Question

A charged particle entering in a magnetic field from outside in a direction perpendicular to the field (1) Will always complete exactly half of a rotation before leaving the field (2) Can never complete one rotation inside the field (3) May or may not complete one rotation in the field depending on its angle of entry into the field (4) All of these

Answer 1

4) all of these.   The completion of half circle is possible if there is a uniform magnetic field in the region, and the boundary of the magnetic field is perpendicular to velocity of the charged particle at the entry.. and at the exit.

Particle cannot turn one full circle inside the field unless the particle is already existing in the field  or, the magnetic field is reduced & varied in time so that charge q executes a small circle.

The charge will move in opposite circular paths depending on the sign of the charge.