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relation
Number of relations $S$ over set $\{0,1,2,3 \}$ such that $(x,y) \in S \Rightarrow x = y$
asked
Dec 27, 2017
in
Set Theory & Algebra
by
Lakshman Patel RJIT
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52.9k
points)

42.1k
views
relations
+24
votes
12
answers
2
GATE201846
The number of possible minheaps containing each value from $\{1,2,3,4,5,6,7\}$ exactly once is _______
asked
Feb 14, 2018
in
Combinatory
by
gatecse
Boss
(
16.6k
points)

8.2k
views
gate2018
permutationandcombination
numericalanswers
+46
votes
7
answers
3
GATE2014247
The product of the nonzero eigenvalues of the matrix is ____ $\begin{pmatrix} 1 & 0 & 0 & 0 & 1 \\ 0 & 1 & 1 & 1 & 0 \\ 0 & 1 & 1 & 1 & 0 \\ 0 & 1 & 1 & 1 & 0 \\ 1 & 0 & 0 & 0 & 1 \end{pmatrix}$
asked
Sep 28, 2014
in
Linear Algebra
by
jothee
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104k
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9.8k
views
gate20142
linearalgebra
eigenvalue
normal
numericalanswers
+33
votes
8
answers
4
GATE19941.6, ISRO200829
The number of distinct simple graphs with up to three nodes is $15$ $10$ $7$ $9$
asked
Oct 4, 2014
in
Graph Theory
by
Kathleen
Veteran
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52.1k
points)

9.5k
views
gate1994
graphtheory
permutationandcombination
normal
isro2008
counting
+63
votes
6
answers
5
GATE201238
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 $15$ $30$ $90$ $360$
asked
Sep 12, 2014
in
Graph Theory
by
gatecse
Boss
(
16.6k
points)

10.1k
views
gate2012
graphtheory
normal
markstoall
counting
+6
votes
6
answers
6
GATE201935
Consider the first order predicate formula $\varphi$: $\forall x [ ( \forall z \: z \mid x \Rightarrow (( z=x) \vee (z=1))) \rightarrow \exists w ( w > x) \wedge (\forall z \: z \mid w \Rightarrow ((w=z) \vee (z=1)))]$ Here $a \mid b$ ... Set of all positive integers $S3:$ Set of all integers Which of the above sets satisfy $\varphi$? S1 and S2 S1 and S3 S2 and S3 S1, S2 and S3
asked
Feb 7
in
Mathematical Logic
by
Arjun
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(
422k
points)

5k
views
gate2019
engineeringmathematics
discretemathematics
mathematicallogic
firstorderlogic
+37
votes
10
answers
7
GATE2016126
The coefficient of $x^{12}$ in $\left(x^{3}+x^{4}+x^{5}+x^{6}+\dots \right)^{3}$ is ___________.
asked
Feb 12, 2016
in
Combinatory
by
Sandeep Singh
Loyal
(
7.2k
points)

8.9k
views
gate20161
permutationandcombination
generatingfunctions
normal
numericalanswers
+15
votes
8
answers
8
GATE20181
Which one of the following is a closed form expression for the generating function of the sequence $\{a_n\}$, where $a_n = 2n +3 \text{ for all } n=0, 1, 2, \dots$? $\frac{3}{(1x)^2}$ $\frac{3x}{(1x)^2}$ $\frac{2x}{(1x)^2}$ $\frac{3x}{(1x)^2}$
asked
Feb 14, 2018
in
Combinatory
by
gatecse
Boss
(
16.6k
points)

6.1k
views
gate2018
generatingfunctions
normal
permutationandcombination
+29
votes
10
answers
9
GATE2015240
The number of onto functions (surjective functions) from set $X = \{1, 2, 3, 4\}$ to set $Y=\{a,b,c\}$ is ______.
asked
Feb 13, 2015
in
Set Theory & Algebra
by
jothee
Veteran
(
104k
points)

7.6k
views
gate20152
settheory&algebra
functions
normal
numericalanswers
+21
votes
4
answers
10
GATE2017119
Let $X$ be a Gaussian random variable with mean 0 and variance $\sigma ^{2}$. Let $Y$ = $\max\left ( X,0 \right )$ where $\max\left ( a,b \right )$ is the maximum of $a$ and $b$. The median of $Y$ is ______________ .
asked
Feb 14, 2017
in
Probability
by
Arjun
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(
422k
points)

5.6k
views
gate20171
probability
numericalanswers
normaldistribution
+21
votes
5
answers
11
GATE201827
Let $N$ be the set of natural numbers. Consider the following sets, $P:$ Set of Rational numbers (positive and negative) $Q:$ Set of functions from $\{0,1\}$ to $N$ $R:$ Set of functions from $N$ to $\{0, 1\}$ $S:$ Set of finite subsets of $N$ Which of the above sets are countable? $Q$ and $S$ only $P$ and $S$ only $P$ and $R$ only $P, Q$ and $S$ only
asked
Feb 14, 2018
in
Set Theory & Algebra
by
gatecse
Boss
(
16.6k
points)

