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
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
Recent questions and answers in Engineering Mathematics
0
votes
1
answer
1
CombinatoricsKenneth Rosen(Ex 5.341)
How many ways are there for a horse race with three horses to finish if ties are possible.(Two or three horses may tie).
answered
59 minutes
ago
in
Combinatory
by
Anu007
Boss
(
17k
points)

7
views
discretemathematics
permutationsandcombinations
0
votes
0
answers
2
CombinatoricsKenneth Rosen(Ex 5.3 31)
The english alphabet contains 21 consonants and five vowels.How many strings of six lowercase letters of the English alphabet contain (b)Exactly two vowels (d)At least two vowels For (b) part I solved it like choose 2 vowels from 5 in $\binom{5}{2}$ ways ... }*6!))$ and both of my answers don't match with the key in Rosen. Please let me know where I am wrong.
asked
1 hour
ago
in
Combinatory
by
Ayush Upadhyaya
Loyal
(
8.8k
points)

20
views
discretemathematics
kennethrosen
permutationsandcombinations
0
votes
0
answers
3
CombinatoricsKenneth Rosen (Ex 5.2 12)
How many ordered pairs of integers (a,b) are needed to guarantee that there are two ordered pairs ($a_{1}$,$b_1$) and ($a_2,b_2)$ such that $a_1$ mod 5=$a_2$ mod 5 and $b_1$ mod 5=$b_2$ mod 5? My answer comes to be 26. Please confirm.
asked
18 hours
ago
in
Combinatory
by
Ayush Upadhyaya
Loyal
(
8.8k
points)

35
views
pigeonholeprinciple
discretemathematics
0
votes
1
answer
4
CombinatoricsKenneth Rosen(Ex5.1 23c)
How many strings of three decimal digits can be formed such that they have exactly two digits that are 4's. My approach as to select 2 positions for these 4's in $\binom{3}{2}$ ways and the last bit will have 10 choices.Now I can permute the string formed in $ ... total such strings should be $\binom{3}{2}$ * 10*$\frac{3!}{2!}$ = 90. But the answer is 27. How?
answered
21 hours
ago
in
Combinatory
by
Soumya29
Loyal
(
9.9k
points)

22
views
kennethrosen
permutationsandcombinations
+1
vote
1
answer
5
Sheldon Ross Chapter 2
If it is assumed that all (52 5) poker hands are equally likely, what is the probability of being dealt (a) a ﬂush? (A hand is said to be a ﬂush if all 5 cards are of the same suit.) (b) one pair? (This occurs when the cards have denominations a, a, ... distinct.) (c) two pairs? (This occurs when the cards have denominations a, a, b, b, c, wherea, b, andc are all distinct.)
answered
1 day
ago
in
Probability
by
neeraj33negi
(
399
points)

12
views
+11
votes
6
answers
6
GATE20011.1
Consider the following statements: S1: The sum of two singular $n \times n$ matrices may be nonsingular S2: The sum of two $n \times n$ nonsingular matrices may be singular Which one of the following statements is correct? $S1$ and $S2$ both are true $S1$ is true, $S2$ is false $S1$ is false, $S2$ is true $S1$ and $S2$ both are false
answered
1 day
ago
in
Linear Algebra
by
Prince Sindhiya
Junior
(
699
points)

981
views
gate2001
linearalgebra
normal
matrices
+1
vote
2
answers
7
Graph Theory Question
Consider a social network with n persons. Two persons A and B are said to be connected if either they are friends or they are related through a sequence of friends: that is, there exists a set of persons F1, . . . , Fm such that A and F1 ... . It is known that there are k persons such that no pair among them is connected. What is the maximum number of friendships possible?
answered
2 days
ago
in
Graph Theory
by
himanshu19
Junior
(
691
points)

231
views
graphconnectivity
+2
votes
1
answer
8
find close form of generating function discrete mathematics kenneth rosen
answered
2 days
ago
in
Mathematical Logic
by
neeraj33negi
(
399
points)

