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Previous GATE
Featured
Most answered questions in Discrete Mathematics
37
votes
7
answers
91
GATE IT 2006 | Question: 11
If all the edge weights of an undirected graph are positive, then any subset of edges that connects all the vertices and has minimum total weight is a Hamiltonian cycle grid hypercube tree
Ishrat Jahan
asked
in
Graph Theory
Oct 31, 2014
by
Ishrat Jahan
8.7k
views
gateit-2006
graph-theory
graph-connectivity
normal
32
votes
7
answers
92
GATE IT 2007 | Question: 23
A partial order $P$ is defined on the set of natural numbers as follows. Here $\frac{x}{y}$ denotes integer division. $(0, 0) \in P.$ $(a, b) \in P$ if and only if $(a \% 10) \leq (b \% 10$) and $(\frac{a}{10},\frac{b}{10})\in P.$ ... $P$? (i) and (iii) (ii) and (iv) (i) and (iv) (iii) and (iv)
Ishrat Jahan
asked
in
Set Theory & Algebra
Oct 29, 2014
by
Ishrat Jahan
11.3k
views
gateit-2007
set-theory&algebra
partial-order
normal
58
votes
7
answers
93
GATE IT 2008 | Question: 4
What is the size of the smallest $\textsf{MIS}$ (Maximal Independent Set) of a chain of nine nodes? $5$ $4$ $3$ $2$
Ishrat Jahan
asked
in
Graph Theory
Oct 27, 2014
by
Ishrat Jahan
49.6k
views
gateit-2008
normal
graph-connectivity
38
votes
7
answers
94
GATE CSE 1999 | Question: 2.2
Two girls have picked $10$ roses, $15$ sunflowers and $15$ daffodils. What is the number of ways they can divide the flowers among themselves? $1638$ $2100$ $2640$ None of the above
Kathleen
asked
in
Combinatory
Sep 23, 2014
by
Kathleen
12.1k
views
gate1999
combinatory
normal
40
votes
7
answers
95
GATE CSE 2005 | Question: 43
Let $f: B \to C$ and $g: A \to B$ be two functions and let $h = f o g$. Given that $h$ is an onto function which one of the following is TRUE? $f$ and $g$ should both be onto functions $f$ should be onto but $g$ need not to be onto $g$ should be onto but $f$ need not be onto both $f$ and $g$ need not be onto
gatecse
asked
in
Set Theory & Algebra
Sep 21, 2014
by
gatecse
9.9k
views
gatecse-2005
set-theory&algebra
functions
normal
40
votes
7
answers
96
GATE CSE 2010 | Question: 28
The degree sequence of a simple graph is the sequence of the degrees of the nodes in the graph in decreasing order. Which of the following sequences can not be the degree sequence of any graph? $7, 6, 5, 4, 4, 3, 2, 1$ $6, 6, 6, 6, 3, 3, 2, 2$ $7, 6, 6, 4, 4, 3, 2, 2$ $8, 7, 7, 6, 4, 2, 1, 1$ I and II III and IV IV only II and IV
gatecse
asked
in
Graph Theory
Sep 21, 2014
by
gatecse
18.4k
views
gatecse-2010
graph-theory
degree-of-graph
37
votes
7
answers
97
GATE CSE 2004 | Question: 77
The minimum number of colours required to colour the following graph, such that no two adjacent vertices are assigned the same color, is $2$ $3$ $4$ $5$
Kathleen
asked
in
Graph Theory
Sep 18, 2014
by
Kathleen
12.6k
views
gatecse-2004
graph-theory
graph-coloring
easy
87
votes
7
answers
98
GATE CSE 2004 | Question: 23, ISRO2007-32