4.7k
views
gate2018
settheory&algebra
countableuncountableset
normal
+35
votes
7
answers
12
GATE2017247
If the ordinary generating function of a sequence $\left \{a_n\right \}_{n=0}^\infty$ is $\large \frac{1+z}{(1z)^3}$, then $a_3a_0$ is equal to ___________ .
asked
Feb 14, 2017
in
Combinatory
by
Arjun
Veteran
(
422k
points)

5.7k
views
gate20172
permutationandcombination
generatingfunctions
numericalanswers
normal
+51
votes
7
answers
13
GATE2016228
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 with an odd number ... in U \ S reacts with an even number of compounds. Which one of the above statements is ALWAYS TRUE? Only I Only II Only III None.
asked
Feb 12, 2016
in
Set Theory & Algebra
by
Akash Kanase
Boss
(
41.4k
points)

4.9k
views
gate20162
settheory&algebra
difficult
sets
+35
votes
8
answers
14
GATE2016127
Consider the recurrence relation $a_1 =8 , a_n =6n^2 +2n+a_{n1}$. Let $a_{99}=K\times 10^4$. The value of $K$ is __________.
asked
Feb 12, 2016
in
Combinatory
by
Sandeep Singh
Loyal
(
7.2k
points)

7.3k
views
gate20161
permutationandcombination
recurrence
normal
numericalanswers
+19
votes
2
answers
15
On a set of n elements, how many relations are there that are both irreflexive and antisymmetric?
asked
Oct 24, 2014
in
Set Theory & Algebra
by
shree
Active
(
3.5k
points)

13.8k
views
settheory&algebra
+57
votes
7
answers
16
GATE2014151
Consider an undirected graph $G$ where selfloops 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 $ac \leq 1$ and $bd \leq 1$. The number of edges in this graph is______.
asked
Sep 28, 2014
in
Graph Theory
by
jothee
Veteran
(
104k
points)

7.7k
views
gate20141
graphtheory
numericalanswers
normal
graphconnectivity
+21
votes
4
answers
17
GATE201826
Consider a matrix P whose only eigenvectors are the multiples of $\begin{bmatrix} 1 \\ 4 \end{bmatrix}$. Consider the following statements. P does not have an inverse P has a repeated eigenvalue P cannot be diagonalized Which one of the following options ... and III are necessarily true Only II is necessarily true Only I and II are necessarily true Only II and III are necessarily true
asked
Feb 14, 2018
in
Linear Algebra
by
gatecse
Boss
(
16.6k
points)

5.6k
views
gate2018
linearalgebra
matrices
eigenvalue
normal
+43
votes
10
answers
18
GATE201233
Suppose a fair sixsided 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 $6$ ? $\dfrac{10}{21}$ $\dfrac{5}{12}$ $\dfrac{2}{3}$ $\dfrac{1}{6}$
asked
Sep 26, 2014
in
Probability
by
gatecse
Boss
(
16.6k
points)

6.3k
views
gate2012
probability
conditionalprobability
normal
+5
votes
10
answers
19
GATE201921
The value of $3^{51} \text{ mod } 5$ is _____
asked
Feb 7
in
Combinatory
by
Arjun
Veteran
(
422k
points)

3.1k
views
gate2019
numericalanswers
permutationandcombination
modulararithmetic
+5
votes
3
answers
20
GATE20195
Let $U = \{1, 2, \dots , n\}$ Let $A=\{(x, X) \mid x \in X, X \subseteq U \}$. Consider the following two statements on $\mid A \mid$. $\mid A \mid = n2^{n1}$ $\mid A \mid = \Sigma_{k=1}^{n} k \begin{pmatrix} n \\ k \end{pmatrix}$ Which of the above statements is/are TRUE? Only I Only II Both I and II Neither I nor II
asked
Feb 7
in
Combinatory
by
Arjun
Veteran
(
422k
points)

2.7k
views
gate2019
engineeringmathematics
discretemathematics
permutationandcombination
+22
votes
6
answers
21
GATE2017252
If the characteristic polynomial of a 3 $\times$ 3 matrix $M$ over $\mathbb{R}$ (the set of real numbers) is $\lambda^3 – 4 \lambda^2 + a \lambda +30, \quad a \in \mathbb{R}$, and one eigenvalue of $M$ is 2, then the largest among the absolute values of the eigenvalues of $M$ is _______
asked
Feb 14, 2017
in
Linear Algebra
by
Madhav
Active
(
1.6k
points)

