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Highest voted questions in Engineering Mathematics
60
votes
6
answers
61
GATE CSE 2000 | Question: 2.6
Let $P(S)$ denotes the power set of set $S.$ Which of the following is always true? $P(P(S)) = P(S)$ $P(S) ∩ P(P(S)) = \{ Ø \}$ $P(S) ∩ S = P(S)$ $S ∉ P(S)$
Let $P(S)$ denotes the power set of set $S.$ Which of the following is always true?$P(P(S)) = P(S)$$P(S) ∩ P(P(S)) = \{ Ø \}$$P(S) ∩ S = P(S)$$S ∉ P(S)$
Kathleen
13.5k
views
Kathleen
asked
Sep 14, 2014
Set Theory & Algebra
gatecse-2000
set-theory&algebra
easy
set-theory
+
–
60
votes
4
answers
62
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
Calculus
gatecse-2012
calculus
maxima-minima
normal
+
–
59
votes
8
answers
63
GATE CSE 2013 | Question: 26
The line graph $L(G)$ of a simple graph $G$ is defined as follows: There is exactly one vertex $v(e)$ in $L(G)$ for each edge $e$ in $G$. For any two edges $e$ and $e'$ in $G$, $L(G)$ has an edge between $v(e)$ and $v(e')$, if and only if ... planar graph is planar. (S) The line graph of a tree is a tree. $P$ only $P$ and $R$ only $R$ only $P, Q$ and $S$ only
The line graph $L(G)$ of a simple graph $G$ is defined as follows:There is exactly one vertex $v(e)$ in $L(G)$ for each edge $e$ in $G$.For any two edges $e$ and $e'$ in ...
Arjun
19.0k
views
Arjun
asked
Sep 24, 2014
Graph Theory
gatecse-2013
graph-theory
normal
graph-connectivity
+
–
59
votes
7
answers
64
GATE CSE 2003 | Question: 32
Which of the following is a valid first order formula? (Here \(\alpha\) and \(\beta\) are first order formulae with $x$ as their only free variable) $((∀x)[α] ⇒ (∀x)[β]) ⇒ (∀x)[α ⇒ β]$ $(∀x)[α] ⇒ (∃x)[α ∧ β]$ $((∀x)[α ∨ β] ⇒ (∃x)[α]) ⇒ (∀x)[α]$ $(∀x)[α ⇒ β] ⇒ (((∀x)[α]) ⇒ (∀x)[β])$
Which of the following is a valid first order formula? (Here \(\alpha\) and \(\beta\) are first order formulae with $x$ as their only free variable)$((∀x)[α] ⇒ (∀x...
Kathleen
16.8k
views
Kathleen
asked
Sep 16, 2014
Mathematical Logic
gatecse-2003
mathematical-logic
first-order-logic
normal
+
–
58
votes
9
answers
65
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
Combinatory
gatecse-2017-set2
combinatory
generating-functions
numerical-answers
normal
+
–
58
votes
7
answers
66
GATE IT 2008 | Question: 4
What is the size of the smallest $\textsf{MIS}$ (Maximal Independent Set) of a chain of nine nodes? $5$ $4$ $3$ $2$
What is the size of the smallest $\textsf{MIS}$ (Maximal Independent Set) of a chain of nine nodes?$5$$4$$3$$2$
Ishrat Jahan
59.0k
views
Ishrat Jahan
asked
Oct 27, 2014
Graph Theory
gateit-2008
normal
graph-connectivity
+
–
58
votes
7
answers
67
GATE CSE 2006 | Question: 24
Given a set of elements $N = {1, 2, ..., n}$ and two arbitrary subsets $A⊆N$ and $B⊆N$, how many of the n! permutations $\pi$ from $N$ to $N$ satisfy $\min(\pi(A)) = \min(\pi(B))$, where $\min(S)$ is the smallest integer in the set of integers $S$, and $\pi$(S) is the set of ... $n! \frac{|A ∩ B|}{|A ∪ B|}$ $\dfrac{|A ∩ B|^2}{^n \mathrm{C}_{|A ∪ B|}}$
Given a set of elements $N = {1, 2, ..., n}$ and two arbitrary subsets $A⊆N$ and $B⊆N$, how many of the n! permutations $\pi$ from $N$ to $N$ satisfy $\min(\pi(A)) = ...
