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Previous GATE
+19
votes
2
answers
1
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
Loyal
(
3.4k
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9.1k
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settheory&algebra
+23
votes
8
answers
2
GATE 2016126
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
Boss
(
9.3k
points)

4.9k
views
gate20161
permutationsandcombinations
generatingfunctions
normal
numericalanswers
+38
votes
5
answers
3
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
Veteran
(
14.6k
points)

5.1k
views
gate2012
graphtheory
normal
markstoall
counting
+19
votes
9
answers
4
GATE20152_40
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
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(
106k
points)

4.5k
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gate20152
settheory&algebra
functions
normal
numericalanswers
+36
votes
4
answers
5
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 ... 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
Veteran
(
48.6k
points)

2.7k
views
gate20162
settheory&algebra
difficult
sets
+18
votes
4
answers
6
GATE2017247
If the ordinary generating function of a sequence $\big \{a_n\big \}_{n=0}^\infty$ is $\large \frac{1+z}{(1z)^3}$, then $a_3a_0$ is equal to ___________ .
asked
Feb 14, 2017
in
Combinatory
by
Arjun
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332k
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2.6k
views
gate20172
permutationsandcombinations
generatingfunctions
numericalanswers
normal
+13
votes
5
answers
7
GATE2017223
$G$ is an undirected graph with $n$ vertices and $25$ edges such that each vertex of $G$ has degree at least $3$. Then the maximum possible value of $n$ is _________ .
asked
Feb 14, 2017
in
Graph Theory
by
Madhav
Active
(
2k
points)

2.7k
views
gate20172
graphtheory
numericalanswers
degreeofgraph
+38
votes
4
answers
8
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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(
106k
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3.7k
views
gate20141
graphtheory
numericalanswers
normal
graphconnectivity
+20
votes
4
answers
9
GATE1997_6.3
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
(
68.9k
points)

4.2k
views
gate1997
settheory&algebra
relations
normal
+13
votes
5
answers
10
GATE2017252
If the characteristic polynomial of a 3 $\times$ 3 matrix $M$ over $\mathbb{R}$ (the set of real numbers) is $\lambda^3 â€“ 4 \lambda^2 + a \lambda +30, \quad a \in \mathbb{R}$, 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
(
2k
points)

2k
views
gate20172
engineeringmathematics
linearalgebra
numericalanswers
eigenvalue
+16
votes
3
answers
11
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 $Ax = b$ where $A=\left [ a_{1}.....a_{n} ... $x=J_{n}$ where $J_{n}$ denotes a $n$dimensional vector of all 1. (B) no solution (C) infinitely many solutions (D) finitely many solutions
asked
Feb 14, 2017
in
Linear Algebra
by
Arjun
Veteran
(
332k
points)

2.2k
views
gate20171
linearalgebra
systemofequations
normal
+10
votes
4
answers
12
GATE2017221
Consider the set $X=\{a, b, c, d, e\}$ under partial ordering $R=\{(a,a), (a, b), (a, c), (a, d), (a, e), (b, b), (b, c), (b, e), (c, c), (c, e), (d, d), (d, e), (e, e) \}$ The Hasse diagram of the partial order $(X, R)$ is shown below. The minimum number of ordered pairs that need to be added to $R$ to make $(X, R)$ a lattice is ______
asked
Feb 14, 2017
in
Set Theory & Algebra
by
khushtak
Boss
(
8.2k
points)

1.9k
views
gate20172
discretemathematics
lattice
numericalanswers
normal
+34
votes
5
answers
13
GATE20151_39
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 $\left\{ \textit{g ... \{ \textit{g}\right\}$ 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
Veteran
(
46.6k
points)

3.9k
views
gate20151
settheory&algebra
functions
difficult
+16
votes
5
answers
14
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
Veteran
(
48.6k
points)

3.6k
views
gate20162
modulararithmetic
normal
numericalanswers
+17
votes
5
answers
15
GATE2017102
Consider the firstorder logic sentence $F:\forall x(\exists yR(x,y))$. Assuming nonempty logical domains, which of the sentences below are implied by $F$? $\exists y(\exists xR(x,y))$ $\exists y(\forall xR(x,y))$ $\forall y(\exists xR(x,y))$ $Â¬\exists x(\forall yÂ¬R(x,y))$ (A) $IV$ only (B) $I$ and $IV$ only (C) $II$ only (D) $II$ and $III$ only
asked
Feb 14, 2017
in
Mathematical Logic
by
khushtak
Boss
(
8.2k
points)

2.7k
views
gate20171
mathematicallogic
firstorderlogic
+12
votes
4
answers
16
GATE2017224
Consider the quadratic equation $x^213x+36=0$ with coefficients in a base $b$. The solutions of this equation in the same base $b$ are $x=5$ and $x=6$. Then $b$= _____
asked
Feb 14, 2017
in
Set Theory & Algebra
by
khushtak
Boss
(
8.2k
points)

2.1k
views
gate20172
polynomials
numericalanswers
numbersystem
+23
votes
6
answers
17
GATE 2016127
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
Boss
(
9.3k
points)

4.2k
views
gate20161
permutationsandcombinations
recurrence
normal
numericalanswers
+31
votes
2
answers
18
GATE20152_55
Which one of the following wellformed formulae is a tautology? $\forall x \, \exists y \, R(x,y) \, \leftrightarrow \, \exists y \, \forall x \, R(x, y)$ $( \forall x \, [\exists y \, R(x,y) \, \rightarrow \, S(x, y)]) \, \rightarrow \, \forall x \ ... R(x, y) \right)]$ $\forall x \, \forall y \, P(x,y) \, \rightarrow \, \forall x \, \forall y \, P(y, x)$
asked
Feb 13, 2015
in
Mathematical Logic
by
jothee
Veteran
(
106k
points)

