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

48 votes

4 answers

121

GATE CSE 2015 Set 2 | Question: 50
In a connected graph, a bridge is an edge whose removal disconnects the graph. Which one of the following statements is true? A tree has no bridges A bridge cannot be part of a simple cycle Every edge of a clique with size $\geq 3$ is a bridge (A clique is any complete subgraph of a graph) A graph with bridges cannot have cycle

In a connected graph, a bridge is an edge whose removal disconnects the graph. Which one of the following statements is true?A tree has no bridgesA bridge cannot be part ...

go_editor

14.6k views

go_editor asked Feb 13, 2015

23 votes

3 answers

122

GATE CSE 1998 | Question: 1.23
How many sub strings of different lengths (non-zero) can be formed from a character string of length $n$? $n$ $n^2$ $2^n$ $\frac{n(n+1)}{2}$

How many sub strings of different lengths (non-zero) can be formed from a character string of length $n$?$n$$n^2$$2^n$$\frac{n(n+1)}{2}$

Kathleen

14.5k views

Kathleen asked Sep 25, 2014

60 votes

4 answers

123

GATE CSE 2014 Set 1 | Question: 5
The value of the dot product of the eigenvectors corresponding to any pair of different eigenvalues of a $4-by-4$ symmetric positive definite matrix is ___________

The value of the dot product of the eigenvectors corresponding to any pair of different eigenvalues of a $4-by-4$ symmetric positive definite matrix is ___________

go_editor

14.5k views

go_editor asked Sep 26, 2014

39 votes

5 answers

124

GATE CSE 2017 Set 2 | Question: 24
Consider the quadratic equation $x^2-13x+36=0$ with coefficients in a base $b$. The solutions of this equation in the same base $b$ are $x=5$ and $x=6$. Then $b=$ _____

Consider the quadratic equation $x^2-13x+36=0$ with coefficients in a base $b$. The solutions of this equation in the same base $b$ are $x=5$ and $x=6$. Then $b=$ _____

khushtak

14.4k views

khushtak asked Feb 14, 2017

86 votes

8 answers

125

GATE CSE 2004 | Question: 79
How many graphs on $n$ labeled vertices exist which have at least $\frac{(n^2 - 3n)}{ 2}$ edges ? $^{\left(\frac{n^2-n}{2}\right)}C_{\left(\frac{n^2-3n} {2}\right)}$ $^{{\large\sum\limits_{k=0}^{\left (\frac{n^2-3n}{2} \right )}}.\left(n^2-n\right)}C_k$ $^{\left(\frac{n^2-n}{2}\right)}C_n$ $^{{\large\sum\limits_{k=0}^n}.\left(\frac{n^2-n}{2}\right)}C_k$

How many graphs on $n$ labeled vertices exist which have at least $\frac{(n^2 - 3n)}{ 2}$ edges ?$^{\left(\frac{n^2-n}{2}\right)}C_{\left(\frac{n^2-3n} {2}\right)}$$^{{\l...

Kathleen

14.4k views

Kathleen asked Sep 18, 2014

29 votes

6 answers

126

GATE CSE 1995 | Question: 1.19
Let $R$ be a symmetric and transitive relation on a set $A$. Then $R$ is reflexive and hence an equivalence relation $R$ is reflexive and hence a partial order $R$ is reflexive and hence not an equivalence relation None of the above

Let $R$ be a symmetric and transitive relation on a set $A$. Then$R$ is reflexive and hence an equivalence relation$R$ is reflexive and hence a partial order$R$ is reflex...

Kathleen

14.4k views

Kathleen asked Oct 8, 2014

0 votes

2 answers

127

How many subgraphs with at least one vertex does K3 have?

