Most answered questions in Engineering Mathematics / GATE Overflow for GATE CSE

29 votes

10 answers

31

GATE CSE 1996 | Question: 2.3
Which of the following is NOT True? (Read $\wedge$ as AND, $\vee$ as OR, $\neg$ as NOT, $\rightarrow$ as one way implication and $\leftrightarrow$ as two way implication) $((x \rightarrow y) \wedge x) \rightarrow y$ ... $(x \rightarrow (x \vee y))$ $((x \vee y) \leftrightarrow (\neg x \rightarrow \neg y))$

Which of the following is NOT True?(Read $\wedge$ as AND, $\vee$ as OR, $\neg$ as NOT, $\rightarrow$ as one way implication and $\leftrightarrow$ as two way implication)...

Kathleen

8.4k views

Kathleen asked Oct 9, 2014

101 votes

10 answers

32

GATE CSE 2014 Set 1 | Question: 51
Consider an undirected graph $G$ where self-loops are not allowed. The vertex set of $G$ is $\{(i,j) \mid1 \leq i \leq 12, 1 \leq j \leq 12\}$. There is an edge between $(a,b)$ and $(c,d)$ if $|a-c| \leq 1$ and $|b-d| \leq 1$. The number of edges in this graph is______.

Consider an undirected graph $G$ where self-loops are not allowed. The vertex set of $G$ is $\{(i,j) \mid1 \leq i \leq 12, 1 \leq j \leq 12\}$. There is an edge between $...

go_editor

26.8k views

go_editor asked Sep 28, 2014

41 votes

10 answers

33

GATE CSE 2003 | Question: 38
Consider the set $\{a, b, c\}$ with binary operators $+$ and $*$ defined as follows: ... $(x, y)$ that satisfy the equations) is $0$ $1$ $2$ $3$

Consider the set $\{a, b, c\}$ with binary operators $+$ and $*$ defined as follows:$$\begin{array}{|c|c|c|c|} \hline \textbf{+} & \textbf{a}& \textbf{b} &\textbf{c...

Kathleen

7.1k views

Kathleen asked Sep 17, 2014

60 votes

10 answers

34

GATE CSE 2003 | Question: 36
How many perfect matching are there in a complete graph of $6$ vertices? $15$ $24$ $30$ $60$

How many perfect matching are there in a complete graph of $6$ vertices?$15$$24$$30$$60$

Kathleen

50.4k views

Kathleen asked Sep 16, 2014

43 votes

10 answers

35

GATE CSE 2003 | Question: 3
Let $P(E)$ denote the probability of the event $E$. Given $P(A) = 1$, $P(B) =\dfrac{1}{2}$, the values of $P(A\mid B)$ and $P(B\mid A)$ respectively are $\left(\dfrac{1}{4}\right),\left(\dfrac{1}{2}\right)$ $\left(\dfrac{1}{2}\right),\left(\dfrac{1}{4}\right)$ $\left(\dfrac{1}{2}\right),{1}$ ${1},\left(\dfrac{1}{2}\right)$

Let $P(E)$ denote the probability of the event $E$. Given $P(A) = 1$, $P(B) =\dfrac{1}{2}$, the values of $P(A\mid B)$ and $P(B\mid A)$ respectively are$\left(\dfrac{1}{4...

Kathleen

11.8k views

Kathleen asked Sep 16, 2014

62 votes

10 answers

36

GATE CSE 2002 | Question: 1.8
"If $X$ then $Y$ unless $Z$" is represented by which of the following formulas in propositional logic? ("$\neg$" is negation, "$\land$" is conjunction, and "$\rightarrow$" is implication) $(X\land \neg Z) \rightarrow Y$ $(X \land Y) \rightarrow \neg Z$ $X \rightarrow(Y\land \neg Z)$ $(X \rightarrow Y)\land \neg Z$

"If $X$ then $Y$ unless $Z$" is represented by which of the following formulas in propositional logic? ("$\neg$" is negation, "$\land$" is conjunction, and "$\rightarrow$...