51
views
kennethrosen
discretemathematics
counting
+1
vote
2
answers
9
Graph Theory vertex degree
Consider an undirected graph with n vertices, vertex 1 has degree 1, while each vertex 2,3......, n – 1 has degree 4. The degree of vertex n is unknown. Which of the following statement must be TRUE? a. Vertex n has degree 1. b. Graph is connected. c. There is a path from vertex 1 to vertex n. d. Spanning tree will include the edge connecting vertex 1 and n.
answered
2 days
ago
in
Graph Theory
by
himanshu19
Junior
(
691
points)

128
views
discretemathematics
graphtheory
0
votes
0
answers
10
CombinatoricsSelf doubt
How many outcomes are possible when 10 coins are tossed? $X_{h} + X_{t}$ =10 where $X_{h}$ denotes the number of heads and it is $\geq$0 and $X_{t}$ denotes the number of tails which is also $\geq$0. This comes out to be .$_{10}^{2 ... Shouldn't the answer to the above problem be $2^{10}$ considering each coin can have 2 outcomes either heads or tails? Which one is correct?
asked
2 days
ago
in
Combinatory
by
Ayush Upadhyaya
Loyal
(
8.8k
points)

28
views
discretemathematics
permutationsandcombinations
0
votes
1
answer
11
CombinatoricsSelf Doubt
In how many ways can we arrange 4 boys and 3 girls in a straight line such that no two girls are together. One approach came to my mind was arrange 4 boys first=4! ways. Now 5 gaps created.Choose 3 for girls and arrange girls=5C3*3! ... !(total ways without restriction) why am I getting a different answer from the former case where I take boys first and then arrange girls?
answered
2 days
ago
in
Combinatory
by
Sumeet Singh
Junior
(
501
points)

28
views
discretemathematics
permutationsandcombinations
+3
votes
1
answer
12
Graph Coloring
A vertex colouring with four colours of a graph G = (V, E) is a mapping V → {R, G, B, Y }. So that any two adjacent vertices does not same colour. Consider the below graphs: The number of vertex colouring possible with 4 colours are _________. ... Red and D with also blue which is other than Green, now this case is clearly violating graph coloring property. How, to solve this one?
answered
2 days
ago
in
Graph Theory
by
Prashank
(
55
points)

103
views
graphtheory
graphcoloring
0
votes
1
answer
13
Rank of a matrix
Let A be a 4×3 real matrix with rank 2. Let B be transpose matrix of A. Which one of the following statement is TRUE? (a) Rank of BA is less than 2. (b) Rank of BA is equal to 2. (c) Rank of BA is greater than 2. (d) Rank of BA can be any number between 1 and 3.
answered
2 days
ago
in
Mathematical Logic
by
Shubhgupta
Junior
(
639
points)

17
views
rankofmatrix
engineeringmathematics
matrix
0
votes
0
answers
14
UGCNETNov2017III70
Consider a Takagi  Sugeno  Kang (TSK) Model consisting of rules of the form : If x1 is Ai1 and ... and xr is Air THEN y =fi (x1, x2, ..., xr) = bi0+bi1 x1+.....+birxr assume, $\alpha$i is the matching degree of rule i, then the total output of the model is given by : (1) y ... 1}^{L}$ fi (x1,x2,....., xr)/$\sum_{i=1}^{L}\alpha$i (4) y = maxi [$\alpha$i fi (x1,x2,....., xr)]
asked
3 days
ago
in
Mathematical Logic
by
Roma_nagpal
(
115
points)

14
views
0
votes
0
answers
15
This question is from graph theory
What is the total number of vertices in a tree if there are 3n vertices of degree 2 and 2n vertices of degree n?
asked
4 days
ago
in
Mathematical Logic
by
Pratyush
(
7
points)

24
views
+33
votes
7
answers
16
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
answered
4 days
ago
in
Mathematical Logic
by
Ayush Upadhyaya
Loyal
(
8.8k
points)

