0 answers

43

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

Let $S$ be the set of all functions $f: \mathbb{R} \rightarrow \mathbb{R}$. Consider the two binary operations + and $\circ$ on $S$ defined as pointwise addition and comp...

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433 views

GO Classes asked Jan 28

4 votes

1 answer

44

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 $\mathrm{W}(\mathrm{R})=n / 2$

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 th...

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491 views

GO Classes asked Jan 28

3 votes

1 answer

45

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)

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 ...

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444 views

GO Classes asked Jan 28

6 votes

2 answers

46

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?

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...

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907 views

GO Classes asked Jan 21

5 votes

2 answers

47

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?

The number of ways that one can divide $10$ distinguishable objects in $3$ indistinguishable non-empty piles, is:$$\left\{\begin{array}{c}10 \\3\end{array}\right\}=9330$$...

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916 views

GO Classes asked Jan 21

2 votes

1 answer

48

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

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 commutativeThere is a rational numbe...

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465 views

GO Classes asked Jan 21

10 votes

1 answer

49

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 $\mathrm{R}$ ... $\forall x \in P . \exists y \in P . x R y$

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-ord...

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627 views

GO Classes asked Jan 21

4 votes

1 answer

50

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?

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 ...

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634 views

GO Classes asked Jan 21

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