Recent questions in Discrete Mathematics / GATE Overflow for GATE CSE

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91

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

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rajveer43 asked Jan 10

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92

GATE 2021 | MATHS | Q-20
Let $ f: \left( -\frac{\pi}{2}, \frac{\pi}{2} \right) \to \mathbb{R} $ be given by $ f(x) = \frac{\pi}{2} + x - \tan^{-1}(x) $. Consider the following statements: $P:$ $ |f(x) - f(y)| < |x - y| $ ... Then the correct option is: (A) both P and Q are TRUE (B) P is TRUE and Q is FALSE (C) P is FALSE and Q is TRUE (D) both P and Q are FALSE

Let $ f: \left( -\frac{\pi}{2}, \frac{\pi}{2} \right) \to \mathbb{R} $ be given by $ f(x) = \frac{\pi}{2} + x - \tan^{-1}(x) $. Consider the following statements: $P:$...

rajveer43

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rajveer43 asked Jan 10

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93

GATE 2022 | MATHS | Q-27
The number of subgroups of a cyclic group of order 12 is ______________________

The number of subgroups of a cyclic group of order 12 is ______________________

rajveer43

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rajveer43 asked Jan 10

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1 answer

94

GATE 2023 | Maths | Sample Ques for CS-IT
Let $G$ be an abelian group and $\Phi: G \rightarrow (\mathbb{Z}, +)$ be a surjective group homomorphism. Let $1 = \Phi(a)$ for some $a \in G$. Consider the following statements: $P$: For every $g \in G$, there exists an $n \in \ ... following statements is/are correct? (A) \(P$ is TRUE (B) $P$ is FALSE (C) $Q$ is TRUE (D) $Q$ is FALSE

Let $G$ be an abelian group and $\Phi: G \rightarrow (\mathbb{Z}, +)$ be a surjective group homomorphism. Let $1 = \Phi(a)$ for some $a \in G$.Consider the follow...

rajveer43

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rajveer43 asked Jan 10

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95

GATE 2022 Stat | Question 16 | Linear Algebra

rajveer43

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rajveer43 asked Jan 9

1 votes

1 answer

96

GATE 2022 | Linear Algebra | Question 11
Let 𝑴 be a 2 × 2 real matrix such that $(𝑰 + 𝑴)^-1 = 𝑰 − 𝛼𝑴$, where 𝛼 is a non-zero real number and 𝑰 is the 2 × 2 identity matrix. If the trace of the matrix 𝑴 is 3, then the value of 𝛼 is (A) 3/4 (B) 1/3 (C) 1/2 (D) 1/4

Let 𝑴 be a 2 × 2 real matrix such that $(𝑰 + 𝑴)^-1 = 𝑰 − 𝛼𝑴$, where 𝛼 is a non-zero real number and 𝑰 is the 2 × 2 identity matrix. If the tra...

rajveer43

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rajveer43 asked Jan 9

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1 answer

97

selfdoubt combinatory
In how many ways can you distribute 4 different choclates to 3 people such that each gets atleast 1 choclate.

In how many ways can you distribute 4 different choclates to 3 people such that each gets atleast 1 choclate.

nihal_chourasiya

195 views

nihal_chourasiya asked Jan 7

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1 answer

98

ISRO 2024
Maximum number of Simple graphs possible with $n$ vertices $2^{n(n-1)/2}$ $2^{(n-1)/2}$ $2^{n(n+1)/2}$ $2^{n(n+1)}$

Maximum number of Simple graphs possible with $n$ vertices$2^{n(n-1)/2}$$2^{(n-1)/2}$$2^{n(n+1)/2}$$2^{n(n+1)}$

Ramayya

190 views

Ramayya asked Jan 7

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1 answer

99

ISRO 2024
If there are five faces and nine vertices in an undirected planar graph, then number of edges is 14 6 12 None of the above

If there are five faces and nine vertices in an undirected planar graph, then number of edges is14612None of the above

Ramayya

297 views

Ramayya asked Jan 7

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2 answers

100

ISRO 2024
Which of the following are true? In a graph G with ‘n’ vertices and ‘e’ edges, sum of degrees of vertices = 2*e. Eccentricity of a connected graph can never be equal to radius of the graph Girth of a graph is the shortest cycle of the graph Graph with equal degree for all vertices is multigraph (i), (ii), (iii) (ii), (iii), (iv) (i), (iii), (iv) None of the above

Which of the following are true?In a graph G with ‘n’ vertices and ‘e’ edges, sum of degrees of vertices = 2*e.Eccentricity of a connected graph...

