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Previous GATE
Featured
Most answered questions in Discrete Mathematics
37
votes
8
answers
61
GATE IT 2005 | Question: 31
Let $f$ be a function from a set $A$ to a set $B$, $g$ a function from $B$ to $C$, and $h$ a function from $A$ to $C$, such that $h(a) = g(f(a))$ for all $a ∈ A.$ Which of the following statements is always true for all such functions $f$ and $g$? ... is onto $h$ is onto $\implies$ $f$ is onto $h$ is onto $\implies$ $g$ is onto $h$ is onto $\implies$ $f$ and $g$ are onto
Ishrat Jahan
asked
in
Set Theory & Algebra
Nov 3, 2014
by
Ishrat Jahan
8.8k
views
gateit-2005
set-theory&algebra
functions
normal
25
votes
8
answers
62
GATE IT 2004 | Question: 5
What is the maximum number of edges in an acyclic undirected graph with $n$ vertices? $n-1$ $n$ $n+1$ $2n-1$
Ishrat Jahan
asked
in
Graph Theory
Nov 1, 2014
by
Ishrat Jahan
6.9k
views
gateit-2004
graph-theory
graph-connectivity
normal
33
votes
8
answers
63
GATE IT 2008 | Question: 28
Consider the following Hasse diagrams. Which all of the above represent a lattice? (i) and (iv) only (ii) and (iii) only (iii) only (i), (ii) and (iv) only
Ishrat Jahan
asked
in
Set Theory & Algebra
Oct 28, 2014
by
Ishrat Jahan
14.9k
views
gateit-2008
set-theory&algebra
lattice
normal
26
votes
8
answers
64
GATE CSE 1996 | Question: 1.1
Let $A$ and $B$ be sets and let $A^c$ and $B^c$ denote the complements of the sets $A$ and $B$. The set $(A-B) \cup (B-A) \cup (A \cap B)$ is equal to $A \cup B$ $A^c \cup B^c$ $A \cap B$ $A^c \cap B^c$
Kathleen
asked
in
Set Theory & Algebra
Oct 9, 2014
by
Kathleen
6.0k
views
gate1996
set-theory&algebra
easy
set-theory
77
votes
8
answers
65
GATE CSE 2014 Set 2 | Question: 50
Consider the following relation on subsets of the set $S$ of integers between $1$ and $2014$. For two distinct subsets $U$ and $V$ of $S$ we say $U\:<\:V$ if the minimum element in the symmetric difference of the two sets is in $U$. Consider the ... $S1$ is true and $S2$ is false $S2$ is true and $S1$ is false Neither $S1$ nor $S2$ is true
go_editor
asked
in
Set Theory & Algebra
Sep 28, 2014
by
go_editor
15.8k
views
gatecse-2014-set2
set-theory&algebra
normal
set-theory
52
votes
8
answers
66
GATE CSE 2013 | Question: 27
What is the logical translation of the following statement? "None of my friends are perfect." $∃x(F (x)∧ ¬P(x))$ $∃ x(¬ F (x)∧ P(x))$ $ ∃x(¬F (x)∧¬P(x))$ $ ¬∃ x(F (x)∧ P(x))$
Arjun
asked
in
Mathematical Logic
Sep 24, 2014
by
Arjun
14.0k
views
gatecse-2013
mathematical-logic
easy
first-order-logic
59
votes
8
answers
67
GATE CSE 2013 | Question: 26
The line graph $L(G)$ of a simple graph $G$ is defined as follows: There is exactly one vertex $v(e)$ in $L(G)$ for each edge $e$ in $G$. For any two edges $e$ and $e'$ in $G$, $L(G)$ has an edge between $v(e)$ and $v(e')$, if and only if ... planar graph is planar. (S) The line graph of a tree is a tree. $P$ only $P$ and $R$ only $R$ only $P, Q$ and $S$ only
Arjun
asked
in
Graph Theory
Sep 24, 2014
by
Arjun
19.0k
views
gatecse-2013
graph-theory
normal
graph-connectivity
48
votes
8
answers
68
GATE CSE 2007 | Question: 84
Suppose that a robot is placed on the Cartesian plane. At each step it is allowed to move either one unit up or one unit right, i.e., if it is at $(i,j)$ then it can move to either $(i + 1, j)$ or $(i,j + 1)$. How many distinct paths are there for the ... $(10,10)$ starting from the initial position $(0,0)$? $^{20}\mathrm{C}_{10}$ $2^{20}$ $2^{10}$ None of the above
Kathleen
asked
in
Combinatory
Sep 21, 2014
by
Kathleen
12.5k
views
gatecse-2007
combinatory
43
votes
8
answers
69
GATE CSE 2007 | Question: 22
Let $\text{ Graph}(x)$ be a predicate which denotes that $x$ is a graph. Let $\text{ Connected}(x)$ be a predicate which denotes that $x$ ... $\forall x \, \Bigl ( \text{ Graph}(x) \implies \lnot \text{ Connected}(x) \Bigr )$
Kathleen
asked
in
Mathematical Logic
Sep 21, 2014
by
Kathleen
8.8k
views
gatecse-2007
mathematical-logic
easy
first-order-logic
27
votes
8
answers
70
GATE CSE 2005 | Question: 50
Let $G(x) = \frac{1}{(1-x)^2} = \sum\limits_{i=0}^\infty g(i)x^i$, where $|x| < 1$. What is $g(i)$? $i$ $i+1$ $2i$ $2^i$
gatecse
asked
in
Combinatory
Sep 21, 2014
