Most viewed questions in Discrete Mathematics / GATE Overflow for GATE CSE

41 votes

7 answers

201

GATE CSE 2005 | Question: 43
Let $f: B \to C$ and $g: A \to B$ be two functions and let $h = f o g$. Given that $h$ is an onto function which one of the following is TRUE? $f$ and $g$ should both be onto functions $f$ should be onto but $g$ need not to be onto $g$ should be onto but $f$ need not be onto both $f$ and $g$ need not be onto

Let $f: B \to C$ and $g: A \to B$ be two functions and let $h = f o g$. Given that $h$ is an onto function which one of the following is TRUE?$f$ and $g$ should both be o...

gatecse

10.1k views

gatecse asked Sep 21, 2014

35 votes

6 answers

202

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 $G_2$ ... $\text{diam}(G_2) = \text{diam}(G)$ $\text{diam}(G)< \text{diam}(G_2)\leq 2\; \text{diam}(G)$

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 shortes...

Arjun

10.1k views

Arjun asked Feb 18, 2021

5 votes

2 answers

203

Kenneth Rosen Edition 6th Exercise 1.1 Question 15 (Page No. 18)
For each of these sentences, determine whether an inclusive or, or an exclusive or, is intended. Explain your answer. Coffee or tea comes with dinner. A password must have at least three digits or be at least eight characters long. ... is a course in number theory or a course in cryptography. You can pay using U.S. dollars or euros.

For each of these sentences, determine whether an inclusive or, or an exclusive or, is intended. Explain your answer.Coffee or tea comes with dinner.A password must have ...

go_editor

10.0k views

go_editor asked Apr 14, 2016

36 votes

8 answers

204

GATE CSE 1987 | Question: 10b
What is the generating function $G(z)$ for the sequence of Fibonacci numbers?

What is the generating function $G(z)$ for the sequence of Fibonacci numbers?

makhdoom ghaya

10.0k views

makhdoom ghaya asked Nov 14, 2016

27 votes

4 answers

205

GATE CSE 1995 | Question: 2.17
Let $A$ be the set of all non-singular matrices over real number and let $*$ be the matrix multiplication operation. Then $A$ is closed under $*$ but $\langle A, *\rangle$ is not a semigroup. $\langle A, *\rangle$ is a semigroup but not a monoid. $\langle A, * \rangle$ is a monoid but not a group. $\langle A, *\rangle$ is a a group but not an abelian group.

Let $A$ be the set of all non-singular matrices over real number and let $*$ be the matrix multiplication operation. Then$A$ is closed under $*$ but $\langle A, *\rangle$...

Kathleen

10.0k views

Kathleen asked Oct 8, 2014

43 votes

5 answers

206

GATE CSE 2006 | Question: 3
The set $\{1,2,3,5,7,8,9\}$ under multiplication modulo $10$ is not a group. Given below are four possible reasons. Which one of them is false? It is not closed $2$ does not have an inverse $3$ does not have an inverse $8$ does not have an inverse

The set $\{1,2,3,5,7,8,9\}$ under multiplication modulo $10$ is not a group. Given below are four possible reasons. Which one of them is false?It is not closed$2$ does no...

Rucha Shelke

10.0k views

Rucha Shelke asked Sep 16, 2014

25 votes

3 answers

207

GATE CSE 2014 Set 2 | Question: 49
The number of distinct positive integral factors of $2014$ is _____________

The number of distinct positive integral factors of $2014$ is _____________

go_editor

10.0k views

go_editor asked Sep 28, 2014

0 votes

1 answer

208

NIELIT 2017 July Scientist B (IT) - Section B: 1
Given an undirected graph $G$ with $V$ vertices and $E$ edges, the sum of the degrees of all vertices is $E$ $2E$ $V$ $2V$

