Questions without answers in Discrete Mathematics / GATE Overflow for GATE CSE

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1

Linear Algebra AX=B
Consider a matrix A (n×m) ,X(m×n) and B(n×n) such that AX=B . If A has k linearly independent columns then what conclusions can we nake about the number of linearly independent columns of B.

Consider a matrix A (n×m) ,X(m×n) and B(n×n) such that AX=B . If A has k linearly independent columns then what conclusions can we nake about the number of linearly in...

Soumya04

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Soumya04 asked 2 days ago

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2

GO Classes CS 2025 | Weekly Quiz 5 | Set Theory | Question: 9
Which of the following statements is $\textbf{TRUE}$? For all sets $A, B$, and $C, A-(B-C)=(A-B)-C$. For all sets $A, B$, and $C,(A-B) \cap(C-B)=(A \cap C)-B$. For all sets $A, B$, and $C,(A-B) \cap(C-B)=A-(B \cup C)$. For all sets $A, B$, and $C$, if $A \cap C=B \cap C$ then $A=B$.

Which of the following statements is $\textbf{TRUE}$?For all sets $A, B$, and $C, A-(B-C)=(A-B)-C$.For all sets $A, B$, and $C,(A-B) \cap(C-B)=(A \cap C)-B$.For all sets ...

GO Classes

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GO Classes asked Apr 10

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3

GO Classes CS 2025 | Weekly Quiz 5 | Set Theory | Question: 10
Which of the following statements is $\textbf{FALSE}$? $C-(B \cup A)=(C-B)-A$ $A-(C \cup B)=(A-B)-C$ $B-(A \cup C)=(B-C)-A$ $A-(B \cup C)=(B-C)-A$

Which of the following statements is $\textbf{FALSE}$?$C-(B \cup A)=(C-B)-A$$A-(C \cup B)=(A-B)-C$$B-(A \cup C)=(B-C)-A$$A-(B \cup C)=(B-C)-A$

GO Classes

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GO Classes asked Apr 10

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4

BME entrance exam
A data file of 1,000,000 records must be stored using bucket hashing. Record length is 350 bytes, the net capacity of a block is 2000 bytes. Keys occupy 32 bytes, while pointers need 8 bytes. Each bucket consists of 2 blocks. How many blocks are needed at least to store the whole structure (i.e. data file + hash table) on disc? Select one:

A data file of 1,000,000 records must be stored using bucket hashing. Record length is 350 bytes, the net capacity of a block is 2000 bytes. Keys occupy 32 bytes, while p...

Ilqar

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Ilqar asked Apr 2

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0 answers

5

#discrete

Çșȇ ʛấẗẻ

68 views

Çșȇ ʛấẗẻ asked Feb 24

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6

Question on Quotient set
What will be quotient set for equivalence relation R={(x,y) ∣ x ≡ y mod 5} in set builder form?

What will be quotient set for equivalence relation R={(x,y) ∣ x ≡ y mod 5} in set builder form?

rick55

72 views

rick55 asked Feb 23

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0 answers

7

Regular expression to finite automata

Çșȇ ʛấẗẻ

217 views

Çșȇ ʛấẗẻ asked Feb 15

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8

COA Self doubt

Çșȇ ʛấẗẻ

98 views

Çșȇ ʛấẗẻ asked Feb 15

1 votes

0 answers

9

Gate 2016
The minimum number of colours that is sufficient to vertex-colour any planar graph is ________. I am confused with the question's language. please correct me if I have a wrong assumption. We need to tell the minimum colors required for a planar graph. Suppose I start ... is only fixed to 4. I understand the answer not to be less than 4. What does the word "any" means here?

The minimum number of colours that is sufficient to vertex-colour any planar graph is ________.I am confused with the question's language.please correct me if I have a wr...

TusharRana

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TusharRana asked Feb 8

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10

Combinatorics & Probability
A rumor is spread randomly among a group of 10 people by successively having one person call someone, who calls someone, and so on. A person can pass the rumor on to anyone except the individual who just called. (a) By how many different paths can a rumor ... in $N$ calls? (c) What is the probability that if $A$ starts the rumor, then $A$ receives the third calls?

A rumor is spread randomly among a group of 10 people by successively having one person call someone, who calls someone, and so on. A person can pass the rumor on to anyo...

Debargha Mitra Roy

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Debargha Mitra Roy asked Feb 8

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11

#self doubt
Can someone please verify it ? isn't should be 8. https://www.toppr.com/ask/question/the-cardinality-of-the-power-set-of-left-phi-left-phiright-left-phi-left/ Let S={ϕ,{ϕ},{ϕ,{ϕ}}} P(s)= Power Set of set S P(s)={ϕ,{ϕ},{ϕ,{ϕ}},{ϕ,{ϕ,{ϕ}}},{{ϕ},{ϕ,{ϕ}}},{ϕ,{ϕ},{ϕ,{ϕ}}}} n(P(s))=6.

Can someone please verify it ? isn't should be 8. https://www.toppr.com/ask/question/the-cardinality-of-the-power-set-of-left-phi-left-phiright-left-phi-left/Let S={ϕ,{�...

Dknights

132 views

Dknights asked Feb 6

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0 answers

12

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.

GO Classes

112 views

GO Classes asked Feb 4

1 votes

0 answers

13

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

Minimum Number of colors in concentric circles.

GO Classes

138 views

GO Classes asked Feb 4

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0 answers

14

madeeasy
plz explain option c

plz explain option c

nihal_chourasiya

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nihal_chourasiya asked Feb 1

3 votes

0 answers

15

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...

GO Classes

437 views

GO Classes asked Jan 28

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0 answers

16

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

Can anyone please explain the statements II and III?

VinayBhojwani

159 views

VinayBhojwani asked Jan 15

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0 answers

17

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

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Malusi asked Jan 12

1 votes

0 answers

18

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

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rajveer43 asked Jan 10

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19

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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20

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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0 answers

21

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

57 views

rajveer43 asked Jan 10

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22

GATE 2022 Stat | Probability | Question 28

rajveer43

3 views

rajveer43 asked Jan 9

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0 answers

23

GATE 2022 Stat | Question 16 | Linear Algebra

rajveer43

45 views

rajveer43 asked Jan 9

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0 answers

24

GATE Statistics 2022 | Question 11 | Linear Algebra
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

2 views

rajveer43 asked Jan 9

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0 answers

25

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

114 views

abhishekbhingarde asked Jan 6

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0 answers

26

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

118 views

Dagi asked Dec 31, 2023

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0 answers

27

#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

139 views

pavan singh asked Dec 30, 2023

1 votes

0 answers

28

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

228 views

USharma02 asked Dec 24, 2023

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29

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

Md Sazzad

147 views

Md Sazzad asked Dec 23, 2023

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0 answers

30

#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

68 views

Dknights asked Dec 21, 2023

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