Rucha Shelke
11.2k
views
Rucha Shelke
asked
Sep 18, 2014
Set Theory & Algebra
gatecse-2006
set-theory&algebra
normal
set-theory
+
–
58
votes
6
answers
68
GATE CSE 2003 | Question: 31
Let $(S, \leq)$ be a partial order with two minimal elements a and b, and a maximum element c. Let P: S \(\to\) {True, False} be a predicate defined on S. Suppose that P(a) = True, P(b) = False and P(x) \(\implies\) P(y) for all $x, y \in S$ satisfying $x \leq y$ ... for all x \(\in\) S such that b ≤ x and x ≠ c P(x) = False for all x \(\in\) S such that a ≤ x and b ≤ x
Let $(S, \leq)$ be a partial order with two minimal elements a and b, and a maximum element c. Let P: S \(\to\) {True, False} be a predicate defined on S. Suppose that P(...
Kathleen
11.7k
views
Kathleen
asked
Sep 16, 2014
Set Theory & Algebra
gatecse-2003
set-theory&algebra
partial-order
normal
propositional-logic
+
–
57
votes
10
answers
69
GATE CSE 2017 Set 2 | Question: 11
Let $p, q, r$ ... $(\neg p \wedge r) \vee (r \rightarrow (p \wedge q))$
Let $p, q, r$ denote the statements ”It is raining”, “It is cold”, and “It is pleasant”, respectively. Then the statement “It is not raining and it is pleas...
khushtak
12.2k
views
khushtak
asked
Feb 14, 2017
Mathematical Logic
gatecse-2017-set2
mathematical-logic
propositional-logic
+
–
57
votes
17
answers
70
GATE CSE 2016 Set 1 | Question: 26
The coefficient of $x^{12}$ in $\left(x^{3}+x^{4}+x^{5}+x^{6}+\dots \right)^{3}$ is ___________.
The coefficient of $x^{12}$ in $\left(x^{3}+x^{4}+x^{5}+x^{6}+\dots \right)^{3}$ is ___________.
Sandeep Singh
25.8k
views
Sandeep Singh
asked
Feb 12, 2016
Combinatory
gatecse-2016-set1
combinatory
generating-functions
normal
numerical-answers
+
–
57
votes
3
answers
71
GATE IT 2005 | Question: 56
Let $G$ be a directed graph whose vertex set is the set of numbers from $1$ to $100$. There is an edge from a vertex $i$ to a vertex $j$ iff either $j = i + 1$ or $j = 3i$. The minimum number of edges in a path in $G$ from vertex $1$ to vertex $100$ is $4$ $7$ $23$ $99$
Let $G$ be a directed graph whose vertex set is the set of numbers from $1$ to $100$. There is an edge from a vertex $i$ to a vertex $j$ iff either $j = i + 1$ or $j = 3i...
Ishrat Jahan
10.6k
views
Ishrat Jahan
asked
Nov 3, 2014
Graph Theory
gateit-2005
graph-theory
graph-connectivity
normal
+
–
57
votes
11
answers
72
GATE CSE 2014 Set 3 | Question: 51
If $G$ is the forest with $n$ vertices and $k$ connected components, how many edges does $G$ have? $\left\lfloor\frac {n}{k}\right\rfloor$ $\left\lceil \frac{n}{k} \right\rceil$ $n-k$ $n-k+1$
If $G$ is the forest with $n$ vertices and $k$ connected components, how many edges does $G$ have?$\left\lfloor\frac {n}{k}\right\rfloor$$\left\lceil \frac{n}{k} \right\r...
go_editor
18.4k
views
go_editor
asked
Sep 28, 2014
Graph Theory
gatecse-2014-set3
graph-theory
graph-connectivity
normal
+
–
57
votes
6
answers
73
GATE CSE 2003 | Question: 72
The following resolution rule is used in logic programming. Derive clause $(P \vee Q)$ from clauses $(P\vee R),(Q \vee ¬R)$ Which of the following statements related to this rule is FALSE? $((P ∨ R)∧(Q ∨ ¬R))⇒(P ∨ Q)$ ... if $(P ∨ R)∧(Q ∨ ¬R)$ is satisfiable $(P ∨ Q)⇒ \text{FALSE}$ if and only if both $P$ and $Q$ are unsatisfiable
The following resolution rule is used in logic programming.Derive clause $(P \vee Q)$ from clauses $(P\vee R),(Q \vee ¬R)$Which of the following statements related to th...
Kathleen
14.2k
views
Kathleen
asked
Sep 17, 2014
Mathematical Logic
gatecse-2003
mathematical-logic
normal
propositional-logic
+
–
56
votes
7
answers
74
GATE CSE 2016 Set 2 | Question: 04
Consider the systems, each consisting of $m$ linear equations in $n$ variables. If $m < n$, then all such systems have a solution. If $m > n$, then none of these systems has a solution. If $m = n$, then there exists a system which has a solution. ... $\text{II}$ and $\text{III}$ are true. Only $\text{III}$ is true. None of them is true.