Given an undirected graph $G$ with $V$ vertices and $E$ edges, the sum of the degrees of all vertices is$E$$2E$$V$$2V$

admin

10.0k views

admin asked Mar 30, 2020

34 votes

6 answers

209

GATE CSE 2004 | Question: 24
Consider the binary relation: $S= \left\{\left(x, y\right) \mid y=x+1 \text{ and } x, y \in \left\{0, 1, 2\right\} \right\}$ The reflexive transitive closure is $S$ ... $\left\{\left(x, y\right) \mid y \leq x \text{ and } x, y \in \left\{0, 1, 2\right\} \right\}$

Consider the binary relation:$S= \left\{\left(x, y\right) \mid y=x+1 \text{ and } x, y \in \left\{0, 1, 2\right\} \right\}$The reflexive transitive closure is $S$ is$\lef...

Kathleen

9.9k views

Kathleen asked Sep 18, 2014

26 votes

4 answers

210

GATE CSE 1993 | Question: 8.1
Consider a simple connected graph $G$ with $n$ vertices and $n$ edges $(n > 2)$. Then, which of the following statements are true? $G$ has no cycles The graph obtained by removing any edge from $G$ is not connected $G$ has at least one cycle The graph obtained by removing any two edges from $G$ is not connected None of the above

Consider a simple connected graph $G$ with $n$ vertices and $n$ edges $(n 2)$. Then, which of the following statements are true?$G$ has no cyclesThe graph obtained by re...

Kathleen

9.9k views

Kathleen asked Sep 29, 2014

27 votes

4 answers

211

GATE CSE 2010 | Question: 4
Consider the set $S = \{1, ω, ω^2\}$, where $ω$ and $ω^2$ are cube roots of unity. If $*$ denotes the multiplication operation, the structure $(S, *)$ forms A Group A Ring An integral domain A field

Consider the set $S = \{1, ω, ω^2\}$, where $ω$ and $ω^2$ are cube roots of unity. If $*$ denotes the multiplication operation, the structure $(S, *)$ formsA GroupA R...

gatecse

9.9k views

gatecse asked Sep 21, 2014

43 votes

9 answers

212

GATE CSE 1996 | Question: 2.1
Let $R$ denote the set of real numbers. Let $f:R\times R \rightarrow R \times R$ be a bijective function defined by $f(x,y) = (x+y, x-y)$. The inverse function of $f$ is given by $f^{-1} (x,y) = \left( \frac {1}{x+y}, \frac{1}{x-y}\right)$ ... $f^{-1}(x,y)=\left [ 2\left(x-y\right),2\left(x+y\right) \right ]$

Let $R$ denote the set of real numbers. Let $f:R\times R \rightarrow R \times R$ be a bijective function defined by $f(x,y) = (x+y, x-y)$. The inverse function of $f$ is ...

Kathleen

9.9k views

Kathleen asked Oct 9, 2014

4 votes

1 answer

213

Kenneth Rosen Edition 6th Exercise 1.1 Question 4 (Page No. 16)
Let p and q be the propositions p : I bought a lottery ticket this week. q : I won the million dollar jackpot. Express each of these propositions as an English sentence. $\neg p$ $p \vee q$ $p \rightarrow q$ $p \wedge q$ $p \leftrightarrow q$ $\neg p \rightarrow \neg q$ $\neg p \wedge \neg q$ $\neg p \vee (p \wedge q)$

Let p and q be the propositionsp : I bought a lottery ticket this week.q : I won the million dollar jackpot.Express each of these propositions as an English sentence.$\ne...

go_editor

9.9k views

go_editor asked Apr 13, 2016

45 votes

4 answers

214

GATE IT 2006 | Question: 2
For the set $N$ of natural numbers and a binary operation $f : N \times N \to N,$ an element $z \in N$ is called an identity for $f,$ if $f (a, z) = a = f(z, a),$ for all $a \in N.$ Which of the following binary operations have an identity? $f (x, y) = x + y - 3$ $f (x, y) = \max(x, y)$ $f (x, y) = x^y$ I and II only II and III only I and III only None of these

For the set $N$ of natural numbers and a binary operation $f : N \times N \to N,$ an element $z \in N$ is called an identity for $f,$ if $f (a, z) = a = f(z, a),$ for all...