Kathleen

14.9k views

Kathleen asked Sep 15, 2014

27 votes

9 answers

37

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 $S$

Choose the correct choice(s) regarding the following proportional logic assertion $S$:$$S: (( P \wedge Q) \rightarrow R) \rightarrow (( P \wedge Q) \rightarrow (Q \righta...

Arjun

8.9k views

Arjun asked Feb 18, 2021

42 votes

9 answers

38

GATE CSE 2020 | Question: 39
Which one of the following predicate formulae is NOT logically valid? Note that $W$ is a predicate formula without any free occurrence of $x$. $\forall x (p(x) \vee W) \equiv \forall x \: ( px) \vee W$ ... $\exists x(p(x) \rightarrow W) \equiv \forall x \: p(x) \rightarrow W$

Which one of the following predicate formulae is NOT logically valid?Note that $W$ is a predicate formula without any free occurrence of $x$.$\forall x (p(x) \vee W) \equ...

Arjun

17.2k views

Arjun asked Feb 12, 2020

38 votes

9 answers

39

GATE CSE 2019 | Question: 10
Let $G$ be an arbitrary group. Consider the following relations on $G$: $R_1: \forall a , b \in G, \: a R_1 b \text{ if and only if } \exists g \in G \text{ such that } a = g^{-1}bg$ ... $R_1$ and $R_2$ $R_1$ only $R_2$ only Neither $R_1$ nor $R_2$

Let $G$ be an arbitrary group. Consider the following relations on $G$:$R_1: \forall a , b \in G, \: a R_1 b \text{ if and only if } \exists g \in G \text{ such that } a ...

Arjun

17.4k views

Arjun asked Feb 7, 2019

12 votes

9 answers

40

ISRO2017-22
Which one of the following Boolean expressions is NOT a tautology? $((a \rightarrow b) \wedge (b \rightarrow c)) \rightarrow (a \rightarrow c)$ $(a \leftrightarrow c) \rightarrow (\sim b\rightarrow (a\wedge c))$ $(a\wedge b \wedge c)\rightarrow (c \vee a)$ $a\rightarrow (b\rightarrow a)$

Which one of the following Boolean expressions is NOT a tautology?$((a \rightarrow b) \wedge (b \rightarrow c)) \rightarrow (a \rightarrow c)$$(a \leftrightarrow c) \rig...

sh!va

7.3k views

sh!va asked May 7, 2017

44 votes

9 answers

41

GATE CSE 2017 Set 2 | Question: 23
$G$ is an undirected graph with $n$ vertices and $25$ edges such that each vertex of $G$ has degree at least $3$. Then the maximum possible value of $n$ is _________ .

$G$ is an undirected graph with $n$ vertices and $25$ edges such that each vertex of $G$ has degree at least $3$. Then the maximum possible value of $n$ is _________ .

Madhav

17.5k views

Madhav asked Feb 14, 2017

58 votes

9 answers

42

GATE CSE 2017 Set 2 | Question: 47
If the ordinary generating function of a sequence $\left \{a_n\right \}_{n=0}^\infty$ is $\large \frac{1+z}{(1-z)^3}$, then $a_3-a_0$ is equal to ___________ .

If the ordinary generating function of a sequence $\left \{a_n\right \}_{n=0}^\infty$ is $\large \frac{1+z}{(1-z)^3}$, then $a_3-a_0$ is equal to ___________ .

Arjun

17.7k views

Arjun asked Feb 14, 2017

25 votes

9 answers

43

GATE CSE 2017 Set 1 | Question: 47
The number of integers between $1$ and $500$ (both inclusive) that are divisible by $3$ or $5$ or $7$ is ____________ .

The number of integers between $1$ and $500$ (both inclusive) that are divisible by $3$ or $5$ or $7$ is ____________ .

