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Previous GATE
Featured
Previous GATE Questions in Discrete Mathematics
20
votes
4
answers
221
GATE CSE 1998 | Question: 1.8
The number of functions from an $m$ element set to an $n$ element set is $m + n$ $m^n$ $n^m$ $m*n$
Kathleen
asked
in
Set Theory & Algebra
Sep 25, 2014
by
Kathleen
8.1k
views
gate1998
set-theory&algebra
combinatory
functions
easy
30
votes
3
answers
222
GATE CSE 1998 | Question: 1.7
Let $R_1$ and $R_2$ be two equivalence relations on a set. Consider the following assertions: $R_1 \cup R_2$ is an equivalence relation $R_1 \cap R_2$ is an equivalence relation Which of the following is correct? Both assertions are true Assertions (i) is true ... (ii) is not true Assertions (ii) is true but assertions (i) is not true Neither (i) nor (ii) is true
Kathleen
asked
in
Set Theory & Algebra
Sep 25, 2014
by
Kathleen
12.4k
views
gate1998
set-theory&algebra
relations
normal
18
votes
5
answers
223
GATE CSE 1998 | Question: 1.6
Suppose $A$ is a finite set with $n$ elements. The number of elements in the largest equivalence relation of A is $n$ $n^2$ $1$ $n+1$
Kathleen
asked
in
Set Theory & Algebra
Sep 25, 2014
by
Kathleen
9.4k
views
gate1998
set-theory&algebra
relations
easy
39
votes
5
answers
224
GATE CSE 1998 | Question: 1.5
What is the converse of the following assertion? I stay only if you go I stay if you go If I stay then you go If you do not go then I do not stay If I do not stay then you go
Kathleen
asked
in
Mathematical Logic
Sep 25, 2014
by
Kathleen
13.8k
views
gate1998
mathematical-logic
easy
propositional-logic
29
votes
4
answers
225
GATE CSE 2012 | Question: 26
Which of the following graphs is isomorphic to
Arjun
asked
in
Graph Theory
Sep 25, 2014
by
Arjun
11.0k
views
gatecse-2012
graph-theory
graph-isomorphism
normal
non-gate
52
votes
8
answers
226
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
14.1k
views
gatecse-2013
mathematical-logic
easy
first-order-logic
59
votes
8
answers
227
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
19.1k
views
gatecse-2013
graph-theory
normal
graph-connectivity
25
votes
2
answers
228
GATE CSE 2013 | Question: 25
Which of the following statements is/are TRUE for undirected graphs? P: Number of odd degree vertices is even. Q: Sum of degrees of all vertices is even. P only Q only Both P and Q Neither P nor Q
Arjun
asked
in
Graph Theory
Sep 24, 2014
by
Arjun
15.9k
views
gatecse-2013
graph-theory
easy
degree-of-graph
20
votes
5
answers
229
GATE CSE 1999 | Question: 3
Mr. X claims the following: If a relation R is both symmetric and transitive, then R is reflexive. For this, Mr. X offers the following proof: “From xRy, using symmetry we get yRx. Now because R is transitive xRy and yRx together imply xRx. Therefore, R is reflexive”. Give an example of a relation R which is symmetric and transitive but not reflexive.
Kathleen
asked
in
Set Theory & Algebra
Sep 23, 2014
by
Kathleen
3.0k
views
gate1999
set-theory&algebra
relations
normal
descriptive
13
votes
3
answers
230
GATE CSE 1999 | Question: 14
Show that the formula $\left[(\sim p \vee q) \Rightarrow (q \Rightarrow p)\right]$ is not a tautology. Let $A$ be a tautology and $B$ any other formula. Prove that $(A \vee B)$ is a tautology.
Kathleen
asked
in
Mathematical Logic
Sep 23, 2014
by
Kathleen
2.4k
views
gate1999
mathematical-logic
normal
propositional-logic
proof
descriptive
33
votes
5
answers
231
GATE CSE 1999 | Question: 5
Let $G$ be a connected, undirected graph. A cut in $G$ is a set of edges whose removal results in $G$ being broken into two or more components, which are not connected with each other. The size of a cut is called its cardinality. A min-cut of $G$ is a cut ... $n$ vertices has a min-cut of cardinality $k$, then $G$ has at least $\left(\frac{n\times k}{2}\right)$ edges.