Consider the systems, each consisting of $m$ linear equations in $n$ variables.If $m < n$, then all such systems have a solution.If $m n$, then none of these systems has...
Akash Kanase
15.8k
views
Akash Kanase
asked
Feb 12, 2016
Linear Algebra
gatecse-2016-set2
linear-algebra
system-of-equations
normal
+
–
56
votes
6
answers
75
GATE CSE 2011 | Question: 30
Which one of the following options is CORRECT given three positive integers $x, y$ and $z$ ... always true irrespective of the value of $x$ $P(x)$ being true means that $x$ has exactly two factors other than $1$ and $x$
Which one of the following options is CORRECT given three positive integers $x, y$ and $z$, and a predicate$$P\left(x\right) = \neg \left(x=1\right)\wedge \forall y \left...
go_editor
13.3k
views
go_editor
asked
Sep 29, 2014
Mathematical Logic
gatecse-2011
mathematical-logic
normal
first-order-logic
+
–
56
votes
3
answers
76
GATE CSE 2010 | Question: 27
What is the probability that divisor of $10^{99}$ is a multiple of $10^{96}$? $\left(\dfrac{1}{625}\right)$ $\left(\dfrac{4}{625}\right)$ $\left(\dfrac{12}{625}\right)$ $\left(\dfrac{16}{625}\right)$
What is the probability that divisor of $10^{99}$ is a multiple of $10^{96}$?$\left(\dfrac{1}{625}\right)$$\left(\dfrac{4}{625}\right)$$\left(\dfrac{12}{625}\right)$$\lef...
gatecse
13.6k
views
gatecse
asked
Sep 21, 2014
Probability
gatecse-2010
probability
normal
+
–
55
votes
6
answers
77
GATE CSE 2015 Set 3 | Question: 37
Suppose $X_i$ for $i=1, 2, 3$ are independent and identically distributed random variables whose probability mass functions are $Pr[X_i = 0] = Pr[X_i = 1] = \frac{1} {2} \text{ for } i = 1, 2, 3$. Define another random variable $Y = X_1X_2 \oplus X_3$, where $\oplus$ denotes XOR. Then $Pr[Y=0 \mid X_3 = 0] =$______.
Suppose $X_i$ for $i=1, 2, 3$ are independent and identically distributed random variables whose probability mass functions are $Pr[X_i = 0] = Pr[X_i = 1] = \frac{1} {2} ...
go_editor
18.4k
views
go_editor
asked
Feb 15, 2015
Probability
gatecse-2015-set3
probability
random-variable
normal
numerical-answers
+
–
54
votes
7
answers
78
TIFR CSE 2017 | Part B | Question: 12
An undirected graph is complete if there is an edge between every pair of vertices. Given a complete undirected graph on $n$ vertices, in how many ways can you choose a direction for the edges so that there are no directed cycles? $n$ $\frac{n(n-1)}{2}$ $n!$ $2^n$ $2^m, \: \text{ where } m=\frac{n(n-1)}{2}$
An undirected graph is complete if there is an edge between every pair of vertices. Given a complete undirected graph on $n$ vertices, in how many ways can you choose a d...
go_editor
6.6k
views
go_editor
asked
Dec 23, 2016
Graph Theory
tifr2017
graph-theory
graph-connectivity
+
–
54
votes
4
answers
79
GATE CSE 2016 Set 1 | Question: 29
Consider the following experiment. Step 1. Flip a fair coin twice. Step 2. If the outcomes are (TAILS, HEADS) then output $Y$ and stop. Step 3. If the outcomes are either (HEADS, HEADS) or (HEADS, TAILS), then output $N$ and stop. Step 4. If ... , TAILS), then go to Step $1.$ The probability that the output of the experiment is $Y$ is (up to two decimal places)
Consider the following experiment.Step 1. Flip a fair coin twice.Step 2. If the outcomes are (TAILS, HEADS) then output $Y$ and stop.Step 3. If the outcomes are either (H...
Sandeep Singh
11.8k
views
Sandeep Singh
asked
Feb 12, 2016
Probability
gatecse-2016-set1
probability
normal
numerical-answers
+
–
54
votes
6
answers
80
GATE CSE 1997 | Question: 6.3
The number of equivalence relations of the set $\{1,2,3,4\}$ is $15$ $16$ $24$ $4$
The number of equivalence relations of the set $\{1,2,3,4\}$ is$15$$16$$24$$4$
Kathleen
21.3k
views
Kathleen
asked
Sep 29, 2014
Set Theory & Algebra
gate1997
set-theory&algebra
relations
normal
+
–
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