Classical mechanics — canonical transformations and generating functions

A mechanical system is described using generalized position $q$ and generalized momentum $p$. Let $Q$ and $P$ denote new generalized position and generalized momentum variables respectively, generated by the generating function $F(q,P)=q^2e^{P}$, and $Q,P$ are canonical coordinates. Let $G(p,Q)$ be a function such that $G(2,e)=0$, and it generates the same canonical coordinates $Q,P$. Then which of the following statements are true?