3.4k
views
gate20152
mathematicallogic
normal
firstorderlogic
+28
votes
5
answers
19
GATE20151_34
Suppose $L = \left\{ p, q, r, s, t\right\}$ is a lattice represented by the following Hasse diagram: For any $x, y ∈ L$, not necessarily distinct , $x ∨ y$ and $x ∧ y$ are join and meet of $x, y$, respectively. Let $L^3 = \left\{\ ... or; z)$. Then $p_r = 0$ $p_r = 1$ $0 < p_r ≤ \frac{1}{5}$ $\frac{1}{5} < p_r < 1$
asked
Feb 13, 2015
in
Set Theory & Algebra
by
makhdoom ghaya
Veteran
(
46.6k
points)

2.7k
views
gate20151
settheory&algebra
normal
lattice
+7
votes
9
answers
20
ISRO201722
Which one of the following Boolean expressions is NOT a tautology? $((a \rightarrow b) \wedge (b \rightarrow c)) \rightarrow (a \rightarrow c)$ $(a \leftrightarrow c) \rightarrow (\sim b\rightarrow (a\wedge c))$ $(a\wedge b \wedge c)\rightarrow (c \vee a)$ $a\rightarrow (b\rightarrow a)$
asked
May 7, 2017
in
Mathematical Logic
by
sh!va
Veteran
(
35.2k
points)

1.9k
views
isro2017
booleanexpressions
mathematicallogic
+33
votes
5
answers
21
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
Veteran
(
48.6k
points)

4k
views
gate20162
mathematicallogic
normal
numericalanswers
propositionallogic
+4
votes
5
answers
22
ISRO20179
The symmetric difference of sets $A=\{1,2, 3,4, 5, 6, 7, 8\}$ and $B= \{1, 3, 5, 6, 7,8,9\}$ is: $\{1, 3, 5, 6, 7,8\}$ $\{2, 4, 9\}$ $\{2, 4\}$ $\{1, 2, 3, 4, 5, 6, 7, 8, 9\}$
asked
May 7, 2017
in
Set Theory & Algebra
by
sh!va
Veteran
(
35.2k
points)

1.9k
views
isro2017
settheory&algebra
sets
+28
votes
8
answers
23
GATE2012_33
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
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(
14.6k
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3.1k
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gate2012
probability
conditionalprobability
bayestheorem
normal
+26
votes
6
answers
24
GATE200336
How many perfect matching are there in a complete graph of $6$ vertices? 15 24 30 60
asked
Sep 16, 2014
in
Graph Theory
by
Kathleen
Veteran
(
68.9k
points)

2.7k
views
gate2003
graphtheory
graphmatching
normal
+23
votes
3
answers
25
GATE2016227
Which one of the following wellformed formulae in predicate calculus is NOT valid ? $(\forall _{x} p(x) \implies \forall _{x} q(x)) \implies (\exists _{x} \neg p(x) \vee \forall _{x} q(x))$ $(\exists x p(x) \vee \exists x q (x)) \implies \exists x (p ... (x) \wedge \exists x q(x))$ $\forall x (p(x) \vee q(x)) \implies (\forall x p(x) \vee \forall x q(x))$
asked
Feb 12, 2016
in
Mathematical Logic
by
Akash Kanase
Veteran
(
48.6k
points)

3.3k
views
gate20162
mathematicallogic
firstorderlogic
normal
+27
votes
7
answers
26
GATE20153_5
The number of 4 digit numbers having their digits in nondecreasing order (from left to right) constructed by using the digits belonging to the set {1, 2, 3} is ________.
asked
Feb 14, 2015
in
Combinatory
by
jothee
Veteran
(
106k
points)

2.1k
views
gate20153
permutationsandcombinations
normal
numericalanswers
+24
votes
4
answers
27
GATE200672
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: $\binom{\frac{n}{2}}{2}.2^{\frac{n}{2}}$ $2^{n2}$ $2^{n3}\times 3$ $2^{n1}$
asked
Apr 24, 2016
in
Graph Theory
by
jothee
Veteran
(
106k
points)

1.8k
views
gate2006
graphtheory
normal
degreeofgraph
+27
votes
5
answers
28
GATE2014147
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 ... function in the interval $(0,2)$ is $1$ There exists a $y$ in the interval $(0,1)$ such that $f(y)$ = $f(2y)$
asked
Sep 28, 2014
in
Calculus
by
jothee
Veteran
(
106k
points)

2.8k
views
gate20141
calculus
continuity
normal
+11
votes
4
answers
29
GATE2016202
Let $f(x)$ be a polynomial and $g(x)=f'(x)$ be its derivative. If the degree of $(f(x)+f(x))$ is $10$, then the degree of $(g(x)  g(x))$ is __________.
asked
Feb 12, 2016
in
Calculus
by
Akash Kanase
Veteran
(
48.6k
points)

1.8k
views
gate20162
calculus
normal
numericalanswers
differentiability
+18
votes
4
answers
30
GATE 2016105
Two eigenvalues of a $3 \times 3$ real matrix $P$ are $(2+\sqrt {1})$ and $3$. The determinant of $P$ is _______
asked
Feb 12, 2016
in
Linear Algebra
by
Sandeep Singh
Boss
(
9.3k
points)

2.2k
views
gate20161
linearalgebra
eigenvalue
numericalanswers
normal
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