1
GATE CSE 2014 Set 3
MCQ (Single Correct Answer)
+2
-0.6
Consider the set of all functions $$f:\left\{ {0,\,1,.....,2014} \right\} \to \left\{ {0,\,1,.....,2014} \right\}$$ such that $$f\left( {f\left( i \right)} \right) = i,\,\,\,$$ for all $$0 \le i \le 2014.$$ Consider the following statements:
$$P$$. For each such function it must be the case that for every $$i$$, $$f\left( i \right) = i$$
$$Q$$. For each such function it must be the case that for some $$i$$, $$f\left( i \right) = 1$$
$$R$$. Each such function must be onto.

Which one of the following id CORRECT?

A
$$P, Q$$ and $$R$$ are true
B
Only $$Q$$ and $$R$$ are true
C
Only $$P$$ and $$Q$$ are true
D
Only $$R$$ is true
2
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 ____
3
GATE CSE 2014 Set 1
Numerical
+2
-0
Let S denote the set of all functions $$f:\,{\{ 0,\,1\} ^4}\, \to \,\{ 0,\,1\} $$. Denote by N the number of functions from S to the set {0, 1}. The value of $${\log _2}$$ $${\log _2}$$ N is___________________
Your input ____
4
GATE CSE 2012
MCQ (Single Correct Answer)
+2
-0.6
How many onto (or subjective) functions are there form an n-element $$(n\, \ge \,2)$$ set to a 2-element set ?
A
$${2^n}$$
B
$${2^n}\, - 1$$
C
$${2^n}\, - 2$$
D
$$2\,({2^n}\, - 2)$$
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