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Previous GATE
Featured
Highest voted questions in Engineering Mathematics
97
votes
8
answers
1
GATE CSE 2012 | Question: 38
Let $G$ be a complete undirected graph on $6$ vertices. If vertices of $G$ are labeled, then the number of distinct cycles of length $4$ in $G$ is equal to $15$ $30$ $90$ $360$
gatecse
asked
in
Graph Theory
Sep 12, 2014
by
gatecse
27.9k
views
gatecse-2012
graph-theory
normal
marks-to-all
counting
93
votes
9
answers
2
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______.
go_editor
asked
in
Graph Theory
Sep 28, 2014
by
go_editor
20.2k
views
gatecse-2014-set1
graph-theory
numerical-answers
normal
graph-connectivity
87
votes
5
answers
3
GATE CSE 2003 | Question: 33
Consider the following formula and its two interpretations \(I_1\) and \(I_2\). \(\alpha: (\forall x)\left[P_x \Leftrightarrow (\forall y)\left[Q_{xy} \Leftrightarrow \neg Q_{yy} \right]\right] \Rightarrow (\forall x)\left[\neg P_x\right]\) \(I_1\) : Domain: ... I_1\) does not Neither \(I_1\) nor \(I_2\) satisfies \(\alpha\) Both \(I_1\) and \(I_2\) satisfies \(\alpha\)
Kathleen
asked
in
Mathematical Logic
Sep 16, 2014
by
Kathleen
11.4k
views
gatecse-2003
mathematical-logic
difficult
first-order-logic
82
votes
8
answers
4
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 ___________.
Sandeep Singh
asked
in
Set Theory & Algebra
Feb 12, 2016
by
Sandeep Singh
15.9k
views
gatecse-2016-set1
set-theory&algebra
functions
normal
numerical-answers
81
votes
9
answers
5
GATE CSE 2016 Set 2 | Question: 28
Consider a set $U$ of $23$ different compounds in a chemistry lab. There is a subset $S$ of $U$ of $9$ compounds, each of which reacts with exactly $3$ compounds of $U$. Consider the following statements: Each compound in U \ S reacts ... \ S reacts with an even number of compounds. Which one of the above statements is ALWAYS TRUE? Only I Only II Only III None.
Akash Kanase
asked
in
Set Theory & Algebra
Feb 12, 2016
by
Akash Kanase
11.9k
views
gatecse-2016-set2
set-theory&algebra
difficult
set-theory
76
votes
8
answers
6
GATE CSE 2016 Set 2 | Question: 01
Consider the following expressions: $false$ $Q$ $true$ $P\vee Q$ $\neg Q\vee P$ The number of expressions given above that are logically implied by $P \wedge (P \Rightarrow Q)$ is ___________.
Akash Kanase
asked
in
Mathematical Logic
Feb 12, 2016
by
Akash Kanase
14.2k
views
gatecse-2016-set2
mathematical-logic
normal
numerical-answers
propositional-logic
76
votes
3
answers
7
GATE CSE 2015 Set 2 | Question: 55
Which one of the following well-formed formulae is a tautology? $\forall x \, \exists y \, R(x,y) \, \leftrightarrow \, \exists y \, \forall x \, R(x, y)$ ... $\forall x \, \forall y \, P(x,y) \, \rightarrow \, \forall x \, \forall y \, P(y, x)$
go_editor
asked
in
Mathematical Logic
Feb 13, 2015
by
go_editor
14.1k
views
gatecse-2015-set2
