1
GATE CSE 2008
+2
-0.6
$$G$$ is a graph on $$n$$ vertices and $$2n-2$$ edges. The edges of $$G$$ can be partitioned into two edge-disjoint spanning trees. Which of the following in NOT true for $$G$$?
A
For every subset of $$k$$ vertices, the induced subgraph has at most $$2k-2$$ edges
B
The minimum cut in $$G$$ has at least two edges
C
There are two edge-disjoint paths between every pair of vertices
D
There are two vertex-disjoint paths between every pair of vertices
2
GATE CSE 2008
+2
-0.6
A binary tree with $$n>1$$ nodes has $${n_1}$$, $${n_2}$$ and $${n_3}$$ nodes of degree one, two and three respectively. The degree of a node is defined as the number of its neighbours.

$${n_3}$$ can be expressed as:

A
$${n_1}$$ $$+$$ $${n_1}$$ $$-$$ $$1$$
B
$${n_1}$$ $$-$$ $$2$$
C
$$\left[ {{{{n_1} + {n_2}} \over 2}} \right]$$
D
$${n_2}$$ $$-$$ $$1$$
3
GATE CSE 2008
+2
-0.6
A binary tree with $$n>1$$ nodes has $${n_1}$$, $${n_2}$$ and $${n_3}$$ nodes of degree one, two and three respectively. The degree of a node is defined as the number of its neighbours.

Starting with the above tree, while there remains a node $$v$$ of degree two in the tree, add an edge between the two neighbours of $$v$$ and then remove $$v$$ from the tree. How many edges will remain at the end of the process?

A
$${2^ * }{n_1} - 3$$
B
$${n_2} + {2^ * }{n_1} - 2$$
C
$${n_3} - {n_2}$$
D
$${n_2} + {n_1} - 2$$
4
GATE CSE 2007
+2
-0.6
Let Graph$$(x)$$ be a predicate which denotes that $$x$$ is a graph. Let Connected$$(x)$$ be a predicate which denotes that $$x$$ is connected. Which of the following first order logic sentences DOES NOT represent the statement: $$Not\,\,\,every\,\,\,graph\,\,\,is\,\,\,connected?$$
A
$$\neg \forall x\left( {Graph\left( x \right) \Rightarrow Connected\left( x \right)} \right)$$
B
$$\exists x\left( {Graph\left( x \right) \wedge \neg Connected\left( x \right)} \right)$$
C
$$\neg \forall x\left( {\neg Graph\left( x \right) \vee Connected\left( x \right)} \right)$$
D
$$\forall x\left( {Graph\left( x \right) \Rightarrow \neg Connected\left( x \right)} \right)$$
GATE CSE Subjects
Discrete Mathematics
Programming Languages
Theory of Computation
Operating Systems
Digital Logic
Computer Organization
Database Management System
Data Structures
Computer Networks
Algorithms
Compiler Design
Software Engineering
Web Technologies
General Aptitude
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