3.8k
views
gate20172
engineeringmathematics
linearalgebra
numericalanswers
eigenvalue
+52
votes
7
answers
22
GATE2015139
Consider the operations $\textit{f (X, Y, Z) = X'YZ + XY' + Y'Z'}$ and $\textit{g (X, Y, Z) = X'YZ + X'YZ' + XY}$ Which one of the following is correct? Both $\left\{\textit{f} \right\}$ and $\left\{ \textit{g}\right\}$ are ... Only $\left\{ \textit{g}\right\}$ is functionally complete Neither $\left\{ \textit{f}\right\}$ nor $\left\{\textit{g}\right\}$ is functionally complete
asked
Feb 13, 2015
in
Set Theory & Algebra
by
makhdoom ghaya
Boss
(
29.9k
points)

7.5k
views
gate20151
settheory&algebra
functions
difficult
+5
votes
8
answers
23
GATE201912
Let $G$ be an undirected complete graph on $n$ vertices, where $n > 2$. Then, the number of different Hamiltonian cycles in $G$ is equal to $n!$ $(n1)!$ $1$ $\frac{(n1)!}{2}$
asked
Feb 7
in
Graph Theory
by
Arjun
Veteran
(
422k
points)

3.2k
views
gate2019
engineeringmathematics
discretemathematics
graphtheory
graphconnectivity
+35
votes
4
answers
24
GATE2017131
Let $A$ be $n\times n$ real valued square symmetric matrix of rank 2 with $\sum_{i=1}^{n}\sum_{j=1}^{n}A^{2}_{ij} =$ 50. Consider the following statements. One eigenvalue must be in $\left [ 5,5 \right ]$ The eigenvalue with the largest ... greater than 5 Which of the above statements about eigenvalues of $A$ is/are necessarily CORRECT? Both I and II I only II only Neither I nor II
asked
Feb 14, 2017
in
Linear Algebra
by
Arjun
Veteran
(
422k
points)

6.1k
views
gate20171
linearalgebra
eigenvalue
normal
+30
votes
4
answers
25
GATE2017248
If a random variable $X$ has a Poisson distribution with mean $5$, then the expectation $E\left [ \left ( x+2 \right )^{2} \right ]$ equals ___.
asked
Feb 14, 2017
in
Probability
by
Kantikumar
Active
(
4.6k
points)

4.6k
views
gate20172
expectation
poissondistribution
numericalanswers
probability
+55
votes
4
answers
26
GATE200333
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: the set of ... , \(I_1\) does not Neither \(I_1\) nor \(I_2\) satisfies \(\alpha\) Both \(I_1\) and \(I_2\) satisfies \(\alpha\)
asked
Sep 16, 2014
in
Mathematical Logic
by
Kathleen
Veteran
(
52.1k
points)

4.3k
views
gate2003
mathematicallogic
difficult
firstorderlogic
+25
votes
3
answers
27
GATE201828
Consider the firstorder logic sentence $\varphi \equiv \exists \: s \: \exists \: t \: \exists \: u \: \forall \: v \: \forall \: w \forall \: x \: \forall \: y \: \psi(s, t, u, v, w, x, y)$ ... than or equal to $3$ There exists no model of $\varphi$ with universe size of greater than $7$ Every model of $\varphi$ has a universe of size equal to $7$
asked
Feb 14, 2018
in
Mathematical Logic
by
gatecse
Boss
(
16.6k
points)

6.7k
views
gate2018
mathematicallogic
normal
firstorderlogic
+35
votes
9
answers
28
GATE2014351
If $G$ is the forest with $n$ vertices and $k$ connected components, how many edges does $G$ have? $\left\lfloor\frac {n}{k}\right\rfloor$ $\left\lceil \frac{n}{k} \right\rceil$ $nk$ $nk+1$
asked
Sep 28, 2014
in
Graph Theory
by
jothee
Veteran
(
104k
points)

4.5k
views
gate20143
graphtheory
graphconnectivity
normal
+52
votes
6
answers
29
GATE2016128
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 ___________.
asked
Feb 12, 2016
in
Set Theory & Algebra
by
Sandeep Singh
Loyal
(
7.2k
points)

6k
views
gate20161
settheory&algebra
functions
normal
numericalanswers
+38
votes
6
answers
30
GATE200544
What is the minimum number of ordered pairs of nonnegative numbers that should be chosen to ensure that there are two pairs $(a,b)$ and $(c,d)$ in the chosen set such that, $a \equiv c\mod 3$ and $b \equiv d \mod 5$ $4$ $6$ $16$ $24$
asked
Sep 21, 2014
in
Combinatory
by
gatecse
Boss
(
16.6k
points)

4.3k
views
gate2005
settheory&algebra
normal
pigeonholeprinciple
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