3.2k
views
gate20153
mathematicallogic
difficult
logicalreasoning
0
votes
3
answers
17
NET nov17 paper2 Q8
Let P and Q be two propositions , ~(P<>Q) is equivalent to : a)P<>~Q b)~P<>Q c)~P<>~Q d)Q>P
answered
4 days
ago
in
Combinatory
by
Ammu9682
(
25
points)

318
views
+22
votes
5
answers
18
GATE2008IT21
Which of the following first order formulae is logically valid? Here $\alpha(x)$ is a first order formula with $x$ as a free variable, and $\beta$ is a first order formula with no free variable. $[\beta \rightarrow (\exists x, \alpha(x))] \rightarrow [\forall x, ... ) \rightarrow \beta]$ $[(\forall x, \alpha(x)) \rightarrow \beta] \rightarrow [\forall x, \alpha(x) \rightarrow \beta]$
answered
5 days
ago
in
Mathematical Logic
by
Ayush Upadhyaya
Loyal
(
8.8k
points)

2.4k
views
gate2008it
firstorderlogic
normal
+13
votes
4
answers
19
GATE200426
The number of different $n \times n $ symmetric matrices with each element being either 0 or 1 is: (Note: $\text{power} \left(2, X\right)$ is same as $2^X$) $\text{power} \left(2, n\right)$ $\text{power} \left(2, n^2\right)$ $\text{power} \left(2,\frac{ \left(n^2+ n \right) }{2}\right)$ $\text{power} \left(2, \frac{\left(n^2  n\right)}{2}\right)$
answered
5 days
ago
in
Linear Algebra
by
janeb abhishek
(
291
points)

2.1k
views
gate2004
linearalgebra
normal
matrices
+20
votes
4
answers
20
GATE200623
$F$ is an $n\times n$ real matrix. $b$ is an $n\times 1$ real vector. Suppose there are two $n\times 1$ vectors, $u$ and $v$ such that, $u ≠ v$ and $Fu = b, Fv = b$. Which one of the following statements is false? Determinant of $F$ is zero. There are an infinite number of solutions to $Fx = b$ There is an $x≠0$ such that $Fx = 0$ $F$ must have two identical rows
answered
5 days
ago
in
Linear Algebra
by
janeb abhishek
(
291
points)

1.3k
views
gate2006
linearalgebra
normal
matrices
0
votes
0
answers
21
Infinite Descending Chain
From Wiki : Given a set S with a partial order ≤, an infinite descending chain is an infinite, strictly decreasing sequence of elements x1 > x2 > ... > xn > ... As an example, in the set of integers, the chain −1, ... used in number theory, while the latter is preferred in set theory and computer science. Now while solving question which definition to use ?
asked
5 days
ago
in
Set Theory & Algebra
by
Na462
Active
(
3.3k
points)

7
views
discretemathematics
0
votes
0
answers
22
self doubt
number of integers in the set {0,1,2,3......,10000}which contain digit 5 exactly once ???? i got the 9*9*9*9 is it right???
asked
5 days
ago
in
Combinatory
by
vijju532
(
87
points)

27
views
discretemathematics
+7
votes
1
answer
23
ISI2017 MMA
Let S ⊆ R. Consider the statement: "There exists a continuous function f:S > S such that f(x) != x for all x belongs to S." This statement is false if S equals A) [2,3] B) (2,3] c) [3,2] union [2,3] D) (infinity to +infinity ... infinity to +infinity, f(x) will definitely be equal to x at some point but we want this to not happen as said in the question. Am I correct?
answered
5 days
ago
in
Set Theory & Algebra
by
Kushagra Chatterjee
Loyal
(
8.2k
points)

284
views
isi2017
functions
usermod
0
votes
1
answer
24
spanning tree
How we get maximum no. of spanning tree for give $n$ node is $n^{(n2)}$
answered
6 days
ago
in
Graph Theory
by
Anil Ji
Active
(
1.5k
points)

