Correct Answer - A
`D` is the `CM` of the rod
In triangle `ADE`:
`tantheta=(L//4)/(3L//4)`
`implies tantheta=1/3impliestheta=tan^(-1)(1//3)`
here `D` is the centre of mass. In equilibrim, `D` will be vertically below `A`. so i equilibrium `AB` will make angle `theta` as calculated above with the vertical.