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Highest voted questions in Engineering Mathematics
78
votes
6
answers
21
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
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 th...
go_editor
15.7k
views
go_editor
asked
Sep 28, 2014
Set Theory & Algebra
gatecse-2014-set3
set-theory&algebra
functions
normal
+
–
78
votes
6
answers
22
GATE CSE 1992 | Question: 92,xv
Which of the following predicate calculus statements is/are valid? $(\forall (x)) P(x) \vee (\forall(x))Q(x) \implies (\forall (x)) (P(x) \vee Q(x))$ $(\exists (x)) P(x) \wedge (\exists (x))Q(x) \implies (\exists (x)) (P(x) \wedge Q(x))$ ... $(\exists (x)) (P(x) \vee Q(x)) \implies \sim (\forall (x)) P(x) \vee (\exists (x)) Q(x)$
Which of the following predicate calculus statements is/are valid?$(\forall (x)) P(x) \vee (\forall(x))Q(x) \implies (\forall (x)) (P(x) \vee Q(x))$$(\exists (x)) P(x) \w...
Arjun
16.7k
views
Arjun
asked
Sep 2, 2014
Mathematical Logic
gate1992
mathematical-logic
normal
first-order-logic
+
–
77
votes
6
answers
23
GATE CSE 2015 Set 1 | Question: 34
Suppose $L = \left\{ p, q, r, s, t\right\}$ is a lattice represented by the following Hasse diagram: For any $x, y \in L$, not necessarily distinct , $x \vee y$ and $x \wedge y$ are join and meet of $x, y$ ... $p_r = 0$ $p_r = 1$ $0 < p_r ≤ \frac{1}{5}$ $\frac{1}{5} < p_r < 1$
Suppose $L = \left\{ p, q, r, s, t\right\}$ is a lattice represented by the following Hasse diagram:For any $x, y \in L$, not necessarily distinct , $x \vee y$ and $x \we...
makhdoom ghaya
17.4k
views
makhdoom ghaya
asked
Feb 13, 2015
Set Theory & Algebra
gatecse-2015-set1
set-theory&algebra
normal
lattice
+
–
77
votes
6
answers
24
GATE CSE 2014 Set 3 | Question: 50
There are two elements $x,\:y$ in a group $(G,*)$ such that every element in the group can be written as a product of some number of $x$'s and $y$'s in some order. It is known that $x*x=y*y=x*y*x*y=y*x*y*x=e$ where $e$ is the identity element. The maximum number of elements in such a group is ____.
There are two elements $x,\:y$ in a group $(G,*)$ such that every element in the group can be written as a product of some number of $x$'s and $y$'s in some order. It is ...
go_editor
15.7k
views
go_editor
asked
Sep 28, 2014
Set Theory & Algebra
gatecse-2014-set3
set-theory&algebra
group-theory
numerical-answers
normal
+
–
77
votes
8
answers
25
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
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 ...
go_editor
16.0k
views
go_editor
asked
Sep 28, 2014
Set Theory & Algebra
gatecse-2014-set2
set-theory&algebra
normal
set-theory
+
–
77
votes
6
answers
26
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.
$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...
Akshay Jindal
23.7k
views
Akshay Jindal
asked
Sep 27, 2014
Graph Theory
gatecse-2008
graph-connectivity
normal
+
–
76
votes
5
answers
27
GATE CSE 2007 | Question: 23
Which of the following graphs has an Eulerian circuit? Any $k$-regular graph where $k$ is an even number. A complete graph on $90$ vertices. The complement of a cycle on $25$ vertices. None of the above
Which of the following graphs has an Eulerian circuit?Any $k$-regular graph where $k$ is an even number.A complete graph on $90$ vertices.The complement of a cycle on $25...
Kathleen
25.5k
views
Kathleen
asked
Sep 21, 2014
Graph Theory
gatecse-2007
graph-theory
normal
graph-connectivity
+
–
75
votes
8
answers
28
GATE CSE 2016 Set 1 | Question: 1
Let $p, q, r, s$ represents the following propositions. $p:x\in\left\{8, 9, 10, 11, 12\right\}$ $q:$ $x$ is a composite number. $r:$ $x$ is a perfect square. $s:$ $x$ is a prime number. The integer $x\geq2$ which satisfies $\neg\left(\left(p\Rightarrow q\right) \wedge \left(\neg r \vee \neg s\right)\right)$ is ____________.
Let $p, q, r, s$ represents the following propositions.$p:x\in\left\{8, 9, 10, 11, 12\right\}$$q:$ $x$ is a composite number.$r:$ $x$ is a perfect square.$s:$ $x$ is a pr...
Sandeep Singh
13.1k
views
Sandeep Singh
asked
Feb 12, 2016
Mathematical Logic
gatecse-2016-set1
mathematical-logic
normal
numerical-answers
propositional-logic
+
–
74
votes
8
answers
29
GATE IT 2005 | Question: 32
An unbiased coin is tossed repeatedly until the outcome of two successive tosses is the same. Assuming that the trials are independent, the expected number of tosses is $3$ $4$ $5$ $6$
An unbiased coin is tossed repeatedly until the outcome of two successive tosses is the same. Assuming that the trials are independent, the expected number of tosses is$3...