Ishrat Jahan

9.7k views

Ishrat Jahan asked Oct 30, 2014

1 votes

2 answers

215

UGC NET CSE | June 2012 | Part 2 | Question: 4
The number of colours required to properly colour the vertices of every planer graph is 2 3 4 5

The number of colours required to properly colour the vertices of every planer graph is2345

go_editor

9.7k views

go_editor asked Jul 4, 2016

46 votes

4 answers

216

GATE CSE 1996 | Question: 2.4
Which one of the following is false? The set of all bijective functions on a finite set forms a group under function composition The set $\{1, 2, \dots p-1\}$ forms a group under multiplication mod $p$, where $p$ is a prime number The set of all strings over a finite ... $\langle G, * \rangle$ if and only if for any pair of elements $a, b \in S, a * b^{-1} \in S$

Which one of the following is false?The set of all bijective functions on a finite set forms a group under function compositionThe set $\{1, 2, \dots p-1\}$ forms a group...

Kathleen

9.7k views

Kathleen asked Oct 9, 2014

26 votes

6 answers

217

GATE CSE 2022 | Question: 26
Which one of the following is the closed form for the generating function of the sequence $\{ a_{n} \}_{n \geq 0}$ defined below? $ a_{n} = \left\{\begin{matrix} n + 1, & \text{n is odd} & \\ 1, & \text{otherwise} & \end{matrix}\right.$ ... $\frac{2x}{(1-x^{2})^{2}} + \frac{1}{1-x}$ $\frac{x}{(1-x^{2})^{2}} + \frac{1}{1-x}$

Which one of the following is the closed form for the generating function of the sequence $\{ a_{n} \}_{n \geq 0}$ defined below?$$ a_{n} = \left\{\begin{matrix} n + 1, &...

Arjun

9.6k views

Arjun asked Feb 15, 2022

36 votes

5 answers

218

GATE CSE 2007 | Question: 85
Suppose that a robot is placed on the Cartesian plane. At each step it is allowed to move either one unit up or one unit right, i.e., if it is at $(i,j)$ then it can move to either $(i + 1, j)$ or $(i,j + 1)$. Suppose that the robot is not allowed to traverse the ... $^{20}\mathrm{C}_{10} - ^{8}\mathrm{C}_{4}\times ^{11}\mathrm{C}_{5}$

Suppose that a robot is placed on the Cartesian plane. At each step it is allowed to move either one unit up or one unit right, i.e., if it is at $(i,j)$ then it can move...

go_editor

9.6k views

go_editor asked Apr 23, 2016

45 votes

4 answers

219

GATE CSE 2016 Set 1 | Question: 2
Let $a_n$ be the number of $n$-bit strings that do NOT contain two consecutive $1's$. Which one of the following is the recurrence relation for $a_n$? $a_n = a_{n-1}+ 2a_{n-2}$ $a_n = a_{n-1}+ a_{n-2}$ $a_n = 2a_{n-1}+ a_{n-2}$ $a_n = 2a_{n-1}+ 2a_{n-2}$

Let $a_n$ be the number of $n$-bit strings that do NOT contain two consecutive $1's$. Which one of the following is the recurrence relation for $a_n$?$a_n = a_{n-1}+ 2a_{...

Sandeep Singh

9.6k views

Sandeep Singh asked Feb 12, 2016

1 votes

1 answer

220

NIELIT 2017 July Scientist B (IT) - Section B: 17
Let $N=\{1,2,3,\dots\}$ be ordered by divisibility, which of the following subset is totally ordered? $(2,6,24)$ $(3,5,15)$ $(2,9,16)$ $(4,15,30)$

Let $N=\{1,2,3,\dots\}$ be ordered by divisibility, which of the following subset is totally ordered?$(2,6,24)$$(3,5,15)$$(2,9,16)$$(4,15,30)$

admin

9.6k views

admin asked Mar 30, 2020

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