Recent questions in Discrete Mathematics

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1

Applied Test Series
A Professor tells 3 Jokes in his maths class each year. How large a set of jokes does the professor need in order never to repeat the exact same triple of jokes over a period of 12 years?_________

LRU asked in Combinatory 3 days ago

by LRU

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0 votes

1 answer

2

GATE ACADEMY TEST SERIES
What is the minimum number of students, each of whom comes from one of the 50 states, who must be enrolled in a university to guarantee that there are at least 100 who come from the same state?

LRU asked in Mathematical Logic Sep 26

by LRU

84 views

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3

Biconditional Operator in the logical expression for Symmetric Relation.
"The logical expression for the symmetric relation should contain the biconditional operator <-> instead of implication -> . Because, if u keep ->, then for the case when F -> T the ... " Could someone plz help, this seems to be correct. Also https://en.wikipedia.org/wiki/Symmetric_relation.

SHM asked in Mathematical Logic Sep 26

by SHM

25 views

0 votes

1 answer

4

Marks Distribution for Engineering and Discrete Maths
Hey all, As per brochure there will be 13 marks alloted for engineering maths. My quer is whether discrete maths will too be included in this 13 marks i.e. EM+DM=13, or Discrete maths will have separate marks? Like in Gate 2021 paper , the combined marks for Engineering and Discrete maths was over 13.

Acejoy asked in Mathematical Logic Sep 11

by Acejoy

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0 votes

1 answer

5

gateacademy testseries
In how many ways can seven different jobs be assigned to four different employees so that each employee is assigned at least one job and the most difficult job is assigned to the best employee?

Sanjay chauhan 123 asked in Combinatory Sep 6

by Sanjay chauhan 123

51 views

1 vote

1 answer

6

gateacademy test series
There are 12 stations on a rail route. How many ways a special train can stop at 4 of these stations, so that no two stops are consecutive stations? please explain in detail

Sanjay chauhan 123 asked in Combinatory Sep 6

by Sanjay chauhan 123

60 views

9 votes

2 answers

7

GATE CSE 2021 Set 2 | Question: 11
Consider the following sets, where $n \geq 2$: $S_1$: Set of all $n \times n$ matrices with entries from the set $\{ a, b, c\}$ $S_2$: Set of all functions from the set $\{0,1,2, \dots, n^2-1\}$ ... There exists a surjection from $S_1$ to $S_2$ There exists a bijection from $S_1$ to $S_2$ There does not exist an injection from $S_1$ to $S_2$

Arjun asked in Set Theory & Algebra Feb 18

by Arjun

1.5k views

7 votes

4 answers

8

GATE CSE 2021 Set 2 | Question: 15
Choose the correct choice(s) regarding the following proportional logic assertion $S$: $S: (( P \wedge Q) \rightarrow R) \rightarrow (( P \wedge Q) \rightarrow (Q \rightarrow R))$ $S$ is neither a tautology nor a contradiction $S$ is a tautology $S$ is a contradiction The antecedent of $S$ is logically equivalent to the consequent of $S$

Arjun asked in Mathematical Logic Feb 18

by Arjun

1.5k views

5 votes

1 answer

9

GATE CSE 2021 Set 2 | Question: 37
For two $n$-dimensional real vectors $P$ and $Q$, the operation $s(P,Q)$ is defined as follows: $s(P,Q) = \displaystyle \sum_{i=1}^n (P[i] \cdot Q[i])$ Let $\mathcal{L}$ be a set of $10$-dimensional non-zero real vectors such that for every pair ... $s(P,Q)=0$. What is the maximum cardinality possible for the set $\mathcal{L}$? $9$ $10$ $11$ $100$

Arjun asked in Set Theory & Algebra Feb 18

by Arjun

1.4k views

7 votes

5 answers

10

GATE CSE 2021 Set 2 | Question: 50
Let $S$ be a set of consisting of $10$ elements. The number of tuples of the form $(A,B)$ such that $A$ and $B$ are subsets of $S$, and $A \subseteq B$ is ___________

Arjun asked in Combinatory Feb 18

by Arjun

2.5k views

3 votes

4 answers

11

GATE CSE 2021 Set 1 | Question: 7
Let $p$ and $q$ be two propositions. Consider the following two formulae in propositional logic. $S_1: (\neg p\wedge(p\vee q))\rightarrow q$ $S_2: q\rightarrow(\neg p\wedge(p\vee q))$ Which one of the following choices is correct? Both $S_1$ and ... but $S_2$ is not a tautology $S_1$ is not a tautology but $S_2$ is a tautology Neither $S_1$ nor $S_2$ is a tautology

Arjun asked in Mathematical Logic Feb 18

by Arjun

1.5k views

2 votes

5 answers

12

GATE CSE 2021 Set 1 | Question: 16
In an undirected connected planar graph $G$, there are eight vertices and five faces. The number of edges in $G$ is _________.