Identify the correct translation into logical notation of the following assertion. Some boys in the class are taller than all the girls Note: $\text{taller} (x, y)$ is true if $x$ is taller than $y$ ... $(\exists x) (\text{boy}(x) \land (\forall y) (\text{girl}(y) \rightarrow \text{taller}(x, y)))$
Kathleen
asked
in
Mathematical Logic
Sep 18, 2014
by
Kathleen
110k
views
gatecse-2004
mathematical-logic
easy
isro2007
first-order-logic
58
votes
7
answers
99
GATE CSE 2006 | Question: 24
Given a set of elements $N = {1, 2, ..., n}$ and two arbitrary subsets $A⊆N$ and $B⊆N$, how many of the n! permutations $\pi$ from $N$ to $N$ satisfy $\min(\pi(A)) = \min(\pi(B))$, where $\min(S)$ is the smallest integer in the set of integers $S$, and $\pi$(S) is the set of ... $n! \frac{|A ∩ B|}{|A ∪ B|}$ $\dfrac{|A ∩ B|^2}{^n \mathrm{C}_{|A ∪ B|}}$
Rucha Shelke
asked
in
Set Theory & Algebra
Sep 18, 2014
by
Rucha Shelke
11.2k
views
gatecse-2006
set-theory&algebra
normal
set-theory
25
votes
7
answers
100
GATE CSE 2006 | Question: 22
Let $E, F$ and $G$ be finite sets. Let $X = (E ∩ F) - (F ∩ G)$ and $Y = (E - (E ∩ G)) - (E - F)$. Which one of the following is true? $X ⊂ Y$ $X ⊃ Y$ $X = Y$ $X - Y ≠ \emptyset$ and $Y - X ≠ \emptyset$
Rucha Shelke
asked
in
Set Theory & Algebra
Sep 17, 2014
by
Rucha Shelke
6.5k
views
gatecse-2006
set-theory&algebra
normal
set-theory
59
votes
7
answers
101
GATE CSE 2003 | Question: 32
Which of the following is a valid first order formula? (Here \(\alpha\) and \(\beta\) are first order formulae with $x$ as their only free variable) $((∀x)[α] ⇒ (∀x)[β]) ⇒ (∀x)[α ⇒ β]$ $(∀x)[α] ⇒ (∃x)[α ∧ β]$ $((∀x)[α ∨ β] ⇒ (∃x)[α]) ⇒ (∀x)[α]$ $(∀x)[α ⇒ β] ⇒ (((∀x)[α]) ⇒ (∀x)[β])$
Kathleen
asked
in
Mathematical Logic
Sep 16, 2014
by
Kathleen
16.7k
views
gatecse-2003
mathematical-logic
first-order-logic
normal
54
votes
7
answers
102
GATE CSE 2009 | Question: 3
Which one of the following is TRUE for any simple connected undirected graph with more than $2$ vertices? No two vertices have the same degree. At least two vertices have the same degree. At least three vertices have the same degree. All vertices have the same degree.
gatecse
asked
in
Graph Theory
Sep 15, 2014
by
gatecse
11.3k
views
gatecse-2009
graph-theory
normal
degree-of-graph
28
votes
7
answers
103
GATE CSE 2009 | Question: 26
Consider the following well-formed formulae: $\neg \forall x(P(x))$ $\neg \exists x(P(x))$ $\neg \exists x(\neg P(x))$ $\exists x(\neg P(x))$ Which of the above are equivalent? $\text{I}$ and $\text{III}$ $\text{I}$ and $\text{IV}$ $\text{II}$ and $\text{III}$ $\text{II}$ and $\text{IV}$
gatecse
asked
in
Mathematical Logic
Sep 15, 2014
by
gatecse
5.5k
views
gatecse-2009
mathematical-logic
normal
first-order-logic
47
votes
7
answers
104
GATE CSE 2000 | Question: 2.7
Let $a, b, c, d$ be propositions. Assume that the equivalence $a ⇔ ( b \vee \neg b)$ and $b ⇔c$ hold. Then the truth-value of the formula $(a ∧ b) → (a ∧ c) ∨ d$ is always True False Same as the truth-value of $b$ Same as the truth-value of $d$
Kathleen
asked
in
