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Previous GATE Questions in Discrete Mathematics
92
votes
12
answers
121
GATE CSE 2015 Set 3 | Question: 24
In a room there are only two types of people, namely $\text{Type 1}$ and $\text{Type 2}$. $\text{Type 1}$ people always tell the truth and $\text{Type 2}$ people always lie. You give a fair coin to a person in that room, without knowing which type ... person is of $\text{Type 2}$, then the result is tail If the person is of $\text{Type 1}$, then the result is tail
go_editor
asked
in
Mathematical Logic
Feb 14, 2015
by
go_editor
17.7k
views
gatecse-2015-set3
mathematical-logic
difficult
logical-reasoning
51
votes
3
answers
122
GATE CSE 2015 Set 3 | Question: 23
Suppose $U$ is the power set of the set $S = \{1, 2, 3, 4, 5, 6\}$. For any $T \in U$, let $|T|$ denote the number of elements in $T$ and $T'$ denote the complement of $T$. For any $T, R \in U \text{ let } T \backslash R$ be the set ... $X \backslash Y = \phi)$ $\forall X \in U, \forall Y \in U, (X \backslash Y = Y' \backslash X')$
go_editor
asked
in
Set Theory & Algebra
Feb 14, 2015
by
go_editor
12.0k
views
gatecse-2015-set3
set-theory&algebra
set-theory
normal
65
votes
16
answers
123
GATE CSE 2015 Set 3 | Question: 5
The number of $4$ digit numbers having their digits in non-decreasing order (from left to right) constructed by using the digits belonging to the set $\{1, 2, 3\}$ is ________.
go_editor
asked
in
Combinatory
Feb 14, 2015
by
go_editor
15.5k
views
gatecse-2015-set3
combinatory
normal
numerical-answers
30
votes
3
answers
124
GATE CSE 2015 Set 3 | Question: 2
Let $\#$ be the binary operator defined as $X\#Y = X'+Y'$ where $X$ and $Y$ are Boolean variables. Consider the following two statements. $(S_1)$ $(P\#Q)\#R = P\#(Q\#R)$ $(S_2)$ $Q\#R = (R\#Q)$ Which are the following is/are true for the ... $R$? Only $S_1$ is true Only $S_2$ is true Both $S_1$ and $S_2$ are true Neither $S_1$ nor $S_2$ are true
go_editor
asked
in
Set Theory & Algebra
Feb 14, 2015
by
go_editor
5.6k
views
gatecse-2015-set3
set-theory&algebra
binary-operation
normal
32
votes
9
answers
125
GATE CSE 2015 Set 1 | Question: 54
Let G be a connected planar graph with 10 vertices. If the number of edges on each face is three, then the number of edges in G is_______________.
makhdoom ghaya
asked
in
Graph Theory
Feb 13, 2015
by
makhdoom ghaya
24.5k
views
gatecse-2015-set1
graph-theory
graph-connectivity
normal
graph-planarity
numerical-answers
76
votes
6
answers
126
GATE CSE 2015 Set 1 | Question: 34
Suppose $L = \left\{ p, q, r, s, t\right\}$ is a lattice represented by the following Hasse diagram: For any $x, y \in L$, not necessarily distinct , $x \vee y$ and $x \wedge y$ are join and meet of $x, y$ ... $p_r = 0$ $p_r = 1$ $0 < p_r ≤ \frac{1}{5}$ $\frac{1}{5} < p_r < 1$
makhdoom ghaya
asked
in
Set Theory & Algebra
Feb 13, 2015
by
makhdoom ghaya
17.2k
views
gatecse-2015-set1
set-theory&algebra
normal
lattice
88
votes
5
answers
127
GATE CSE 2015 Set 2 | Question: 55
Which one of the following well-formed formulae is a tautology? $\forall x \, \exists y \, R(x,y) \, \leftrightarrow \, \exists y \, \forall x \, R(x, y)$ ... $\forall x \, \forall y \, P(x,y) \, \rightarrow \, \forall x \, \forall y \, P(y, x)$
go_editor
asked
in
Mathematical Logic
Feb 13, 2015
by
go_editor
20.9k
views
gatecse-2015-set2
mathematical-logic
normal
first-order-logic
38
votes
5
answers
128
GATE CSE 2015 Set 2 | Question: 54
Let $X$ and $Y$ denote the sets containing $2$ and $20$ distinct objects respectively and $F$ denote the set of all possible functions defined from $X$ to $Y$. Let $f$ be randomly chosen from $F$. The probability of $f$ being one-to-one is ______.
go_editor
asked
in
Set Theory & Algebra
Feb 13, 2015
by
go_editor
8.2k
views
gatecse-2015-set2
set-theory&algebra
functions
normal
numerical-answers
48
votes
4
answers
129
GATE CSE 2015 Set 2 | Question: 50
In a connected graph, a bridge is an edge whose removal disconnects the graph. Which one of the following statements is true? A tree has no bridges A bridge cannot be part of a simple cycle Every edge of a clique with size $\geq 3$ is a bridge (A clique is any complete subgraph of a graph) A graph with bridges cannot have cycle
go_editor
asked
in
Graph Theory
Feb 13, 2015
by
go_editor
14.6k
views
gatecse-2015-set2
graph-theory
graph-connectivity
easy
44
votes
5
answers
130
GATE CSE 2015 Set 1 | Question: 26
$\sum\limits_{x=1}^{99}\frac{1}{x(x+1)}$ = ______.
