Best placed in the ಪೂರ್ವ
East suits study for the obvious reason: morning light, and the tradition’s preference for facing east while reading.
What the ಪೂರ್ವ governs
East is Indra’s direction and the Sun’s: the first light, and the direction the tradition orients study, prayer and the start of the day towards. Like the north it wants openness rather than mass.
Where the ಅಧ್ಯಯನ ಕಕ್ಷ belongs
A study is placed for concentration and for morning light, which puts it in the same corner family as the pooja room. Seating direction matters as much as the room here: the tradition seats the reader facing east or north.