1
GATE CSE 2013
MCQ (Single Correct Answer)
+1
-0.3
Function $$f$$ is known at the following points: GATE CSE 2013 Discrete Mathematics - Calculus Question 28 English

The value of $$\int\limits_0^3 {f\left( x \right)dx} $$ computed using the trapezoidal rule is

A
$$8.983$$
B
$$9.003$$
C
$$9.017$$
D
$$9.045$$
2
GATE CSE 2013
MCQ (Single Correct Answer)
+1
-0.3
Consider an undirected random$$^ \circ $$ graph of eight vertices. The probability that there is an edge between a pair of vertices is 1/2. What is the expected number of unordered cycles of length three?
A
$$1/8$$
B
$$1$$
C
$$7$$
D
$$8$$
3
GATE CSE 2013
MCQ (Single Correct Answer)
+1
-0.3
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.
A
P only
B
Q only
C
Both P and Q
D
Neither P and Q
4
GATE CSE 2013
MCQ (Single Correct Answer)
+2
-0.6
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 $$e$$ and $$e'$$

$$\,\,\,\,$$ Which of the following statements is/are TRUE?

(P) The line graph of a cycle is a cycle.
(Q) The line graph of a clique is a clique.
(R) The line graph of a planar graph is planar.
(S) The line graph of a tree is a tree.

A
P only
B
P and R only
C
R only
D
P, Q and S only
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