Ishrat Jahan
33.2k
views
Ishrat Jahan
asked
Nov 3, 2014
Probability
gateit-2005
probability
binomial-distribution
expectation
normal
+
–
74
votes
11
answers
30
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 $f(y)$ = $-f(2-y)$
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 exis...
go_editor
21.2k
views
go_editor
asked
Sep 28, 2014
Calculus
gatecse-2014-set1
calculus
continuity
normal
+
–
73
votes
8
answers
31
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
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(\ex...
khushtak
17.4k
views
khushtak
asked
Feb 14, 2017
Mathematical Logic
gatecse-2017-set1
mathematical-logic
first-order-logic
+
–
73
votes
6
answers
32
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 ? $1$ $2$ $3$ $n$
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
21.7k
views
Ishrat Jahan
asked
Oct 29, 2014
Graph Theory
gateit-2007
graph-theory
graph-connectivity
normal
+
–
71
votes
6
answers
33
GATE CSE 2016 Set 2 | Question: 27
Which one of the following well-formed formulae in predicate calculus is NOT valid ? $(\forall _{x} p(x) \implies \forall _{x} q(x)) \implies (\exists _{x} \neg p(x) \vee \forall _{x} q(x))$ ... $\forall x (p(x) \vee q(x)) \implies (\forall x p(x) \vee \forall x q(x))$
Which one of the following well-formed formulae in predicate calculus is NOT valid ?$(\forall _{x} p(x) \implies \forall _{x} q(x)) \implies (\exists _{x} \neg p(x) \vee ...
Akash Kanase
17.0k
views
Akash Kanase
asked
Feb 12, 2016
Mathematical Logic
gatecse-2016-set2
mathematical-logic
first-order-logic
normal
+
–
71
votes
5
answers
34
GATE CSE 2010 | Question: 30
Suppose the predicate $F(x, y, t)$ is used to represent the statement that person $x$ can fool person $y$ at time $t$. Which one of the statements below expresses best the meaning of the formula, $\qquad∀x∃y∃t(¬F(x,y,t))$ Everyone can ... time No one can fool everyone all the time Everyone cannot fool some person all the time No one can fool some person at some time
Suppose the predicate $F(x, y, t)$ is used to represent the statement that person $x$ can fool person $y$ at time $t$.Which one of the statements below expresses best the...
gatecse
82.4k
views
gatecse
asked
Sep 21, 2014
Mathematical Logic
gatecse-2010
mathematical-logic
easy
first-order-logic
+
–
71
votes
5
answers
35
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
14.2k
views
Kathleen
asked
Sep 12, 2014
Mathematical Logic
gatecse-2008
easy
mathematical-logic
first-order-logic
+
–
69
votes
10
answers
36
GATE CSE 2019 | Question: 35
Consider the first order predicate formula $\varphi$: $\forall x [ ( \forall z \: z | x \Rightarrow (( z=x) \vee (z=1))) \rightarrow \exists w ( w > x) \wedge (\forall z \: z | w \Rightarrow ((w=z) \vee (z=1)))]$ Here $a \mid b$ denotes ... of all integers Which of the above sets satisfy $\varphi$? $S_1$ and $S_2$ $S_1$ and $S_3$ $S_2$ and $S_3$ $S_1, S_2$ and $S_3$
Consider the first order predicate formula $\varphi$:$\forall x [ ( \forall z \: z | x \Rightarrow (( z=x) \vee (z=1))) \rightarrow \exists w ( w x) \wedge (\forall z \:...
Arjun
20.3k
views
Arjun
asked
Feb 7, 2019
Mathematical Logic
gatecse-2019
engineering-mathematics
discrete-mathematics
mathematical-logic
first-order-logic
2-marks
+
–
68
votes
9
answers
37
GATE IT 2008 | Question: 21
Which of the following first order formulae is logically valid? Here $\alpha(x)$ is a first order formula with $x$ as a free variable, and $\beta$ ... $[(\forall x, \alpha(x)) \rightarrow \beta] \rightarrow [\forall x, \alpha(x) \rightarrow \beta]$
Which of the following first order formulae is logically valid? Here $\alpha(x)$ is a first order formula with $x$ as a free variable, and $\beta$ is a first order formul...
Ishrat Jahan
15.2k
views
Ishrat Jahan
asked
Oct 27, 2014
Mathematical Logic
gateit-2008
first-order-logic
normal
+
–
67
votes
9
answers
38
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
20.5k
views
Arjun
asked
Feb 14, 2017
Linear Algebra
gatecse-2017-set1
linear-algebra
system-of-equations
normal
+
–
67
votes
10
answers
39
GATE CSE 2016 Set 1 | Question: 27
Consider the recurrence relation $a_1 =8 , a_n =6n^2 +2n+a_{n-1}$. Let $a_{99}=K\times 10^4$. The value of $K$ is __________.
Consider the recurrence relation $a_1 =8 , a_n =6n^2 +2n+a_{n-1}$. Let $a_{99}=K\times 10^4$. The value of $K$ is __________.
Sandeep Singh
29.5k
views
Sandeep Singh
asked
Feb 12, 2016
Combinatory
gatecse-2016-set1
combinatory
recurrence-relation
normal
numerical-answers
+
–
66
votes
6
answers
40
GATE CSE 2017 Set 2 | Question: 26
$P$ and $Q$ are considering to apply for a job. The probability that $P$ applies for the job is $\dfrac{1}{4},$ the probability that $P$ applies for the job given that $Q$ applies for the job is $\dfrac{1}{2},$ and the probability that $Q$ applies for the ... $\left(\dfrac{5}{6}\right)$ $\left(\dfrac{7}{8}\right)$ $\left(\dfrac{11}{12}\right)$
$P$ and $Q$ are considering to apply for a job. The probability that $P$ applies for the job is $\dfrac{1}{4},$ the probability that $P$ applies for the job given that $Q...
Arjun
12.7k
views
Arjun
asked
Feb 14, 2017
Probability
gatecse-2017-set2
probability
conditional-probability
+
–
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