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Previous GATE
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Previous GATE Questions in Discrete Mathematics
23
votes
9
answers
91
GATE CSE 1987 | Question: 10e
Show that the conclusion $(r \to q)$ follows from the premises$:p, (p \to q) \vee (p \wedge (r \to q))$
makhdoom ghaya
asked
in
Mathematical Logic
Nov 14, 2016
by
makhdoom ghaya
5.1k
views
gate1987
mathematical-logic
propositional-logic
proof
descriptive
36
votes
8
answers
92
GATE CSE 1987 | Question: 10b
What is the generating function $G(z)$ for the sequence of Fibonacci numbers?
makhdoom ghaya
asked
in
Combinatory
Nov 14, 2016
by
makhdoom ghaya
9.8k
views
gate1987
combinatory
generating-functions
descriptive
3
votes
1
answer
93
GATE CSE 1987 | Question: 9f
Give the composition tables (Cayley Tables) of the two non-isomorphic groups of order $4$ with elements $e, a, b, c$ where $c$ is the identity element. Use the order $e, a, b, c$ for the rows and columns.
makhdoom ghaya
asked
in
Set Theory & Algebra
Nov 14, 2016
by
makhdoom ghaya
882
views
gate1987
set-theory&algebra
group-theory
group-isomorphism
descriptive
out-of-gate-syllabus
24
votes
2
answers
94
GATE CSE 1987 | Question: 9e
How many true inclusion relations are there of the form $A \subseteq B$, where $A$ and $B$ are subsets of a set $S$ with $n$ elements?
makhdoom ghaya
asked
in
Set Theory & Algebra
Nov 14, 2016
by
makhdoom ghaya
3.1k
views
gate1987
set-theory&algebra
relations
descriptive
11
votes
1
answer
95
GATE CSE 1987 | Question: 9d
Specify an adjacency-lists representation of the undirected graph given above.
makhdoom ghaya
asked
in
Graph Theory
Nov 14, 2016
by
makhdoom ghaya
1.6k
views
gate1987
graph-theory
easy
graph-connectivity
descriptive
15
votes
3
answers
96
GATE CSE 1987 | Question: 9c
Show that the number of odd-degree vertices in a finite graph is even.
makhdoom ghaya
asked
in
Graph Theory
Nov 14, 2016
by
makhdoom ghaya
1.8k
views
gate1987
graph-theory
degree-of-graph
descriptive
proof
23
votes
3
answers
97
GATE CSE 1987 | Question: 9b
How many one-to-one functions are there from a set $A$ with $n$ elements onto itself?
makhdoom ghaya
asked
in
Set Theory & Algebra
Nov 14, 2016
by
makhdoom ghaya
4.2k
views
gate1987
set-theory&algebra
functions
descriptive
24
votes
4
answers
98
GATE CSE 1987 | Question: 9a
How many binary relations are there on a set $A$ with $n$ elements?
makhdoom ghaya
asked
in
Set Theory & Algebra
Nov 14, 2016
by
makhdoom ghaya
5.8k
views
gate1987
set-theory&algebra
relations
descriptive
2
votes
2
answers
99
GATE CSE 1987 | Question: 2f
State whether the following statements are TRUE or FALSE: Every infinite cyclic group is isomorphic to the infinite cyclic group of integers under addition.
makhdoom ghaya
asked
in
Graph Theory
Nov 9, 2016
by
makhdoom ghaya
917
views
gate1987
graph-theory
graph-isomorphism
true-false
out-of-gate-syllabus
4
votes
1
answer
100
GATE CSE 1987 | Question: 2e
State whether the following statement is TRUE or FALSE: There is a linear-time algorithm for testing the planarity of finite graphs.
makhdoom ghaya
asked
in
Graph Theory
Nov 9, 2016
by
makhdoom ghaya
1.3k
views
gate1987
graph-theory
graph-planarity
true-false
22
votes
4
answers
101
GATE CSE 1987 | Question: 2d
State whether the following statements are TRUE or FALSE: The union of two equivalence relations is also an equivalence relation.
