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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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59.2k
points)

42.2k
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relations
+19
votes
2
answers
2
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)

13.9k
views
settheory&algebra
+3
votes
1
answer
3
19. a) What is the probability that two people chosen at random were born during the same month of the year?
asked
Nov 25, 2014
in
Probability
by
Sahil Gupta
Active
(
1.1k
points)

13.7k
views
probability
+72
votes
8
answers
4
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
(
17.5k
points)

11.5k
views
gate2012
graphtheory
normal
markstoall
counting
+49
votes
7
answers
5
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
Veteran
(
105k
points)

11.2k
views
gate20142
linearalgebra
eigenvalue
normal
numericalanswers
+39
votes
9
answers
6
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
(
52.2k
points)

10.5k
views
gate1994
graphtheory
permutationandcombination
normal
isro2008
counting
+40
votes
11
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)

9.8k
views
gate20161
permutationandcombination
generatingfunctions
normal
numericalanswers
+29
votes
13
answers
8
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
(
17.5k
points)

9.8k
views
gate2018
permutationandcombination
numericalanswers
+69
votes
8
answers
9
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
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(
105k
points)

8.6k
views
gate20141
graphtheory
numericalanswers
normal
graphconnectivity
+32
votes
4
answers
10
GATE19976.3
The number of equivalence relations of the set $\{1,2,3,4\}$ is $15$ $16$ $24$ $4$
asked
Sep 29, 2014
in
Set Theory & Algebra
by
Kathleen
Veteran
(
52.2k
points)

8.4k
views
gate1997
settheory&algebra
relations
normal
+59
votes
10
answers
11
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
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(
30.8k
points)

8.4k
views
gate20151
settheory&algebra
functions
difficult
+34
votes
10
answers
12
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
(
105k
points)

8.2k
views
gate20152
settheory&algebra
functions
normal
numericalanswers
+41
votes
8
answers
13
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)

8k
views
gate20161
permutationandcombination
recurrence
normal
numericalanswers
+30
votes
3
answers
14
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
(
17.5k
points)

7.9k
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gate2018
mathematicallogic
normal
firstorderlogic
+59
votes
5
answers
15
GATE2016201
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 ___________.
asked
Feb 12, 2016
in
Mathematical Logic
by
Akash Kanase
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41.9k
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7.5k
views
gate20162
mathematicallogic
normal
numericalanswers
propositionallogic
+3
votes
3
answers
16
Reflexive ,symmetric relation
How many relations are reflexive or symmetric on set of n element?
asked
Jul 10, 2016
in
Combinatory
by
Anjali_aspirant
Junior
(
951
points)

7.4k
views
relations
+29
votes
6
answers
17
GATE2016229
The value of the expression $13^{99}\pmod{17}$ in the range $0$ to $16$, is ________.
asked
Feb 12, 2016
in
Combinatory
by
Akash Kanase
Boss
(
41.9k
points)

7.2k
views
gate20162
modulararithmetic
normal
numericalanswers
+43
votes
4
answers
18
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
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(
431k
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7.2k
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gate20171
linearalgebra
eigenvalue
normal
+19
votes
10
answers
19
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
(
17.5k
points)

7.1k
views
gate2018
generatingfunctions
normal
permutationandcombination
+48
votes
10
answers
20
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
(
17.5k
points)

7k
views
gate2012
probability
conditionalprobability
normal
+7
votes
8
answers
21
ISRO201473
How many different trees are there with four nodes $A, B, C$ and $D$? 30 60 90 120
asked
Sep 23, 2015
in
Combinatory
by
ajit
Active
(
2.5k
points)

7k
views
permutationandcombination
isro2014
+29
votes
4
answers
22
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
(
17.5k
points)

6.9k
views
gate2018
linearalgebra
matrices
eigenvalue
normal
+2
votes
1
answer
23
Let a relation R be defined on the set of all real numbers by a R b <=> 1 + ab > 0 thus R is ?
asked
Nov 2, 2017
in
Set Theory & Algebra
by
techbrk3
(
409
points)

6.9k
views
+58
votes
6
answers
24
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)

6.8k
views
gate20161
settheory&algebra
functions
normal
numericalanswers
+24
votes
5
answers
25
GATE20057
The time complexity of computing the transitive closure of a binary relation on a set of $n$ elements is known to be: $O(n)$ $O(n \log n)$ $O \left( n^{\frac{3}{2}} \right)$ $O\left(n^3\right)$
asked
Sep 22, 2014
in
Set Theory & Algebra
by
Kathleen
Veteran
(
52.2k
points)

6.6k
views
gate2005
settheory&algebra
normal
relations
+47
votes
2
answers
26
GATE2015255
Which one of the following wellformed formulae is a tautology? $\forall x \, \exists y \, R(x,y) \, \leftrightarrow \, \exists y \, \forall x \, R(x, y)$ ... $\forall x \, \forall y \, P(x,y) \, \rightarrow \, \forall x \, \forall y \, P(y, x)$
asked
Feb 13, 2015
in
Mathematical Logic
by
jothee
Veteran
(
105k
points)

6.5k
views
gate20152
mathematicallogic
normal
firstorderlogic
+23
votes
4
answers
27
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
Veteran
(
431k
points)

6.4k
views
gate20171
probability
numericalanswers
normaldistribution
+35
votes
5
answers
28
GATE201713
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 $Ax = b$ ... of equations 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
asked
Feb 14, 2017
in
Linear Algebra
by
Arjun
Veteran
(
431k
points)

6.4k
views
gate20171
linearalgebra
systemofequations
normal
+37
votes
7
answers
29
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
(
431k
points)

6.4k
views
gate20172
permutationandcombination
generatingfunctions
numericalanswers
normal
+38
votes
1
answer
30
GATE201412
Suppose you break a stick of unit length at a point chosen uniformly at random. Then the expected length of the shorter stick is ________ .
asked
Sep 26, 2014
in
Probability
by
Arjun
Veteran
(
431k
points)

6.4k
views
gate20141
probability
uniformdistribution
expectation
numericalanswers
normal
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