The Gateway to Computer Science Excellence
For all GATE CSE Questions
Toggle navigation
GATE Overflow
Facebook Login
Google Login
or
Email or Username
Password
Remember
Login
Register

I forgot my password
All Activity
Questions
Unanswered
Tags
Subjects
Users
Ask
Lists
Previous
Blogs
New Blog
Exams
First time here? Checkout the
FAQ
!
x
×
Close
Use the google search bar on side panel. It searches through all previous GATE/other questions. For hardcopy of previous year questions please see
here
Hot questions in Engineering Mathematics
Recent
Hot!
Most votes
Most answers
Most views
Featured
Previous GATE
Recent
Hot!
Most votes
Most answers
Most views
Featured
Previous GATE
+2
votes
0
answers
1
relation
asked
Dec 27, 2017
in
Set Theory & Algebra
by
Lakshman Patel RJIT
Boss
(
10.3k
points)

20.2k
views
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)

12.5k
views
settheory&algebra
+27
votes
10
answers
3
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
(
7.8k
points)

6.5k
views
gate20161
permutationsandcombinations
generatingfunctions
normal
numericalanswers
+35
votes
6
answers
4
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
(
103k
points)

6.5k
views
gate20142
linearalgebra
eigenvalue
normal
numericalanswers
+26
votes
6
answers
5
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
Veteran
(
359k
points)

3.9k
views
gate20172
permutationsandcombinations
generatingfunctions
numericalanswers
normal
+40
votes
7
answers
6
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
(
40.3k
points)

5.3k
views
gate20151
settheory&algebra
functions
difficult
+20
votes
6
answers
7
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
(
43k
points)

4.8k
views
gate20162
modulararithmetic
normal
numericalanswers
+29
votes
4
answers
8
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
(
359k
points)

3.9k
views
gate20171
linearalgebra
eigenvalue
normal
+40
votes
6
answers
9
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
(
7.8k
points)

4.3k
views
gate20161
settheory&algebra
functions
normal
numericalanswers
+10
votes
10
answers
10
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
(
18.3k
points)

3.8k
views
gate2018
permutationsandcombinations
numericalanswers
+9
votes
7
answers
11
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
Combinatory
by
gatecse
Boss
(
18.3k
points)

2.9k
views
gate2018
generatingfunctions
normal
+43
votes
5
answers
12
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
(
103k
points)

5.1k
views
gate20141
graphtheory
numericalanswers
normal
graphconnectivity
+26
votes
6
answers
13
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 $F$? $\exists y(\exists xR(x,y))$ $\exists y(\forall xR(x,y))$ $\forall y(\exists xR(x,y))$ $Â¬\exists x(\forall yÂ¬R(x,y))$ IV only I and IV only II only II and III only
asked
Feb 14, 2017
in
Mathematical Logic
by
khushtak
Loyal
(
7.7k
points)

3.9k
views
gate20171
mathematicallogic
firstorderlogic
+29
votes
7
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
(
7.8k
points)

5.3k
views
gate20161
permutationsandcombinations
recurrence
normal
numericalanswers
+17
votes
3
answers
15
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
(
359k
points)

3.6k
views
gate20171
probability
randomvariable
numericalanswers
+48
votes
5
answers
16
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
(
18.3k
points)

7k
views
gate2012
graphtheory
normal
markstoall
counting
+23
votes
4
answers
17
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
Veteran
(
359k
points)

3.5k
views
gate20171
linearalgebra
systemofequations
normal
+36
votes
9
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
(
18.3k
points)

4.3k
views
gate2012
probability
conditionalprobability
normal
+3
votes
2
answers
19
How many transitive relations are there on a set with n elementsÂ if a)n=1 Â b) n=2 Â c) n=3
asked
Mar 7, 2017
in
Set Theory & Algebra
by
Sanjay Sharma
Boss
(
49.5k
points)

4k
views
+8
votes
8
answers
20
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
(
18.3k
points)

2.6k
views
gate2018
graphtheory
graphsearch
normal
+16
votes
7
answers
21
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)

3.7k
views
gate20172
graphtheory
numericalanswers
degreeofgraph
+9
votes
8
answers
22
GATE2017147
The number of integers between $1$ and $500$ (both inclusive) that are divisible by $3$ or $5$ or $7$ is ____________ .
asked
Feb 14, 2017
in
Set Theory & Algebra
by
Arjun
Veteran
(
359k
points)

2.9k
views
gate20171
settheory&algebra
normal
numericalanswers
sets
+24
votes
9
answers
23
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
(
103k
points)

6k
views
gate20152
settheory&algebra
functions
normal
numericalanswers
+18
votes
5
answers
24
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
(
7.7k
points)

3k
views
gate20172
polynomials
numericalanswers
+13
votes
4
answers
25
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
(
18.3k
points)

2.3k
views
gate2018
settheory&algebra
countableset
normal
+10
votes
3
answers
26
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, ... 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
(
18.3k
points)

3k
views
gate2018
mathematicallogic
normal
firstorderlogic
+11
votes
3
answers
27
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
(
18.3k
points)

2.3k
views
gate2018
linearalgebra
matrices
eigenvalue
normal
+36
votes
7
answers
28
GATE2015324
In a room there are only two types of people, namely Type 1 and Type 2. Type 1 people always tell the truth and Type 2 people always lie. You give a fair coin to a person in that room, without knowing which type he is from and tell him to toss it and hide the ... The result is tail If the person is of Type 2, then the result is tail If the person is of Type 1, then the result is tail
asked
Feb 14, 2015
in
Mathematical Logic
by
jothee
Veteran
(
103k
points)

3.5k
views
gate20153
mathematicallogic
difficult
logicalreasoning
+31
votes
6
answers
29
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
(
59.6k
points)

3.6k
views
gate2003
graphtheory
graphmatching
normal
+40
votes
3
answers
30
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
(
59.6k
points)

2.9k
views
gate2003
mathematicallogic
difficult
firstorderlogic
Page:
1
2
3
4
5
6
...
199
next »
Quick search syntax
tags
tag:apple
author
user:martin
title
title:apple
content
content:apple
exclude
tag:apple
force match
+apple
views
views:100
score
score:10
answers
answers:2
is accepted
isaccepted:true
is closed
isclosed:true
Members at the site
Balaji Jegan
Verma Ashish
rohan.1737
Swapnil Naik
Rustam Ali
ankitgupta.1729
Shaik Masthan
Somoshree Datta 5
Recent Posts
List of Available Exams
New Assignment on Network programming : P2P simulation
Theory of Computation  GO Classroom
Probability  GO Classroom
Daily Quiz
All categories
General Aptitude
1.4k
Engineering Mathematics
6k
Discrete Mathematics
4.1k
Probability
840
Linear Algebra
568
Calculus
413
Digital Logic
2.3k
Programming & DS
4.3k
Algorithms
3.7k
Theory of Computation
4.7k
Compiler Design
1.7k
Operating System
3.4k
Databases
3.4k
CO & Architecture
2.9k
Computer Networks
3.4k
Non GATE
1.2k
Others
1.3k
Admissions
506
Exam Queries
482
Tier 1 Placement Questions
22
Job Queries
64
Projects
16
Follow @csegate
Gatecse
Recent Blog Comments
what is non tech sllybus of kvs pgt computer...
Nice 2 know. You are welcome. :)
Hello @Arjun, I got books now...thanks for your...
You may contact FedEx local delivery office. It...
41,053
questions
47,651
answers
147,212
comments
62,380
users