Arjun asked in Graph Theory Feb 18

by Arjun

1.9k views

7 votes

2 answers

13

GATE CSE 2021 Set 1 | Question: 19
There are $6$ jobs with distinct difficulty levels, and $3$ computers with distinct processing speeds. Each job is assigned to a computer such that: The fastest computer gets the toughest job and the slowest computer gets the easiest job. Every computer gets at least one job. The number of ways in which this can be done is ___________.

Arjun asked in Combinatory Feb 18

by Arjun

2.2k views

7 votes

4 answers

14

GATE CSE 2021 Set 1 | Question: 34
Let $G$ be a group of order $6$, and $H$ be a subgroup of $G$ such that $1<|H|<6$. Which one of the following options is correct? Both $G$ and $H$ are always cyclic $G$ may not be cyclic, but $H$ is always cyclic $G$ is always cyclic, but $H$ may not be cyclic Both $G$ and $H$ may not be cyclic

Arjun asked in Set Theory & Algebra Feb 18

by Arjun

1.9k views

10 votes

6 answers

15

GATE CSE 2021 Set 1 | Question: 36
Let $G=(V, E)$ be an undirected unweighted connected graph. The diameter of $G$ is defined as: $\text{diam}(G)=\displaystyle \max_{u,v\in V} \{\text{the length of shortest path between $u$ and $v$}\}$ Let $M$ be the adjacency matrix of $G$. Define graph $G_2$ ... $\text{diam}(G_2) = \text{diam}(G)$ $\text{diam}(G)< \text{diam}(G_2)\leq 2\; \text{diam}(G)$

Arjun asked in Graph Theory Feb 18

by Arjun

1.8k views

5 votes

5 answers

16

GATE CSE 2021 Set 1 | Question: 43
A relation $R$ is said to be circular if $a\text{R}b$ and $b\text{R}c$ together imply $c\text{R}a$. Which of the following options is/are correct? If a relation $S$ is reflexive and symmetric, then $S$ is an equivalence relation ... and circular, then $S$ is an equivalence relation. If a relation $S$ is transitive and circular, then $S$ is an equivalence relation.

Arjun asked in Set Theory & Algebra Feb 18

by Arjun

1.5k views

3 votes

3 answers

17

JEST2020
Let G(V,E) be a simple graph. Let G’(V,E’) be a graph obtained from G such that (u,v) is an edge in G’ if (u,v) is not an edge in G. Which of the following is true? At least one of G or G’ are connected. G is necessarily disconnected. Both G and G’ are disconnected. None of the above.

vivek_mishra asked in Graph Theory Feb 15

by vivek_mishra

264 views

1 vote

0 answers

18

JEST2020
For two n-bit strings x, y ∈ {0, 1}n, define z := x ⊕ y to be the bitwise XOR of the two strings (that is, if xi, yi, zi denote the i-th bits of x, y, z respectively, then zi = xi + yi mod 2). A function h : {0, 1}n → {0, 1}n is called linear if h(x ⊕ y) = h(x) ⊕ h(y), for every x, y ∈ {0, 1}n. The number of such linear functions for n ≥ 2: 2^n 2^2n 2^(n+1) n

vivek_mishra asked in Combinatory Feb 15

by vivek_mishra

234 views

2 votes

3 answers

19

UGCNET-Oct2020-II: 1
The number of positive integers not exceeding $100$ that are either odd or the square of an integer is _______ $63$ $59$ $55$ $50$

jothee asked in Set Theory & Algebra Nov 20, 2020

by jothee

1.3k views

2 votes

2 answers

20

UGCNET-Oct2020-II: 2
How many ways are there to pack six copies of the same book into four identical boxes, where a box can contain as many as six books? $4$ $6$ $7$ $9$

jothee asked in Combinatory Nov 20, 2020

by jothee

1.2k views

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