by
gatecse
8.1k
views
gatecse-2005
normal
generating-functions
86
votes
8
answers
71
GATE CSE 2004 | Question: 79
How many graphs on $n$ labeled vertices exist which have at least $\frac{(n^2 - 3n)}{ 2}$ edges ? $^{\left(\frac{n^2-n}{2}\right)}C_{\left(\frac{n^2-3n} {2}\right)}$ $^{{\large\sum\limits_{k=0}^{\left (\frac{n^2-3n}{2} \right )}}.\left(n^2-n\right)}C_k$ $^{\left(\frac{n^2-n}{2}\right)}C_n$ $^{{\large\sum\limits_{k=0}^n}.\left(\frac{n^2-n}{2}\right)}C_k$
Kathleen
asked
in
Graph Theory
Sep 18, 2014
by
Kathleen
14.3k
views
gatecse-2004
graph-theory
combinatory
normal
counting
42
votes
8
answers
72
GATE CSE 2004 | Question: 73
The inclusion of which of the following sets into $S = \left\{ \left\{1, 2\right\}, \left\{1, 2, 3\right\}, \left\{1, 3, 5\right\}, \left\{1, 2, 4\right\}, \left\{1, 2, 3, 4, 5\right\} \right\} $ is necessary and sufficient to make $S$ a complete lattice under the partial order defined by ... $\{1\}, \{1, 3\}$ $\{1\}, \{1, 3\}, \{1, 2, 3, 4\}, \{1, 2, 3, 5\}$
Kathleen
asked
in
Set Theory & Algebra
Sep 18, 2014
by
Kathleen
12.8k
views
gatecse-2004
set-theory&algebra
partial-order
normal
37
votes
8
answers
73
GATE CSE 2006 | Question: 28
A logical binary relation $\odot$ ... $(\sim A\odot B)$ $\sim(A \odot \sim B)$ $\sim(\sim A\odot\sim B)$ $\sim(\sim A\odot B)$
Rucha Shelke
asked
in
Set Theory & Algebra
Sep 18, 2014
by
Rucha Shelke
5.8k
views
gatecse-2006
set-theory&algebra
binary-operation
34
votes
8
answers
74
GATE CSE 2002 | Question: 13
In how many ways can a given positive integer $n \geq 2$ be expressed as the sum of $2$ positive integers (which are not necessarily distinct). For example, for $n=3$, the number of ways is $2$, i.e., $1+2, 2+1$. Give only ... $n \geq k$ be expressed as the sum of $k$ positive integers (which are not necessarily distinct). Give only the answer without explanation.
Kathleen
asked
in
Combinatory
Sep 15, 2014
by
Kathleen
7.2k
views
gatecse-2002
combinatory
normal
descriptive
balls-in-bins
39
votes
8
answers
75
GATE CSE 2002 | Question: 1.25, ISRO2008-30, ISRO2016-6
The maximum number of edges in a $n$-node undirected graph without self loops is $n^2$ $\frac{n(n-1)}{2}$ $n-1$ $\frac{(n+1)(n)}{2}$
Kathleen
asked
in
Graph Theory
Sep 15, 2014
by
Kathleen
17.5k
views
gatecse-2002
graph-theory
easy
isro2008
isro2016
graph-connectivity
33
votes
8
answers
76
GATE CSE 2009 | Question: 24
The binary operation $\Box$ ... following is equivalent to $P \vee Q$? $\neg Q \Box \neg P$ $P\Box \neg Q$ $\neg P\Box Q$ $\neg P\Box \neg Q$
gatecse
asked
in
Mathematical Logic
Sep 15, 2014
by
gatecse
8.5k
views
gatecse-2009
mathematical-logic
easy
propositional-logic
40
votes
8
answers
77
GATE CSE 2009 | Question: 23
Which one of the following is the most appropriate logical formula to represent the statement? "Gold and silver ornaments are precious". The following notations are used: $G(x): x$ is a gold ornament $S(x): x$ is a silver ornament $P(x): x$ ... $\forall x((G(x) \vee S(x)) \implies P(x))$
gatecse
asked
in
Mathematical Logic
Sep 15, 2014
by
gatecse
8.4k
views
gatecse-2009
mathematical-logic
easy
first-order-logic
17
votes
8
answers
78
GATE CSE 2008 | Question: 24
Let $P =\sum \limits_ {i\;\text{odd}}^{1\le i \le 2k} i$ and $Q = \sum\limits_{i\;\text{even}}^{1 \le i \le 2k} i$, where $k$ is a positive integer. Then $P = Q - k$ $P = Q + k$ $P = Q$ $P = Q + 2k$
Kathleen
asked
in
Combinatory
Sep 11, 2014
by
Kathleen
5.5k
views
gatecse-2008
combinatory
easy
summation
28
votes
8
answers
79
GATE CSE 2008 | Question: 2
If $P, Q, R$ are subsets of the universal set U, then $(P\cap Q\cap R) \cup (P^c \cap Q \cap R) \cup Q^c \cup R^c$ is $Q^c \cup R^c$ $P \cup Q^c \cup R^c$ $P^c \cup Q^c \cup R^c$ U
Kathleen
asked
in
Set Theory & Algebra
Sep 11, 2014
by
Kathleen
9.2k
views
gatecse-2008
normal
set-theory&algebra
set-theory
0
votes
7
answers
80
NIELIT 2017 July Scientist B (CS) - Section B: 13
For the graph shown, which of the following paths is a Hamilton circuit? $ABCDCFDEFAEA$ $AEDCBAF$ $AEFDCBA$ $AFCDEBA$
admin
asked
in
Graph Theory
Mar 30, 2020
by
admin
2.1k
views
nielit2017july-scientistb-cs
discrete-mathematics
graph-theory
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