Ramayya

453 views

Ramayya asked Jan 7

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101

Made easy test series
Consider a strongly connected directed graph G(V, F), where |V| = 101. The minimum possible value of IEl is

Consider a strongly connected directed graph G(V, F), where |V| = 101. The minimum possible value of IEl is

abhishekbhingarde

115 views

abhishekbhingarde asked Jan 6

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1 answer

102

How to find continuity and Diffrentiability
The real function f(x) = cos (|x|) is

The real function f(x) = cos (|x|) is

Hritik1204

81 views

Hritik1204 asked Jan 5

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1 answer

103

MADE EASY TEST SERIES
Pls solve it

Pls solve it

Dadu

189 views

Dadu asked Jan 2

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1 answer

104

If |x| <1. Find the sum to infinity of the series 3 + 8x + 13x^2 + .......
If |x| < 1. Find the sum to infinity of the series $3 + 8x + 13x^2 + 18x^3 + ----- \infty$ $(3+2x)/(1-x^2)$ $(3-2x)/(1+x^2)$ $(2x-3)/(1-x^2)$ $(3+2x)/(1+x^2)$

If |x| < 1. Find the sum to infinity of the series $3 + 8x + 13x^2 + 18x^3 + - \infty$$(3+2x)/(1-x^2)$$(3-2x)/(1+x^2)$$(2x-3)/(1-x^2)$$(3+2x)/(1+x^2)$

gautham_reddy

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gautham_reddy asked Jan 1

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105

Worksheet on Recurrence Relation
Find recurrence relations that are satisfied by the sequence formed from the following functions. (a) an = n!/15! (b) an = n2 − 6n + 8

Find recurrence relations that are satisfied by the sequence formed from the followingfunctions.(a) an = n!/15! (b) an = n2 − 6n + 8

Dagi

126 views

Dagi asked Dec 31, 2023

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0 answers

106

#logic
Sir, In discrete mathematics 2024's lecture-17, at 15:30 you said "Every proposition variable is also a compound proposition". How it's possible Sir??? becoz by the definition of compound proposition, a proposition must contain a logical operator for being a compound proposition. @Deepak Poonia

Sir, In discrete mathematics 2024's lecture-17, at 15:30 you said "Every proposition variable is also a compound proposition". How it's possible Sir??? becoz by the defin...

pavan singh

141 views

pavan singh asked Dec 30, 2023

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1 answer

107

A tree has 2n vertices of degree 1, 3n vertices of degree 2 and n vertices of degree 3. Determine the number of vertices and edges in the tree.

SURAJ7201

283 views

SURAJ7201 asked Dec 29, 2023

1 votes

0 answers

108

Mathematical Logic: Which of the following is a logical consequence of $∀x(p(x)∨q(x))$
The following question is on the NPTEL archive of Assignment 2 of Discrete Mathematics Course,(Link : assessment id-15 (nptel.ac.in)) . I am not able to get how the answer is given option A but I am getting B, C and D. I have also attached my reasoning below. Let me know If I am missing something.

The following question is on the NPTEL archive of Assignment 2 of Discrete Mathematics Course,(Link : assessment id-15 (nptel.ac.in)) . I am not able to get howthe answe...

USharma02

243 views

USharma02 asked Dec 24, 2023

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109

How many strings are there of lowercase letters of length four or less, not counting the empty string?

Md Sazzad

152 views

Md Sazzad asked Dec 23, 2023

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0 answers

110

#self doubt
If [dn,/] is a lattice, then x=n/x for all x belongs to dn

If [dn,/] is a lattice, then x=n/x for all x belongs to dn

Dknights

69 views

Dknights asked Dec 21, 2023

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