Q. A beam of electron moving along positive y- direction enters in a region of magnetic fields. If the beam goes undefected through this region then where are the field ( B) and ( E ) directed?

See for electron to pass undfected the resultant of magnetic and electric forces should be 0. Suppose electric field is acting in z direction so deflscts electron in + z direction . To counter this magnetic field should act in negative x direction by Flemings left hand rule . Take current in opposite direction of motion of electron . Hope it helps