Kathleen
asked
in
Graph Theory
Sep 23, 2014
by
Kathleen
6.4k
views
gate1999
graph-theory
graph-connectivity
normal
descriptive
proof
9
votes
1
answer
232
GATE CSE 1999 | Question: 4
Let $G$ be a finite group and $H$ be a subgroup of $G$. For $a \in G$, define $aH=\left\{ah \mid h \in H\right\}$. Show that $|aH| = |bH|.$ Show that for every pair of elements $a, b \in G$, either $aH = bH$ or $aH$ and $bH$ are disjoint. Use the above to argue that the order of $H$ must divide the order of $G.$
Kathleen
asked
in
Set Theory & Algebra
Sep 23, 2014
by
Kathleen
3.2k
views
gate1999
set-theory&algebra
group-theory
descriptive
proof
15
votes
4
answers
233
GATE CSE 1999 | Question: 2.3
Let $L$ be a set with a relation $R$ which is transitive, anti-symmetric and reflexive and for any two elements $a, b \in L$, let the least upper bound $lub (a, b)$ and the greatest lower bound $glb (a, b)$ exist. Which of the following is/are true? $L$ is a poset $L$ is a Boolean algebra $L$ is a lattice None of the above
Kathleen
asked
in
Set Theory & Algebra
Sep 23, 2014
by
Kathleen
5.6k
views
gate1999
set-theory&algebra
normal
relations
multiple-selects
38
votes
7
answers
234
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
39
votes
5
answers
235
GATE CSE 1999 | Question: 1.15
The number of articulation points of the following graph is $0$ $1$ $2$ $3$
Kathleen
asked
in
Graph Theory
Sep 23, 2014
by
Kathleen
8.8k
views
gate1999
graph-theory
graph-connectivity
normal
30
votes
5
answers
236
GATE CSE 1999 | Question: 1.3
The number of binary strings of $n$ zeros and $k$ ones in which no two ones are adjacent is $^{n-1}C_k$ $^nC_k$ $^nC_{k+1}$ None of the above
Kathleen
asked
in
Combinatory
Sep 23, 2014
by
Kathleen
9.0k
views
gate1999
combinatory
normal
23
votes
2
answers
237
GATE CSE 1999 | Question: 1.2
The number of binary relations on a set with $n$ elements is: $n^2$ $2^n$ $2^{n^2}$ None of the above
Kathleen
asked
in
Set Theory & Algebra
Sep 23, 2014
by
Kathleen
11.2k
views
gate1999
set-theory&algebra
relations
combinatory
easy
36
votes
6
answers
238
GATE CSE 2005 | Question: 7
The time complexity of computing the transitive closure of a binary relation on a set of $n$ elements is known to be: $O(n)$ $O(n \log n)$ $O \left( n^{\frac{3}{2}} \right)$ $O\left(n^3\right)$
Kathleen
asked
in
Set Theory & Algebra
Sep 22, 2014
by
Kathleen
24.5k
views
gatecse-2005
set-theory&algebra
normal
relations
48
votes
8
answers
239
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
41
votes
3
answers
240
GATE CSE 2007 | Question: 26
Consider the set $S =\{ a , b , c , d\}.$ Consider the following $4$ partitions $π_1,π_2,π_3,π_4$ on $S : π_1 =\{\overline{abcd}\},\quad π_2 =\{\overline{ab}, \overline{cd}\},$ ... $π_i \prec π_j$ if and only if $π_i$ refines $π_j$. The poset diagram for $(S',\prec)$ is:
Kathleen
asked
in
Set Theory & Algebra
Sep 21, 2014
by
Kathleen
13.4k
views
gatecse-2007
set-theory&algebra
normal
partial-order
descriptive
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