Piyush Kapoor

14.3k views

Piyush Kapoor asked Oct 8, 2015

53 votes

6 answers

128

GATE CSE 2001 | Question: 2.15
How many undirected graphs (not necessarily connected) can be constructed out of a given set $V=\{v_1, v_2, \dots v_n\}$ of $n$ vertices? $\frac{n(n-1)} {2}$ $2^n$ $n!$ $2^\frac{n(n-1)} {2} $

How many undirected graphs (not necessarily connected) can be constructed out of a given set $V=\{v_1, v_2, \dots v_n\}$ of $n$ vertices?$\frac{n(n-1)} {2}$$2^n$$n!$$2^\f...

Kathleen

14.2k views

Kathleen asked Sep 14, 2014

53 votes

8 answers

129

GATE CSE 2013 | Question: 27
What is the logical translation of the following statement? "None of my friends are perfect." $∃x(F (x)∧ ¬P(x))$ $∃ x(¬ F (x)∧ P(x))$ $ ∃x(¬F (x)∧¬P(x))$ $ ¬∃ x(F (x)∧ P(x))$

What is the logical translation of the following statement?"None of my friends are perfect."$∃x(F (x)∧ ¬P(x))$$∃ x(¬ F (x)∧ P(x))$$ ∃x(¬F (x)∧¬P(x))$$ ¬�...

Arjun

14.2k views

Arjun asked Sep 24, 2014

57 votes

6 answers

130

GATE CSE 2003 | Question: 72
The following resolution rule is used in logic programming. Derive clause $(P \vee Q)$ from clauses $(P\vee R),(Q \vee ¬R)$ Which of the following statements related to this rule is FALSE? $((P ∨ R)∧(Q ∨ ¬R))⇒(P ∨ Q)$ ... if $(P ∨ R)∧(Q ∨ ¬R)$ is satisfiable $(P ∨ Q)⇒ \text{FALSE}$ if and only if both $P$ and $Q$ are unsatisfiable

The following resolution rule is used in logic programming.Derive clause $(P \vee Q)$ from clauses $(P\vee R),(Q \vee ¬R)$Which of the following statements related to th...

Kathleen

14.2k views

Kathleen asked Sep 17, 2014

71 votes

5 answers

131

GATE CSE 2008 | Question: 30
Let $\text{fsa}$ and $\text{pda}$ be two predicates such that $\text{fsa}(x)$ means $x$ is a finite state automaton and $\text{pda}(y)$ means that $y$ is a pushdown automaton. Let $\text{equivalent}$ ...

Let $\text{fsa}$ and $\text{pda}$ be two predicates such that $\text{fsa}(x)$ means $x$ is a finite state automaton and $\text{pda}(y)$ means that $y$ is a pushdown autom...

Kathleen

14.1k views

Kathleen asked Sep 12, 2014

63 votes

5 answers

132

GATE CSE 2014 Set 3 | Question: 2
Let $X$ and $Y$ be finite sets and $f:X \to Y$ be a function. Which one of the following statements is TRUE? For any subsets $A$ and $B$ of $X, |f(A \cup B)| = |f(A)| + |f(B)|$ For any subsets $A$ and $B$ of $X, f(A \cap B) = f(A) \cap f(B)$ For any subsets $A$ ... $S$ and $T$ of $Y, f^{-1}(S \cap T) = f^{-1}(S) \cap f^{-1}(T)$

Let $X$ and $Y$ be finite sets and $f:X \to Y$ be a function. Which one of the following statements is TRUE?For any subsets $A$ and $B$ of $X, |f(A \cup B)| = |f(A)| + |f...

go_editor

14.1k views

go_editor asked Sep 28, 2014

9 votes

2 answers

133

Please explain this question .. Number of trivial substrings in “GATE2013” are: A. 37 B. 35 C. 2 D. 36

vijay dwivedi

14.1k views

vijay dwivedi asked Jun 7, 2015

39 votes

5 answers

134

GATE CSE 2000 | Question: 2.5
A relation $R$ is defined on the set of integers as $xRy$ iff $(x + y)$ is even. Which of the following statements is true? $R$ is not an equivalence relation $R$ is an equivalence relation having $1$ equivalence class $R$ is an equivalence relation having $2$ equivalence classes $R$ is an equivalence relation having $3$ equivalence classes

A relation $R$ is defined on the set of integers as $xRy$ iff $(x + y)$ is even. Which of the following statements is true?$R$ is not an equivalence relation$R$ is an equ...

