The value of the integral given below is $$$\int_0^\pi {{x^2}\,\cos \,x\,dx} $$$

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?

Which one of the following statements is TRUE about every $$n\,\, \times \,n$$ matrix with only real eigen values?

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 ______.