Recent questions in Discrete Mathematics / GATE Overflow for GATE CSE

5 votes

2 answers

81

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:$$\left\{\begin{array}{c}10 \\3\end{array}\right\}=9330$$...

GO Classes

959 views

GO Classes asked Jan 21

2 votes

1 answer

82

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...

GO Classes

485 views

GO Classes asked Jan 21

10 votes

1 answer

83

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...

GO Classes

691 views

GO Classes asked Jan 21

4 votes

1 answer

84

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 ...

GO Classes

702 views

GO Classes asked Jan 21

6 votes

1 answer

85

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.

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 ...

GO Classes

484 views

GO Classes asked Jan 21

0 votes

0 answers

86

Madeeasy test 45, question 48
Can anyone please explain the statements II and III?

Can anyone please explain the statements II and III?

VinayBhojwani

172 views

VinayBhojwani asked Jan 15

0 votes

1 answer

87

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).

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

178 views

Rohit Chakraborty asked Jan 15

3 votes

1 answer

88

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?

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 subgra...

GO Classes

491 views

GO Classes asked Jan 13

8 votes

1 answer

89

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 $A \subseteq B$ $B \subseteq A$ $(B-A) \cup A=B$

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

643 views

GO Classes asked Jan 13

5 votes

1 answer

90

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 $F(2,3)=$

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

555 views

GO Classes asked Jan 13

2 votes

1 answer

91

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 $b^4 c^2 b^2 c$ $c^2 b^4 c b^2$ $c b^2 c^2 b^4$ $c b c^2 b^3$

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...

GO Classes

452 views

GO Classes asked Jan 13

9 votes

1 answer

92

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.

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 ...

GO Classes

616 views

GO Classes asked Jan 13

7 votes

2 answers

93

GO Classes Test Series 2024 | Mock GATE | Test 11 | Question: 44
Acceptable input for a certain pocket calculator is a finite sequence of characters each of which is either a digit or a sign. The first character must be a digit, the last character must be a digit, and any character that is a sign must be followed by a digit. There ... by $N_k=a N _{k-1}+b N _{k-2}$, for $k \geq 3$. What is $a+ b?$

Acceptable input for a certain pocket calculator is a finite sequence of characters each of which is either a digit or a sign. The first character must be a digit, the la...

GO Classes

583 views

GO Classes asked Jan 13

0 votes

0 answers

94

Consider a weighted undirected graph with positive edge weights and let (u, v) be an [2] edge in the graph. It is known that the shortest path from source vertex r to u has weight 53 and shortest path from r to v has weight 65. Which statement is always true?

Consider a weighted undirected graph with positive edge weights and let (u, v) be an edge in the graph. It is known that the shortest path from source vertex r to u hasw...

Malusi

128 views

Malusi asked Jan 12

0 votes

2 answers

95

Confusion between implication with its converse.
I have given two propositions p: You drive over 65 mph q: You get a speeding ticket Here are two natural language statements Driving over 65 mph is sufficient for getting a speeding ticket (answer key: $p \to q$) Whenever you get a speeding ... , anything that comes after when/whenever is the antecedent, it should be $p \to q$. Where I am wrong here?

I have given two propositionsp: You drive over 65 mphq: You get a speeding ticketHere are two natural language statementsDriving over 65 mph is sufficient for getting a s...

tbhaxor

193 views

tbhaxor asked Jan 11

0 votes

1 answer

96

Why inclusive or is used with Either...Or... here?
There are 2 propositions p: It is below freezing q: It is snowing. I want to write the symbolic form of: Either it is below freezing or it is snowing, but it is not snowing if it is freezing. This is what I came up with: ... . Second part it clear to me, but in the first shouldn't it will be exclusive or, because of Either...or...?

There are 2 propositionsp: It is below freezingq: It is snowing.I want to write the symbolic form of: Either it is below freezing or it is snowing, but it is not snowing ...

tbhaxor

154 views

tbhaxor asked Jan 11

0 votes

1 answer

97

GATE 2018 | MATHS | Q-40
Which one of the following statements is true? (A) Every group of order 12 has a non-trivial proper normal subgroup (B) Some group of order 12 does not have a non-trivial proper normal subgroup (C) Every group of order 12 has a subgroup of order 6 (D) Every group of order 12 has an element of order 12

Which one of the following statements is true?(A) Every group of order 12 has a non-trivial proper normal subgroup(B) Some group of order 12 does not have a non-trivial p...

rajveer43

143 views

rajveer43 asked Jan 11

0 votes

1 answer

98

Made Easy Mock Test 2

Rohit Chakraborty

287 views

Rohit Chakraborty asked Jan 11

1 votes

0 answers

99

GATE 2019 | maths | set theory
Consider the following statements: I.The set $ \mathbb{R} $ is uncountable. II.The set $ \{ f : f \text{ is a function from } \mathbb{N} \text{ to } \{0, 1\} \} $ is uncountable. III.The set $ \{ p : p \text{ is a prime number} \} $ is uncountable. ... of the above statements are TRUE? (A)] I and IV only (B) II and IV only (C) II and III only (D) I, II, and IV only

Consider the following statements: I.The set $ \mathbb{R} $ is uncountable.II.The set $ \{ f : f \text{ is a function from } \mathbb{N} \text{ to } \{0, 1\} \} $ is uncou...

rajveer43

80 views

rajveer43 asked Jan 10

0 votes

0 answers

100

GATE 2021 | MATHS | QUESTION
Let $ \mathbb{F} $ be a finite field, and $ \mathbb{F}^{\times} $ be the group of all nonzero elements of $ \mathbb{F} $ under multiplication. If $ \mathbb{F}^{\times} $ has a subgroup of order $ 17 $, then the smallest possible order of the field $ \mathbb{F} $ is ____________________________

Let $ \mathbb{F} $ be a finite field, and $ \mathbb{F}^{\times} $ be the group of all nonzero elements of $ \mathbb{F} $ under multiplication. If $ \mathbb{F}^{\times} $ ...

rajveer43

130 views

rajveer43 asked Jan 10

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