We present the gravitational coupling function and potential function in a General Scalar Tensor Theory from Noether symmetry approach. Some exact cosmological solutions are presented in the spatially flat, homogeneous and isotropic background. The solutions are exponentially expanding without any graceful exit from inflation. Also the solutions asymptotically reduce to Einstein's theory with finite value of the coupling function supporting the earlier claim of Santiago et al. Further it is shown that in a particular case the effective Newtonian constant is determined by the effective potential of the scalar field.