Mathematical Logic
Sep 14, 2014
by
Kathleen
12.0k
views
gatecse-2000
mathematical-logic
normal
propositional-logic
30
votes
7
answers
105
GATE CSE 2008 | Question: 31
$P$ and $Q$ are two propositions. Which of the following logical expressions are equivalent? $P ∨ \neg Q$ $\neg(\neg P ∧ Q)$ $(P ∧ Q) ∨ (P ∧ \neg Q) ∨ (\neg P ∧ \neg Q)$ $(P ∧ Q) ∨ (P ∧ \neg Q) ∨ (\neg P ∧ Q)$ Only I and II Only I, II and III Only I, II and IV All of I, II, III and IV
Kathleen
asked
in
Mathematical Logic
Sep 12, 2014
by
Kathleen
8.3k
views
gatecse-2008
normal
mathematical-logic
propositional-logic
39
votes
7
answers
106
GATE CSE 2008 | Question: 23
Which of the following statements is true for every planar graph on $n$ vertices? The graph is connected The graph is Eulerian The graph has a vertex-cover of size at most $\frac{3n}{4}$ The graph has an independent set of size at least $\frac{n}{3}$
Kathleen
asked
in
Graph Theory
Sep 11, 2014
by
Kathleen
55.0k
views
gatecse-2008
graph-theory
normal
graph-planarity
49
votes
6
answers
107
GO Classes Weekly Quiz 5 | Propositional Logic | Question: 16
If $\text{F1, F2}$ and $\text{F3}$ are propositional formulae/expressions, over some set of propositional variables, such that $\mathrm{F} 1 \vee F 2 \rightarrow \mathrm{F} 3$ is a contradiction, then which of the following is/are ... is a tautology. $\text{F3}$ is a contradiction. $\text{F1} \mathrm{v} \text{F2}$ is a tautology.
GO Classes
asked
in
Mathematical Logic
Mar 26, 2023
by
GO Classes
1.5k
views
goclasses2024_wq5
goclasses
mathematical-logic
propositional-logic
multiple-selects
2-marks
26
votes
6
answers
108
GATE CSE 2022 | Question: 26
Which one of the following is the closed form for the generating function of the sequence $\{ a_{n} \}_{n \geq 0}$ defined below? $ a_{n} = \left\{\begin{matrix} n + 1, & \text{n is odd} & \\ 1, & \text{otherwise} & \end{matrix}\right.$ ... $\frac{2x}{(1-x^{2})^{2}} + \frac{1}{1-x}$ $\frac{x}{(1-x^{2})^{2}} + \frac{1}{1-x}$
Arjun
asked
in
Combinatory
Feb 15, 2022
by
Arjun
9.3k
views
gatecse-2022
combinatory
generating-functions
2-marks
15
votes
6
answers
109
GATE CSE 2022 | Question: 41
Consider the following recurrence: $\begin{array}{} f(1) & = & 1; \\ f(2n) & = & 2f(n) - 1, & \; \text{for}\; n \geq 1; \\ f(2n+1) & = & 2f(n) + 1, & \; \text{for}\; n \geq 1. \end{array}$ Then, which of the following statements is/are $\text{TRUE}?$ ... $f(2^{n}) = 1$ $f(5 \cdot 2^{n}) = 2^{n+1} + 1$ $f(2^{n} + 1) = 2^{n} + 1$
Arjun
asked
in
Combinatory
Feb 15, 2022
by
Arjun
7.7k
views
gatecse-2022
combinatory
recurrence-relation
multiple-selects
2-marks
25
votes
6
answers
110
GATE CSE 2021 Set 2 | Question: 50
Let $S$ be a set of consisting of $10$ elements. The number of tuples of the form $(A,B)$ such that $A$ and $B$ are subsets of $S$, and $A \subseteq B$ is ___________
Arjun
asked
in
Combinatory
Feb 18, 2021
by
Arjun
11.8k
views
gatecse-2021-set2
combinatory
counting
numerical-answers
2-marks
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