makhdoom ghaya
asked
in
Set Theory & Algebra
Nov 9, 2016
by
makhdoom ghaya
5.5k
views
gate1987
set-theory&algebra
relations
true-false
26
votes
3
answers
102
GATE CSE 1992 | Question: 14b
Consider the set of integers $\{1,2,3,4,6,8,12,24\}$ together with the two binary operations LCM (lowest common multiple) and GCD (greatest common divisor). Which of the following algebraic structures does this represent? group ring field lattice
go_editor
asked
in
Set Theory & Algebra
Apr 24, 2016
by
go_editor
4.6k
views
gate1992
set-theory&algebra
partial-order
lattice
normal
7
votes
2
answers
103
GATE CSE 1992 | Question: 15.b
Let $S$ be the set of all integers and let $n > 1$ be a fixed integer. Define for $a,b \in S, a R b$ iff $a-b$ is a multiple of $n$. Show that $R$ is an equivalence relation and find its equivalence classes for $n = 5$.
go_editor
asked
in
Set Theory & Algebra
Apr 24, 2016
by
go_editor
3.3k
views
gate1992
set-theory&algebra
normal
relations
descriptive
43
votes
8
answers
104
GATE CSE 2006 | Question: 73
The $2^n$ vertices of a graph $G$ corresponds to all subsets of a set of size $n$, for $n \geq 6$. Two vertices of $G$ are adjacent if and only if the corresponding sets intersect in exactly two elements. The number of connected components in $G$ is: $n$ $n + 2$ $2^{\frac{n}{2}}$ $\frac{2^{n}}{n}$
go_editor
asked
in
Graph Theory
Apr 24, 2016
by
go_editor
8.6k
views
gatecse-2006
graph-theory
normal
graph-connectivity
89
votes
6
answers
105
GATE CSE 2006 | Question: 72
The $2^n$ vertices of a graph $G$ corresponds to all subsets of a set of size $n$, for $n \geq 6$. Two vertices of $G$ are adjacent if and only if the corresponding sets intersect in exactly two elements. The maximum degree of a vertex in $G$ is: $\binom{\frac{n}{2}}{2}.2^{\frac{n}{2}}$ $2^{n-2}$ $2^{n-3}\times 3$ $2^{n-1}$
go_editor
asked
in
Graph Theory
Apr 24, 2016
by
go_editor
17.7k
views
gatecse-2006
graph-theory
normal
degree-of-graph
36
votes
5
answers
106
GATE CSE 2007 | Question: 85
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 $(i,j + 1)$. Suppose that the robot is not allowed to traverse the ... $^{20}\mathrm{C}_{10} - ^{8}\mathrm{C}_{4}\times ^{11}\mathrm{C}_{5}$
go_editor
asked
in
Combinatory
Apr 23, 2016
by
go_editor
9.4k
views
gatecse-2007
combinatory
normal
discrete-mathematics
91
votes
9
answers
107
GATE CSE 2016 Set 1 | Question: 28
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 ___________.
Sandeep Singh
asked
in
Set Theory & Algebra
Feb 12, 2016
by
Sandeep Singh
21.5k
views
gatecse-2016-set1
set-theory&algebra
functions
normal
numerical-answers
66
votes
10
answers
108
GATE CSE 2016 Set 1 | Question: 27
Consider the recurrence relation $a_1 =8 , a_n =6n^2 +2n+a_{n-1}$. Let $a_{99}=K\times 10^4$. The value of $K$ is __________.
Sandeep Singh
asked
in
Combinatory
Feb 12, 2016
by
Sandeep Singh
28.1k
views
gatecse-2016-set1
combinatory
recurrence-relation
normal
numerical-answers
57
votes
17
answers
109
GATE CSE 2016 Set 1 | Question: 26
The coefficient of $x^{12}$ in $\left(x^{3}+x^{4}+x^{5}+x^{6}+\dots \right)^{3}$ is ___________.
Sandeep Singh
asked
in
Combinatory
Feb 12, 2016
by
Sandeep Singh
25.8k
views
gatecse-2016-set1
combinatory
generating-functions
normal
numerical-answers
71
votes
7
answers
110
GATE CSE 2016 Set 1 | Question: 1
Let $p, q, r, s$ represents the following propositions. $p:x\in\left\{8, 9, 10, 11, 12\right\}$ $q:$ $x$ is a composite number. $r:$ $x$ is a perfect square. $s:$ $x$ is a prime number. The integer $x\geq2$ which satisfies $\neg\left(\left(p\Rightarrow q\right) \wedge \left(\neg r \vee \neg s\right)\right)$ is ____________.
Sandeep Singh
asked
in
Mathematical Logic
Feb 12, 2016
by
Sandeep Singh
12.9k
views
gatecse-2016-set1
mathematical-logic
normal
numerical-answers
propositional-logic
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