1
GATE CSE 2014 Set 3
Numerical
+2
-0
There are two elements $$x, y$$ in a group $$\left( {G,\, * } \right)$$ such that every elements in the group can be written as a product of some number of $$x's$$ and $$y's$$ in some order. It is known that
$$x * x = y * y = x * y * x * y = y * x * y * x = e$$
where $$e$$ is the identity element. The maximum number of elements in such a group is ______.
Your input ____
2
GATE CSE 2014 Set 3
Numerical
+1
-0
let $$G$$ be a group with $$15$$ elements. Let $$L$$ be a subgroup of $$G$$. It is known that $$L \ne G$$ and that the size of $$L$$ is at least $$4$$. The size of $$L$$ is ______.
Your input ____
3
GATE CSE 2014 Set 3
MCQ (Single Correct Answer)
+2
-0.6
Let $$\delta $$ denote the minimum degree of a vertex in a graph. For all planar graphs on $$n$$ vertices with $$\delta \ge 3$$, which one of the following is TRUE?
A
In any planar embedding, the number of faces is at least $${n \over 2} + 2$$
B
In any planar embedding, the number of faces is less than $${n \over 2} + 2$$
C
There is a planar embedding in which the number of facess is less than $${n \over 2} + 2$$
D
There is a planar embedding in which the number of faces is at most $${n \over {\delta + 1}}$$
4
GATE CSE 2014 Set 3
MCQ (Single Correct Answer)
+2
-0.6
If $$G$$ is a forest with $$n$$ vertices and $$k$$ connected components, how many edges does $$G$$ have?
A
$$\left\lfloor {n/k} \right\rfloor $$
B
$$\left\lceil {n/k} \right\rceil \,$$
C
$$n - k$$
D
$$n - k + 1$$
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