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39 votes
7 answers
3
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 $\frac{n}{3}$
Which of the following statements is true for every planar graph on $n$ vertices?The graph is connectedThe graph is EulerianThe graph has a vertex-cover of size at most $...
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58 votes
7 answers
4
GATE IT 2008 | Question: 4
What is the size of the smallest $\textsf{MIS}$ (Maximal Independent Set) of a chain of nine nodes? $5$ $4$ $3$ $2$
What is the size of the smallest $\textsf{MIS}$ (Maximal Independent Set) of a chain of nine nodes?$5$$4$$3$$2$
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60 votes
10 answers
5
GATE CSE 2003 | Question: 36
How many perfect matching are there in a complete graph of $6$ vertices? $15$ $24$ $30$ $60$
How many perfect matching are there in a complete graph of $6$ vertices?$15$$24$$30$$60$
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5 votes
2 answers
7
How many transitive relations are there on a set with n elements if a)n=1   b) n=2  c) n=3
How many transitive relations are there on a set with n elements if a)n=1 b) n=2 c) n=3
How many transitive relations are there on a set with n elements ifa)n=1 b) n=2 c) n=3
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13 votes
3 answers
8
relation
Number of relations $S$ over set $\{0,1,2,3 \}$ such that $(x,y) \in S \Rightarrow x = y$
Number of relations $S$ over set $\{0,1,2,3 \}$ such that $(x,y) \in S \Rightarrow x = y$
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99 votes
8 answers
9
GATE CSE 2014 Set 2 | Question: 47
The product of the non-zero eigenvalues of the matrix is ____ $\begin{pmatrix} 1 & 0 & 0 & 0 & 1 \\ 0 & 1 & 1 & 1 & 0 \\ 0 & 1 & 1 & 1 & 0 \\ 0 & 1 & 1 & 1 & 0 \\ 1 & 0 & 0 & 0 & 1 \end{pmatrix}$
The product of the non-zero eigenvalues of the matrix is ____$\begin{pmatrix} 1 & 0 & 0 & 0 & 1 \\ 0 & 1 & 1 & 1 & 0 \\ 0 & 1 & 1 & 1 & 0 \\ 0 & 1 & 1 & 1 & 0 \\ 1 & 0 & ...
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113 votes
9 answers
10
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 $15$ $30$ $90$ $360$
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$$36...
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1 votes
1 answer
12
Graph
1. Suppose that G is a non-directed graph with 12 edges. Suppose that G has 6 vertices of degree 3 and the rest have degrees less than 3. The minimum number of vertices G can have? a) 2 b) 0 c)1 d)3 I am getting 3..plz verify
1. Suppose that G is a non-directed graph with 12 edges. Suppose that G has 6 vertices of degree 3 and the rest have degrees less than 3. The minimum number of vertices G...
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73 votes
8 answers
13
GATE IT 2005 | Question: 32
An unbiased coin is tossed repeatedly until the outcome of two successive tosses is the same. Assuming that the trials are independent, the expected number of tosses is $3$ $4$ $5$ $6$
An unbiased coin is tossed repeatedly until the outcome of two successive tosses is the same. Assuming that the trials are independent, the expected number of tosses is$3...
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67 votes
10 answers
14
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 __________.
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 __________.
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39 votes
9 answers
16
GATE CSE 2014 Set 2 | Question: 3
The maximum number of edges in a bipartite graph on $12$ vertices is____
The maximum number of edges in a bipartite graph on $12$ vertices is____
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19 votes
2 answers
18
On a set of n elements, how many relations are there that are both irreflexive and antisymmetric?
On a set of n elements, how many relations are there that are both irreflexive and antisymmetric? Please explain how to calculate .
On a set of n elements, how many relations are there that are both irreflexive and antisymmetric?Please explain how to calculate .
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57 votes
17 answers
19
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 ___________.
The coefficient of $x^{12}$ in $\left(x^{3}+x^{4}+x^{5}+x^{6}+\dots \right)^{3}$ is ___________.
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76 votes
5 answers
20
GATE CSE 2007 | Question: 23
Which of the following graphs has an Eulerian circuit? Any $k$-regular graph where $k$ is an even number. A complete graph on $90$ vertices. The complement of a cycle on $25$ vertices. None of the above
Which of the following graphs has an Eulerian circuit?Any $k$-regular graph where $k$ is an even number.A complete graph on $90$ vertices.The complement of a cycle on $25...
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