18
views
engineeringmathematics
discretemathematics
graphtheory
0
votes
0
answers
25
Kenneth rosen
How many nonisomorphic directed graphs are there with $n$ vertices when $n$ is $2$ $3$ $4$
asked
6 days
ago
in
Graph Theory
by
swati96
(
37
points)

16
views
engineeringmathematics
discretemathematics
kennethrosen
graphtheory
0
votes
0
answers
26
Kenneth rosen
How many nonisomorphic graphs are there with six vertices and four edges?
asked
6 days
ago
in
Graph Theory
by
swati96
(
37
points)

5
views
engineeringmathematics
discretemathematics
graphtheory
0
votes
0
answers
27
Graphs, kenneth rosen
How many nonisomorphic simple graphs are there with five vertices and three edges?
asked
6 days
ago
in
Graph Theory
by
swati96
(
37
points)

6
views
engineeringmathematics
discretemathematics
kennethrosen
graphtheory
0
votes
0
answers
28
Graphs, kenneth rosen
How many nonisomorphic simple graphs are there with five vertices and three edges?
[closed]
asked
6 days
ago
in
Graph Theory
by
swati96
(
37
points)

5
views
engineeringmathematics
discretemathematics
graphtheory
+26
votes
6
answers
29
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
answered
6 days
ago
in
Mathematical Logic
by
Ayush Upadhyaya
Loyal
(
8.8k
points)

3.5k
views
gate20171
mathematicallogic
firstorderlogic
+1
vote
2
answers
30
planar graphs
Is there any subgraph homoemorphic to K5 present in G1 for the following question? Which one of the following graphs is NOT planar? (A) G1 (B) G2 (C) G3 (D) G4 In this question planar drawings( no 2 edges intersect) for G2, G3 and G4 exists, thats why ... 't find any subgraph homoemorphic to K5 in G1 as a graph is non planar iff it contains a subgraph homoemorphic to K5 or K3,3...
answered
6 days
ago
in
Graph Theory
by
Prashank
(
55
points)

308
views
graphtheory
graphplanarity
+25
votes
9
answers
31
GATE2014149
A pennant is a sequence of numbers, each number being $1$ or $2$. An $n$pennant is a sequence of numbers with sum equal to $n$. For example, $(1,1,2)$ is a $4$pennant. The set of all possible $1$pennants is ${(1)}$, the set of all possible $2$pennants is ${( ... ), (1,2)}$. Note that the pennant $(1,2)$ is not the same as the pennant $(2,1)$. The number of $10$pennants is________
answered
Jun 17
in
Combinatory
by
Kumar Ashish
Junior
(
545
points)

1.8k
views
gate20141
permutationsandcombinations
numericalanswers
normal
0
votes
2
answers
32
self doubt
What is the English of both statement ∀x((x!=0)→∃y(xy=100)) ∀x∃y((x!=0)→(xy=100))
answered
Jun 16
in
Mathematical Logic
by
Deepakk Poonia (Dee)
Boss
(
13.2k
points)

32
views
+2
votes
3
answers
33
UGCNETDec2014III57
The resolvent of the set of clauses $(A \vee B, \sim A \vee D, C \vee \sim B)$ is $A \vee​ B$ $C \vee​ D$ $A \vee​ C$ $A \vee​ D$
answered
Jun 16
in
Mathematical Logic
by
Prasanjeet Ghosh
Active
(
1.3k
points)

571
views
ugcnetdec2014iii
mathematicallogic
+2
votes
3
answers
34
UGCNETDec2014III55
Equivalent logical expression for the Well Formed Formula $(WFF)$, $\sim(\forall x) F\left[x\right]$ is $\forall x (\sim F\left[x\right])$ $\sim (\exists x) F\left[x\right]$ $\exists x (\sim F\left[x\right])​$ $\forall x F\left[x\right]$
answered
Jun 16
in
Mathematical Logic
by
Prasanjeet Ghosh
Active
(
1.3k
points)

