Question

Distance between a convex lens and a plane mirror is 15cm ,the parallel rays incident of the convex lens after reflection from the mirror final image formed at the optical centre of the lens draw the ray diagram and find focal length of convex lens

Answer 1

The parallel rays (to principal axes)  after being incident on the convex lens tend to converge at the focus of the lens.  
There a plane mirror between the lens and its focus.  The rays get reflected with the same angles of incidence and reflection.  The plane mirror does not change the converging distance of the rays.
The path traveled by the rays after refraction from the lens = 15 cm + 15 cm = 30 cm
Focal length =30 cm