Arjun

11.7k views

Arjun asked Feb 14, 2017

67 votes

9 answers

44

GATE CSE 2017 Set 1 | Question: 3
Let $c_{1}.....c_{n}$ be scalars, not all zero, such that $\sum_{i=1}^{n}c_{i}a_{i}$ = 0 where $a_{i}$ are column vectors in $R^{n}$. Consider the set of linear equations $Ax = b$ ... has a unique solution at $x=J_{n}$ where $J_{n}$ denotes a $n$-dimensional vector of all 1. no solution infinitely many solutions finitely many solutions

Let $c_{1}.....c_{n}$ be scalars, not all zero, such that $\sum_{i=1}^{n}c_{i}a_{i}$ = 0 where $a_{i}$ are column vectors in $R^{n}$.Consider the set of linear equations$...

Arjun

20.3k views

Arjun asked Feb 14, 2017

23 votes

9 answers

45

GATE CSE 1987 | Question: 10e
Show that the conclusion $(r \to q)$ follows from the premises$:p, (p \to q) \vee (p \wedge (r \to q))$

Show that the conclusion $(r \to q)$ follows from the premises$:p, (p \to q) \vee (p \wedge (r \to q))$

makhdoom ghaya

5.2k views

makhdoom ghaya asked Nov 14, 2016

92 votes

9 answers

46

GATE CSE 2016 Set 1 | Question: 28
A function $f: \Bbb{N^+} \rightarrow \Bbb{N^+}$ , defined on the set of positive integers $\Bbb{N^+}$, satisfies the following properties: $f(n)=f(n/2)$ if $n$ is even $f(n)=f(n+5)$ if $n$ is odd Let $R=\{ i \mid \exists{j} : f(j)=i \}$ be the set of distinct values that $f$ takes. The maximum possible size of $R$ is ___________.

A function $f: \Bbb{N^+} \rightarrow \Bbb{N^+}$ , defined on the set of positive integers $\Bbb{N^+}$, satisfies the following properties: $f(n)=f(n/2)...

Sandeep Singh

21.6k views

Sandeep Singh asked Feb 12, 2016

9 votes

9 answers

47

Kenneth Rosen Edition 6 Question 45 (Page No. 346)
How many bit strings of length eight contain either three consecutive 0s or four consecutive 1s?

How many bit strings of length eight contain either three consecutive 0s or four consecutive 1s?

Anu

9.2k views

Anu asked Jul 13, 2015

31 votes

9 answers

48

GATE CSE 2015 Set 3 | Question: 15
In the given matrix $\begin{bmatrix} 1 & -1 & 2 \\ 0 & 1 & 0 \\ 1 & 2 & 1 \end{bmatrix}$ , one of the eigenvalues is $1.$ The eigenvectors corresponding to the eigenvalue $1$ ... $\left\{a\left(- \sqrt{2},0,1\right) \mid a \neq 0, a \in \mathbb{R}\right\}$

In the given matrix $\begin{bmatrix} 1 & -1 & 2 \\ 0 & 1 & 0 \\ 1 & 2 & 1 \end{bmatrix}$ , one of the eigenvalues is $1.$ The eigenvectors corresponding to the eigenvalue...

go_editor

17.7k views

go_editor asked Feb 14, 2015

33 votes

9 answers

49

GATE CSE 2015 Set 1 | Question: 54
Let G be a connected planar graph with 10 vertices. If the number of edges on each face is three, then the number of edges in G is_______________.

Let G be a connected planar graph with 10 vertices. If the number of edges on each face is three, then the number of edges in G is_______________.

makhdoom ghaya

24.6k views

makhdoom ghaya asked Feb 13, 2015

50 votes

9 answers

50

GATE IT 2005 | Question: 36
Let $P(x)$ and $Q(x)$ ...

Let $P(x)$ and $Q(x)$ be arbitrary predicates. Which of the following statements is always TRUE?$\left(\left(\forall x \left(P\left(x\right) \vee Q\left(x\right)\right)\r...

Ishrat Jahan

14.8k views

Ishrat Jahan asked Nov 3, 2014

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