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Previous GATE
+20
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
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settheory&algebra
+25
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7
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2
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
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7.7k
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4.8k
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gate20161
permutationsandcombinations
recurrence
normal
numericalanswers
+26
votes
8
answers
3
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
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7.7k
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5.8k
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gate20161
permutationsandcombinations
generatingfunctions
normal
numericalanswers
+38
votes
6
answers
4
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 $\left\{ \textit{g}\right\}$ 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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39.8k
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4.6k
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gate20151
settheory&algebra
functions
difficult
+44
votes
5
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
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17.9k
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6.1k
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gate2012
graphtheory
normal
markstoall
counting
+28
votes
4
answers
6
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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98.8k
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5.5k
views
gate20142
linearalgebra
eigenvalue
normal
numericalanswers
+22
votes
9
answers
7
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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98.8k
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5.3k
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gate20152
settheory&algebra
functions
normal
numericalanswers
+26
votes
4
answers
8
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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339k
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3.4k
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gate20172
permutationsandcombinations
generatingfunctions
numericalanswers
normal
+6
votes
7
answers
9
GATE201846
The number of possible minheaps containing each value from $\{1,2,3,4,5,6,7\}$ exactly once is _______
asked
Feb 14
in
Combinatory
by
gatecse
Boss
(
17.9k
points)

2.5k
views
gate2018
permutationsandcombinations
heap
numericalanswers
+7
votes
6
answers
10
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
in
Set Theory & Algebra
by
gatecse
Boss
(
17.9k
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1.7k
views
gate2018
generatingfunctions
normal
+38
votes
4
answers
11
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 of ... 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
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42.4k
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3.1k
views
gate20162
settheory&algebra
difficult
sets
+17
votes
5
answers
12
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
(
1.9k
points)

3.3k
views
gate20172
graphtheory
numericalanswers
degreeofgraph
+22
votes
3
answers
13
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} \ ... 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
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339k
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3.1k
views
gate20171
linearalgebra
systemofequations
normal
+41
votes
4
answers
14
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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98.8k
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4.2k
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gate20141
graphtheory
numericalanswers
normal
graphconnectivity
+3
votes
2
answers
15
ISRODEC20171
Suppose $A$ is a finite set with $n$ elements.The number of elements and the rank of the largest equivalence relation on $A$ are $\{n,1\}$ $\{n,n\}$ $\{n^2,1\}$ $\{1,n^2\}$
asked
Dec 17, 2017
in
Linear Algebra
by
gatecse
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17.9k
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2k
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isrodec2017
+21
votes
4
answers
16
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
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59.4k
points)

4.9k
views
gate1997
settheory&algebra
relations
normal
+20
votes
5
answers
17
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
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1.9k
points)

2.5k
views
gate20172
engineeringmathematics
linearalgebra
numericalanswers
eigenvalue
+7
votes
7
answers
18
GATE201830
Let $G$ be a simple undirected graph. Let $T_D$ be a depth first search tree of $G$. Let $T_B$ be a breadth first search tree of $G$. Consider the following statements. No edge of $G$ is a cross edge with respect to $T_D$. (A cross edge in $G$ is between two nodes ... mid ij \mid =1$. Which of the statements above must necessarily be true? I only II only Both I and II Neither I nor II
asked
Feb 14
in
Graph Theory
by
gatecse
Boss
(
17.9k
points)

1.7k
views
gate2018
graphtheory
normal
+18
votes
4
answers
19
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
Loyal
(
7.5k
points)

2.4k
views
gate20172
discretemathematics
lattice
numericalanswers
normal
+9
votes
2
answers
20
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
in
Linear Algebra
by
gatecse
Boss
(
17.9k
points)

1.5k
views
gate2018
linearalgebra
matrices
eigenvalue
normal
+5
votes
3
answers
21
GATE201828
Consider the firstorder logic sentence $$\varphi \equiv \exists \: s \: \exists \: t \: \exists \: u \: \forall \: v \: \forall \: w \forall \: x \: \forall \: y \: \psi(s, t, u, v, w, x, y)$$ where $\psi(s, t, u, v, w, ... of size less 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
in
Mathematical Logic
by
gatecse
Boss
(
17.9k
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1.9k
views
gate2018
mathematicallogic
normal
+26
votes
5
answers
22
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 $F$? $\exists y(\exists xR(x,y))$ $\exists y(\forall xR(x,y))$ $\forall y(\exists xR(x,y))$ $¬\exists x(\forall y¬R(x,y))$ IV only I and IV only II only II and III only
asked
Feb 14, 2017
in
Mathematical Logic
by
khushtak
Loyal
(
7.5k
points)

3.4k
views
gate20171
mathematicallogic
firstorderlogic
+8
votes
3
answers
23
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
in
Set Theory & Algebra
by
gatecse
Boss
(
17.9k
points)

1.5k
views
gate2018
settheory&algebra
#countableset
normal
+5
votes
6
answers
24
GATE201816
The value of $\int^{\pi/4} _0 x \cos(x^2) dx$ correct to three decimal places (assuming that $\pi = 3.14$) is ____
asked
Feb 14
in
Calculus
by
gatecse
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17.9k
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1.6k
views
gate2018
calculus
integration
normal
numericalanswers
+4
votes
3
answers
25
GATE201844
Consider Guwahati, (G) and Delhi (D) whose temperatures can be classified as high $(H)$, medium $(M)$ and low $(L)$. Let $P(H_G)$ denote the probability that Guwahati has high temperature. Similarly, $P(M_G)$ and $P(L_G)$ denotes the ... (L_G)=0.3$, then the probability (correct to two decimal places) that Guwahati has high temperature given that Delhi has high temperature is _____
asked
Feb 14
in
Probability
by
gatecse
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17.9k
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1.5k
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gate2018
probability
conditionalprobability
numericalanswers
+18
votes
5
answers
26
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
(
42.4k
points)

4.3k
views
gate20162
modulararithmetic
normal
numericalanswers
+7
votes
5
answers
27
GATE201818
The chromatic number of the following graph is _____
asked
Feb 14
in
Graph Theory
by
gatecse
Boss
(
17.9k
points)

1.2k
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gate2018
graphtheory
chromaticnumber
numericalanswers
+17
votes
4
answers
28
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
Loyal
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7.5k
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2.7k
views
gate20172
polynomials
numericalanswers
numbersystem
+3
votes
4
answers
29
GATE201819
Let $G$ be a finite group on $84$ elements. The size of a largest possible proper subgroup of $G$ is _____
asked
Feb 14
in
Set Theory & Algebra
by
gatecse
Boss
(
17.9k
points)

1.5k
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gate2018
groups
numericalanswers
+4
votes
5
answers
30
GATE201815
Two people, P and Q, decide to independently roll two identical dice, each with 6 faces, numbered 1 to 6. The person with the lower number wins. In case of a tie, they roll the dice repeatedly until there is no tie. Define a trial as a throw ... probable and that all trials are independent. THe probability (rounded to $3$ decimal places) that one of them wins on the third trial is ____
asked
Feb 14
in
Probability
by
gatecse
Boss
(
17.9k
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1.3k
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gate2018
probability
normal
numericalanswers
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