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Previous GATE
Featured
Previous GATE Questions in Discrete Mathematics
40
votes
4
answers
331
GATE CSE 1992 | Question: 14a
If $G$ is a group of even order, then show that there exists an element $a≠e$, the identity in $G$, such that $a^2 = e$.
Kathleen
asked
in
Set Theory & Algebra
Sep 13, 2014
by
Kathleen
7.1k
views
gate1992
set-theory&algebra
group-theory
normal
descriptive
proof
33
votes
3
answers
332
GATE CSE 1992 | Question: 03,iii
How many edges can there be in a forest with $p$ components having $n$ vertices in all?
Kathleen
asked
in
Graph Theory
Sep 13, 2014
by
Kathleen
6.3k
views
gate1992
graph-theory
graph-connectivity
descriptive
24
votes
4
answers
333
GATE CSE 1992 | Question: 02,xvi
Which of the following is/are a tautology? $a \vee b \to b \wedge c$ $a \wedge b \to b \vee c$ $a \vee b \to \left(b \to c \right)$ $a \to b \to \left(b \to c \right)$
Kathleen
asked
in
Mathematical Logic
Sep 13, 2014
by
Kathleen
9.7k
views
gate1992
mathematical-logic
easy
propositional-logic
multiple-selects
9
votes
4
answers
334
GATE CSE 1992 | Question: 02,viii
A non-planar graph with minimum number of vertices has $9$ edges, $6$ vertices $6$ edges, $4$ vertices $10$ edges, $5$ vertices $9$ edges, $5$ vertices
Kathleen
asked
in
Graph Theory
Sep 12, 2014
by
Kathleen
3.1k
views
gate1992
graph-theory
normal
graph-planarity
10
votes
1
answer
335
GATE CSE 1992 | Question: 01,x
Maximum number of edges in a planar graph with $n$ vertices is _____
Kathleen
asked
in
Graph Theory
Sep 12, 2014
by
Kathleen
5.4k
views
gate1992
graph-theory
graph-planarity
easy
fill-in-the-blanks
52
votes
2
answers
336
GATE CSE 1991 | Question: 16,a
Find the number of binary strings $w$ of length $2n$ with an equal number of $1's$ and $0's$ and the property that every prefix of $w$ has at least as many $0's$ as $1's.$
Kathleen
asked
in
Combinatory
Sep 12, 2014
by
Kathleen
6.3k
views
gate1991
combinatory
normal
descriptive
catalan-number
39
votes
9
answers
337
GATE CSE 1991 | Question: 03,xii
If $F_1$, $F_2$ and $F_3$ are propositional formulae such that $F_1 \land F_2 \rightarrow F_3$ and $F_1 \land F_2 \rightarrow \sim F_3$ are both tautologies, then which of the following is true: Both $F_1$ and $F_2$ are tautologies The conjunction $F_1 \land F_2$ is not satisfiable Neither is tautologous Neither is satisfiable None of the above
Kathleen
asked
in
Mathematical Logic
Sep 12, 2014
by
Kathleen
8.6k
views
gate1991
mathematical-logic
normal
propositional-logic
multiple-selects
43
votes
4
answers
338
GATE CSE 1991 | Question: 02-iv
Match the pairs in the following questions by writing the corresponding letters only. ...
Kathleen
asked
in
Combinatory
Sep 12, 2014
by
Kathleen
4.9k
views
gate1991
combinatory
normal
match-the-following
51
votes
4
answers
339
GATE CSE 1991 | Question: 01,xv
The maximum number of possible edges in an undirected graph with $n$ vertices and $k$ components is ______.
Kathleen
asked
in
Graph Theory
Sep 12, 2014
by
Kathleen
11.4k
views
gate1991
graph-theory
graph-connectivity
normal
fill-in-the-blanks
19
votes
3
answers
340
GATE CSE 1991 | Question: 01,xiv
If the longest chain in a partial order is of length $n$, then the partial order can be written as a _____ of $n$ antichains.