mathematical-logic
normal
first-order-logic
76
votes
9
answers
8
GATE CSE 2014 Set 2 | Question: 47
The product of the non-zero eigenvalues of the matrix is ____ $\begin{pmatrix} 1 & 0 & 0 & 0 & 1 \\ 0 & 1 & 1 & 1 & 0 \\ 0 & 1 & 1 & 1 & 0 \\ 0 & 1 & 1 & 1 & 0 \\ 1 & 0 & 0 & 0 & 1 \end{pmatrix}$
go_editor
asked
in
Linear Algebra
Sep 28, 2014
by
go_editor
28.4k
views
gatecse-2014-set2
linear-algebra
eigen-value
normal
numerical-answers
74
votes
5
answers
9
GATE CSE 2006 | Question: 72
The $2^n$ vertices of a graph $G$ corresponds to all subsets of a set of size $n$, for $n \geq 6$. Two vertices of $G$ are adjacent if and only if the corresponding sets intersect in exactly two elements. The maximum degree of a vertex in $G$ is: $\binom{\frac{n}{2}}{2}.2^{\frac{n}{2}}$ $2^{n-2}$ $2^{n-3}\times 3$ $2^{n-1}$
go_editor
asked
in
Graph Theory
Apr 24, 2016
by
go_editor
14.2k
views
gatecse-2006
graph-theory
normal
degree-of-graph
72
votes
4
answers
10
GATE CSE 2004 | Question: 23, ISRO2007-32
Identify the correct translation into logical notation of the following assertion. Some boys in the class are taller than all the girls Note: $\text{taller} (x, y)$ is true if $x$ is taller than $y$ ... $(\exists x) (\text{boy}(x) \land (\forall y) (\text{girl}(y) \rightarrow \text{taller}(x, y)))$
Kathleen
asked
in
Mathematical Logic
Sep 19, 2014
by
Kathleen
11.3k
views
gatecse-2004
mathematical-logic
easy
isro2007
first-order-logic
70
votes
11
answers
11
GATE CSE 2015 Set 3 | Question: 24
In a room there are only two types of people, namely $\text{Type 1}$ and $\text{Type 2}$. $\text{Type 1}$ people always tell the truth and $\text{Type 2}$ people always lie. You give a fair coin to a person in that room, without knowing which type ... person is of $\text{Type 2}$, then the result is tail If the person is of $\text{Type 1}$, then the result is tail
go_editor
asked
in
Mathematical Logic
Feb 14, 2015
by
go_editor
12.9k
views
gatecse-2015-set3
mathematical-logic
difficult
logical-reasoning
70
votes
15
answers
12
GATE CSE 2012 | Question: 33
Suppose a fair six-sided die is rolled once. If the value on the die is $1, 2,$ or $3,$ the die is rolled a second time. What is the probability that the sum total of values that turn up is at least $6$ ? $\dfrac{10}{21}$ $\dfrac{5}{12}$ $\dfrac{2}{3}$ $\dfrac{1}{6}$
gatecse
asked
in
Probability
Sep 26, 2014
by
gatecse
16.9k
views
gatecse-2012
probability
conditional-probability
normal
69
votes
6
answers
13
GATE CSE 2008 | Question: 42
$G$ is a graph on $n$ vertices and $2n-2$ edges. The edges of $G$ can be partitioned into two edge-disjoint spanning trees. Which of the following is NOT true for $G$? For every subset of $k$ vertices, the induced subgraph has at ... least $2$ edge-disjoint paths between every pair of vertices. There are at least $2$ vertex-disjoint paths between every pair of vertices.
