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Previous GATE
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Previous GATE Questions in Discrete Mathematics
43
votes
2
answers
81
GATE CSE 1989 | Question: 1-v
The number of possible commutative binary operations that can be defined on a set of $n$ elements (for a given $n$) is ___________.
makhdoom ghaya
asked
in
Set Theory & Algebra
Nov 27, 2016
by
makhdoom ghaya
6.5k
views
gate1989
descriptive
set-theory&algebra
binary-operation
21
votes
6
answers
82
GATE CSE 1989 | Question: 1-iv
The transitive closure of the relation $\left\{(1, 2), (2, 3), (3, 4), (5, 4)\right\}$ on the set $\left\{1, 2, 3, 4, 5\right\}$ is ___________.
makhdoom ghaya
asked
in
Set Theory & Algebra
Nov 27, 2016
by
makhdoom ghaya
7.1k
views
gate1989
set-theory&algebra
relations
descriptive
9
votes
2
answers
83
GATE CSE 1990 | Question: 17c
Show that the elements of the lattice $(N, \leq)$, where $N$ is the set of positive intergers and $a \leq b$ if and only if $a$ divides $b$, satisfy the distributive property.
makhdoom ghaya
asked
in
Set Theory & Algebra
Nov 26, 2016
by
makhdoom ghaya
1.9k
views
gate1990
descriptive
set-theory&algebra
lattice
0
votes
0
answers
84
GATE CSE 1990 | Question: 17b
Show, using resolution, that the following well-formed formula is valid for all interpretations: $\left(\forall x \forall y \left(f \left(x, y \right) \Leftarrow \neg y \left(y, x \right) = \left(\forall x \left(f \left(x, x \right)\right)$
closed
makhdoom ghaya
asked
in
Mathematical Logic
Nov 26, 2016
by
makhdoom ghaya
510
views
gate1990
descriptive
first-order-logic
bad-question
27
votes
2
answers
85
GATE CSE 1990 | Question: 3-xi
A graph is planar if and only if, It does not contain a subgraph homeomorphic to $k_{5}$ and $k_{3, 3}$. It does not contain a subgraph isomorphic to $k_{5}$ and $k_{3, 3}$. It does not contain a subgraph isomorphic to $k_{5}$ or $k_{3, 3}$ It does not contain a subgraph homeomorphic to $k_{5}$ or $k_{3, 3}$.
makhdoom ghaya
asked
in
Graph Theory
Nov 23, 2016
by
makhdoom ghaya
12.5k
views
gate1990
normal
graph-theory
graph-planarity
multiple-selects
29
votes
6
answers
86
GATE CSE 1990 | Question: 3-x
Indicate which of the following well-formed formulae are valid: $\left(P\Rightarrow Q\right) {\wedge} \left(Q \Rightarrow R\right) \Rightarrow \left(P \Rightarrow R\right)$ ...
makhdoom ghaya
asked
in
Mathematical Logic
Nov 22, 2016
by
makhdoom ghaya
9.3k
views
gate1990
normal
mathematical-logic
propositional-logic
multiple-selects
12
votes
2
answers
87
GATE CSE 1990 | Question: 3-ix
The number of ways in which $5\; A's, 5\; B's$ and $5\; C's$ can be arranged in a row is: $15!/(5!)^{3}$ $15!$ $\left(\frac{15}{5}\right)$ $15!(5!3!)$.
makhdoom ghaya
asked
in
Combinatory
Nov 22, 2016
by
makhdoom ghaya
3.1k
views
gate1990
normal
combinatory
20
votes
2
answers
88
GATE CSE 1990 | Question: 3-iii
The number of rooted binary trees with $n$ nodes is, Equal to the number of ways of multiplying $(n+1)$ matrices. Equal to the number of ways of arranging $n$ out of $2 n$ distinct elements. Equal to $\frac{1}{(n+1)}\binom{2n}{n}$. Equal to $n!$.
makhdoom ghaya
asked
in
Combinatory
Nov 19, 2016
by
makhdoom ghaya
5.3k
views
gate1990
normal
combinatory
catalan-number
multiple-selects
21
votes
2
answers
89
GATE CSE 1990 | Question: 2-x
Match the pairs in the following questions: ...
makhdoom ghaya
asked
in
Set Theory & Algebra
Nov 19, 2016
by
makhdoom ghaya
3.9k
views
gate1990
match-the-following
set-theory&algebra
group-theory
18
votes
1
answer
90
GATE CSE 1990 | Question: 1-viii
A graph which has the same number of edges as its complement must have number of vertices congruent to ________ or ________ modulo $4$.
makhdoom ghaya
asked
in
Graph Theory
Nov 18, 2016
by
makhdoom ghaya
5.2k
views
gate1990
graph-theory
graph-connectivity
fill-in-the-blanks
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
884
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
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