Kathleen
asked
in
Set Theory & Algebra
Sep 12, 2014
by
Kathleen
5.7k
views
gate1991
set-theory&algebra
partial-order
normal
fill-in-the-blanks
111
votes
9
answers
341
GATE CSE 2012 | Question: 38
Let $G$ be a complete undirected graph on $6$ vertices. If vertices of $G$ are labeled, then the number of distinct cycles of length $4$ in $G$ is equal to $15$ $30$ $90$ $360$
gatecse
asked
in
Graph Theory
Sep 12, 2014
by
gatecse
34.6k
views
gatecse-2012
graph-theory
normal
marks-to-all
counting
30
votes
7
answers
342
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
70
votes
5
answers
343
GATE CSE 2008 | Question: 30
Let $\text{fsa}$ and $\text{pda}$ be two predicates such that $\text{fsa}(x)$ means $x$ is a finite state automaton and $\text{pda}(y)$ means that $y$ is a pushdown automaton. Let $\text{equivalent}$ ...
Kathleen
asked
in
Mathematical Logic
Sep 12, 2014
by
Kathleen
13.8k
views
gatecse-2008
easy
mathematical-logic
first-order-logic
17
votes
8
answers
344
GATE CSE 2008 | Question: 24
Let $P =\sum \limits_ {i\;\text{odd}}^{1\le i \le 2k} i$ and $Q = \sum\limits_{i\;\text{even}}^{1 \le i \le 2k} i$, where $k$ is a positive integer. Then $P = Q - k$ $P = Q + k$ $P = Q$ $P = Q + 2k$
Kathleen
asked
in
Combinatory
Sep 11, 2014
by
Kathleen
5.5k
views
gatecse-2008
combinatory
easy
summation
39
votes
7
answers
345
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
54.9k
views
gatecse-2008
graph-theory
normal
graph-planarity
28
votes
8
answers
346
GATE CSE 2008 | Question: 2
If $P, Q, R$ are subsets of the universal set U, then $(P\cap Q\cap R) \cup (P^c \cap Q \cap R) \cup Q^c \cup R^c$ is $Q^c \cup R^c$ $P \cup Q^c \cup R^c$ $P^c \cup Q^c \cup R^c$ U
Kathleen
asked
in
Set Theory & Algebra
Sep 11, 2014
by
Kathleen
9.2k
views
gatecse-2008
normal
set-theory&algebra
set-theory
78
votes
6
answers
347
GATE CSE 1992 | Question: 92,xv
Which of the following predicate calculus statements is/are valid? $(\forall (x)) P(x) \vee (\forall(x))Q(x) \implies (\forall (x)) (P(x) \vee Q(x))$ $(\exists (x)) P(x) \wedge (\exists (x))Q(x) \implies (\exists (x)) (P(x) \wedge Q(x))$ ... $(\exists (x)) (P(x) \vee Q(x)) \implies \sim (\forall (x)) P(x) \vee (\exists (x)) Q(x)$
Arjun
asked
in
Mathematical Logic
Sep 2, 2014
by
Arjun
16.2k
views
gate1992
mathematical-logic
normal
first-order-logic
45
votes
3
answers
348
GATE CSE 2013 | Question: 47
Which one of the following is NOT logically equivalent to $¬∃x(∀ y (α)∧∀z(β ))$ ? $∀ x(∃ z(¬β )→∀ y(α))$ $∀x(∀ z(β )→∃ y(¬α))$ $∀x(∀ y(α)→∃z(¬β ))$ $∀x(∃ y(¬α)→∃z(¬β ))$
gatecse
asked
in
Mathematical Logic
Aug 21, 2014
by
gatecse
11.8k
views
mathematical-logic
normal
marks-to-all
gatecse-2013
first-order-logic
33
votes
3
answers
349
GATE CSE 2013 | Question: 1
A binary operation $\oplus$ on a set of integers is defined as $x \oplus y = x^{2}+y^{2}$. Which one of the following statements is TRUE about $\oplus$? Commutative but not associative Both commutative and associative Associative but not commutative Neither commutative nor associative
gatecse
asked
in
Set Theory & Algebra
Aug 7, 2014
by
gatecse
7.4k
views
gatecse-2013
set-theory&algebra
easy
binary-operation
26
votes
3
answers
350
GATE CSE 2012 | Question: 17
Let $G$ be a simple undirected planar graph on $10$ vertices with $15$ edges. If $G$ is a connected graph, then the number of bounded faces in any embedding of $G$ on the plane is equal to $3$ $4$ $5$ $6$
gatecse
asked
in
Graph Theory
Aug 5, 2014
by
gatecse
10.0k
views
gatecse-2012
graph-theory
graph-planarity
normal
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