Kathleen

14.1k views

Kathleen asked Sep 14, 2014

30 votes

5 answers

135

GATE CSE 2017 Set 1 | Question: 30
Let $u$ and $v$ be two vectors in $\mathbf{R}^{2}$ whose Euclidean norms satisfy $\left \| u \right \| = 2\left \| v \right \|$. What is the value of $\alpha$ such that $w = u + \alpha v$ bisects the angle between $u$ and $v$? $2$ $\frac{1}{2}$ $1$ $\frac{ -1}{2}$

Let $u$ and $v$ be two vectors in $\mathbf{R}^{2}$ whose Euclidean norms satisfy $\left \| u \right \| = 2\left \| v \right \|$. What is the value of $\alpha$ such that $...

Arjun

14.1k views

Arjun asked Feb 14, 2017

43 votes

6 answers

136

GATE IT 2008 | Question: 27
$G$ is a simple undirected graph. Some vertices of $G$ are of odd degree. Add a node $v$ to $G$ and make it adjacent to each odd degree vertex of $G$. The resultant graph is sure to be regular complete Hamiltonian Euler

$G$ is a simple undirected graph. Some vertices of $G$ are of odd degree. Add a node $v$ to $G$ and make it adjacent to each odd degree vertex of $G$. The resultant graph...

Ishrat Jahan

14.0k views

Ishrat Jahan asked Oct 28, 2014

60 votes

4 answers

137

GATE CSE 2012 | Question: 9
Consider the function $f(x) = \sin(x)$ in the interval $x =\left[\frac{\pi}{4},\frac{7\pi}{4}\right]$. The number and location(s) of the local minima of this function are One, at $\dfrac{\pi}{2}$ One, at $\dfrac{3\pi}{2}$ Two, at $\dfrac{\pi}{2}$ and $\dfrac{3\pi}{2}$ Two, at $\dfrac{\pi}{4}$ and $\dfrac{3\pi}{2}$

Consider the function $f(x) = \sin(x)$ in the interval $x =\left[\frac{\pi}{4},\frac{7\pi}{4}\right]$. The number and location(s) of the local minima of this function are...

gatecse

14.0k views

gatecse asked Aug 5, 2014

40 votes

5 answers

138

GATE CSE 1996 | Question: 2.2
Let $R$ be a non-empty relation on a collection of sets defined by $_{A}R_ B$ if and only if $A \cap B = \phi$. Then, (pick the true statement) $A$ is reflexive and transitive $R$ is symmetric and not transitive $R$ is an equivalence relation $R$ is not reflexive and not symmetric

Let $R$ be a non-empty relation on a collection of sets defined by $_{A}R_ B$ if and only if $A \cap B = \phi$. Then, (pick the true statement)$A$ is reflexive and transi...

Kathleen

14.0k views

Kathleen asked Oct 9, 2014

39 votes

5 answers

139

GATE CSE 1998 | Question: 1.5
What is the converse of the following assertion? I stay only if you go I stay if you go If I stay then you go If you do not go then I do not stay If I do not stay then you go

What is the converse of the following assertion?I stay only if you goI stay if you goIf I stay then you goIf you do not go then I do not stayIf I do not stay then you go

Kathleen

14.0k views

Kathleen asked Sep 25, 2014

7 votes

3 answers

140

ISRO2018-38
The number of edges in a regular graph of degree: $d$ and $n$ vertices is: maximum of $n$ and $d$ $n +d$ $nd$ $nd/2$

The number of edges in a regular graph of degree: $d$ and $n$ vertices is:maximum of $n$ and $d$ $n +d$$nd$$nd/2$

Arjun

14.0k views

Arjun asked Apr 22, 2018

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