Akshay Jindal
asked
in
Graph Theory
Sep 27, 2014
by
Akshay Jindal
18.5k
views
gatecse-2008
graph-connectivity
normal
69
votes
8
answers
14
GATE CSE 2006 | Question: 25
Let $S = \{1, 2, 3,\ldots, m\}, m >3.$ Let $X_1,\ldots,X_n$ be subsets of $S$ each of size $3.$ Define a function $f$ from $S$ to the set of natural numbers as, $f(i)$ is the number of sets $X_j$ that contain the element $i.$ That is $f(i)=\left | \left\{j \mid i\in X_j \right\} \right|$ then $ \sum_{i=1}^{m} f(i)$ is: $3m$ $3n$ $2m+1$ $2n+1$
Rucha Shelke
asked
in
Set Theory & Algebra
Sep 18, 2014
by
Rucha Shelke
7.9k
views
gatecse-2006
set-theory&algebra
normal
functions
68
votes
4
answers
15
GATE CSE 2014 Set 3 | Question: 49
Consider the set of all functions $f:\{0,1, \dots,2014\} \to \{0,1,\dots, 2014\}$ such that $ f\left(f\left(i\right)\right)=i$, for all $0 \leq i \leq 2014$. Consider the following statements: $P$. For each such function it must be the case that for every ... is CORRECT? $P, Q$ and $R$ are true Only $Q$ and $R$ are true Only $P$ and $Q$ are true Only $R$ is true
go_editor
asked
in
Set Theory & Algebra
Sep 28, 2014
by
go_editor
11.6k
views
gatecse-2014-set3
set-theory&algebra
functions
normal
68
votes
7
answers
16
GATE CSE 2004 | Question: 79
How many graphs on $n$ labeled vertices exist which have at least $\frac{(n^2 - 3n)}{ 2}$ edges ? $^{\left(\frac{n^2-n}{2}\right)}C_{\left(\frac{n^2-3n} {2}\right)}$ $^{{\large\sum\limits_{k=0}^{\left (\frac{n^2-3n}{2} \right )}}.\left(n^2-n\right)}C_k$ $^{\left(\frac{n^2-n}{2}\right)}C_n$ $^{{\large\sum\limits_{k=0}^n}.\left(\frac{n^2-n}{2}\right)}C_k$
Kathleen
asked
in
Graph Theory
Sep 19, 2014
by
Kathleen
10.6k
views
gatecse-2004
graph-theory
combinatory
normal
counting
67
votes
6
answers
17
GATE IT 2007 | Question: 25
What is the largest integer $m$ such that every simple connected graph with $n$ vertices and $n$ edges contains at least $m$ different spanning trees ? $1$ $2$ $3$ $n$
Ishrat Jahan
asked
in
Graph Theory
Oct 30, 2014
by
Ishrat Jahan
15.2k
views
gateit-2007
graph-theory
graph-connectivity
normal
65
votes
6
answers
18
GATE CSE 2017 Set 1 | Question: 02
Consider the first-order logic sentence $F:\forall x(\exists yR(x,y))$. Assuming non-empty logical domains, which of the sentences below are implied by $F$? $\exists y(\exists xR(x,y))$ $\exists y(\forall xR(x,y))$ $\forall y(\exists xR(x,y))$ $¬\exists x(\forall y¬R(x,y))$ IV only I and IV only II only II and III only
khushtak
asked
in
Mathematical Logic
Feb 14, 2017
by
khushtak
13.1k
views
gatecse-2017-set1
mathematical-logic
first-order-logic
65
votes
7
answers
19
GATE CSE 2014 Set 2 | Question: 50
Consider the following relation on subsets of the set $S$ of integers between $1$ and $2014$. For two distinct subsets $U$ and $V$ of $S$ we say $U\:<\:V$ if the minimum element in the symmetric difference of the two sets is in $U$. Consider the ... $S1$ is true and $S2$ is false $S2$ is true and $S1$ is false Neither $S1$ nor $S2$ is true
go_editor
asked
in
Set Theory & Algebra
Sep 28, 2014
by
go_editor
11.2k
views
gatecse-2014-set2
set-theory&algebra
normal
set-theory
65
votes
7
answers
20
GATE CSE 2014 Set 1 | Question: 47
A function $f(x)$ is continuous in the interval $[0,2]$. It is known that $f(0) = f(2) = -1$ and $f(1) = 1$. Which one of the following statements must be true? There exists a $y$ in the interval $(0,1)$ such that $f(y) = f(y+1)$ For every $y$ ... the function in the interval $(0,2)$ is $1$ There exists a $y$ in the interval $(0,1)$ such that $f(y)$ = $-f(2-y)$
go_editor
asked
in
Calculus
Sep 28, 2014
by
go_editor
15.4k
views
gatecse-2014-set1
calculus
continuity
normal
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