makhdoom ghaya
asked
in
Combinatory
Feb 13, 2015
by
makhdoom ghaya
8.1k
views
gatecse-2015-set1
combinatory
normal
numerical-answers
summation
64
votes
6
answers
131
GATE CSE 2015 Set 1 | Question: 16
For a set $A$, the power set of $A$ is denoted by $2^{A}$. If $A = \left\{5,\left\{6\right\}, \left\{7\right\}\right\}$, which of the following options are TRUE? $\varnothing \in 2^{A}$ $\varnothing \subseteq 2^{A}$ ... I and III only II and III only I, II and III only I, II and IV only
makhdoom ghaya
asked
in
Set Theory & Algebra
Feb 13, 2015
by
makhdoom ghaya
15.4k
views
gatecse-2015-set1
set-theory&algebra
set-theory
normal
25
votes
2
answers
132
GATE CSE 2015 Set 1 | Question: 28
The binary operator $\neq$ ... about the binary operator $\neq$ ? Both commutative and associative Commutative but not associative Not commutative but associative Neither commutative nor associative
makhdoom ghaya
asked
in
Set Theory & Algebra
Feb 13, 2015
by
makhdoom ghaya
6.3k
views
gatecse-2015-set1
set-theory&algebra
easy
binary-operation
51
votes
15
answers
133
GATE CSE 2015 Set 2 | Question: 40
The number of onto functions (surjective functions) from set $X = \{1, 2, 3, 4\}$ to set $Y=\{a,b,c\}$ is ______.
go_editor
asked
in
Set Theory & Algebra
Feb 12, 2015
by
go_editor
19.3k
views
gatecse-2015-set2
set-theory&algebra
functions
normal
numerical-answers
34
votes
3
answers
134
GATE CSE 2015 Set 1 | Question: 14
Which one of the following is NOT equivalent to $p ↔ q$? $(\neg p ∨ q) ∧ (p ∨ \neg q)$ $(\neg p ∨ q) ∧ (q → p)$ $(\neg p ∧ q) ∨ ( p ∧ \neg q)$ $(\neg p ∧ \neg q) ∨ (p ∧ q)$
makhdoom ghaya
asked
in
Mathematical Logic
Feb 12, 2015
by
makhdoom ghaya
7.5k
views
gatecse-2015-set1
mathematical-logic
easy
propositional-logic
28
votes
6
answers
135
GATE CSE 2015 Set 2 | Question: 28
A graph is self-complementary if it is isomorphic to its complement. For all self-complementary graphs on $n$ vertices, $n$ is A multiple of 4 Even Odd Congruent to 0 $mod$ 4, or, 1 $mod$ 4.
go_editor
asked
in
Graph Theory
Feb 12, 2015
by
go_editor
12.6k
views
gatecse-2015-set2
graph-theory
graph-isomorphism
out-of-syllabus-now
23
votes
6
answers
136
GATE CSE 2015 Set 2 | Question: 18
The cardinality of the power set of $\{0, 1, 2, \dots , 10\}$ is _______
go_editor
asked
in
Set Theory & Algebra
Feb 12, 2015
by
go_editor
5.1k
views
gatecse-2015-set2
set-theory&algebra
set-theory
easy
numerical-answers
38
votes
2
answers
137
GATE CSE 2015 Set 2 | Question: 16
Let $R$ be the relation on the set of positive integers such that $aRb$ and only if $a$ and $b$ are distinct and let have a common divisor other than $1.$ Which one of the following statements about $R$ is true? $R$ is ... but not symmetric not transitive $R$ is transitive but not reflexive and not symmetric $R$ is symmetric but not reflexive and not transitive
go_editor
asked
in
Set Theory & Algebra
Feb 12, 2015
by
go_editor
7.6k
views
gatecse-2015-set2
set-theory&algebra
relations
normal
18
votes
2
answers
138
GATE CSE 2015 Set 2 | Question: 9
The number of divisors of $2100$ is ____.
go_editor
asked
in
Set Theory & Algebra
Feb 12, 2015
by
go_editor
8.9k
views
gatecse-2015-set2
set-theory&algebra
number-theory
easy
numerical-answers
33
votes
6
answers
139
GATE CSE 2015 Set 2 | Question: 3
Consider the following two statements. $S_1$: If a candidate is known to be corrupt, then he will not be elected $S_2$: If a candidate is kind, he will be elected Which one of the following statements follows from $S_1$ and $S_2$ as per sound inference ... If a person is kind, he is not known to be corrupt If a person is not kind, he is not known to be corrupt
go_editor
asked
in
Mathematical Logic
Feb 12, 2015
by
go_editor
8.8k
views
gatecse-2015-set2
mathematical-logic
normal
logical-reasoning
29
votes
4
answers
140
GATE CSE 2015 Set 1 | Question: 5
If $g(x) = 1 - x$ and $h(x) = \frac{x}{x-1}$, then $\frac{g(h(x))}{h(g(x))}$ is: $\frac{h(x)}{g(x)}$ $\frac{-1}{x}$ $\frac{g(x)}{h(x)}$ $\frac{x}{(1-x)^{2}}$
makhdoom ghaya
asked
in
Set Theory & Algebra
Feb 11, 2015
by
makhdoom ghaya
6.4k
views
gatecse-2015-set1
set-theory&algebra
functions
normal
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