431
views
ugcnetdec2014iii
mathematicallogic
+2
votes
1
answer
35
Random_Doubt
if it is given > "Every satisfiable propositional formula is not tautology" then what will it corresponds to? i am writing its hindi, which among below two are correct? "har ek satisfiable formula tautology nahi hota hai" // it is indeed truth. "koi bhi satisfiable formula hua, to wo tautology nahii hoga" // this is false.
answered
Jun 16
in
Mathematical Logic
by
Vegeta
(
21
points)

33
views
discretemathematics
propositionallogic
0
votes
0
answers
36
General
From last few days I am trying to solve Sheldon Ross problems. But not able to solve it. So those who have solved it kindly tell me how to strengthen the concepts as to solve the problems...........and also is the level of problems given in it are as per GATE requirement??
asked
Jun 16
in
Probability
by
mbisht
(
171
points)

9
views
+5
votes
3
answers
37
TIFR2010A13
A cube whose faces are colored is split into $1000$ small cubes of equal size. The cubes thus obtained are mixed thoroughly. The probability that a cube drawn at random will have exactly two colored faces is: $0.096$ $0.12$ $0.104$ $0.24$ None of the above
answered
Jun 15
in
Probability
by
sutanay3
Active
(
1.2k
points)

388
views
tifr2010
probability
0
votes
2
answers
38
IIT M video questions
P(x,y,z), xy=z, Universe is interger; write in logic form If xy=x for all y, then x =0. Thank you
answered
Jun 14
in
Mathematical Logic
by
Deepakk Poonia (Dee)
Boss
(
13.2k
points)

51
views
propositionallogic
firstorderlogic
logicalreasoning
0
votes
1
answer
39
self doubt
dog(x) = x is a dog Int (x) = x is intelligent write in logic form No dogs are intelligent.
answered
Jun 14
in
Mathematical Logic
by
Deepakk Poonia (Dee)
Boss
(
13.2k
points)

31
views
propositionallogic
firstorderlogic
logicalreasoning
+14
votes
7
answers
40
GATE200724
Suppose we uniformly and randomly select a permutation from the $20 !$ permutations of $1, 2, 3\ldots ,20.$ What is the probability that $2$ appears at an earlier position than any other even number in the selected permutation? $\left(\dfrac{1}{2} \right)$ $\left(\dfrac{1}{10}\right)$ $\left(\dfrac{9!}{20!}\right)$ None of these
answered
Jun 14
in
Probability
by
sutanay3
Active
(
1.2k
points)

2.6k
views
gate2007
probability
easy
To see more, click for all the
questions in this category
.
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
Lakshay Kakkar
N.Vijayadurga
c0dew0rm
Shubhgupta
Sukannya
Sachin Mittal 1
Anu007
Mr.Simple
Raju Kalagoni
Sourajit25
once_2019
Ayush Upadhyaya
Recent Posts
My failure, Oh wait SUCCESS journey
ALGORITHMS CHECKLIST:
A Failure who got into IISc
ISRO written test results are out!!
UGC NET 2018 Admit Card available for Download
All categories
General Aptitude
1.3k
Engineering Mathematics
5.2k
Discrete Mathematics
3.6k
Probability
651
Linear Algebra
527
Calculus
387
Digital Logic
2k
Programming & DS
3.7k
Algorithms
3.2k
Theory of Computation
4k
Compiler Design
1.6k
Operating System
2.8k
Databases
3k
CO & Architecture
2.6k
Computer Networks
3k
Non GATE
1k
Others
1.3k
Admissions
486
Exam Queries
435
Tier 1 Placement Questions
18
Job Queries
56
Projects
9
Follow @csegate
Gatecse
Recent questions and answers in Engineering Mathematics
Recent Blog Comments
Suggestion...please read the theory and do the ...
Your story in one liner... "Failure is ...
Nopes...anyone upgraded to main campus?please ...
@Balaji Jegan Have you counted all the sorting ...
@Mukesh Chaudhary Please verify the syllabus ...
36,187
questions
43,631
answers
124,060
comments
42,906
users