A charged particle q is moving in the presence of a magnetic field B which is inclined to an angle 30° with the direction of the motion of the particle. Draw the trajectory followed by the particle in the presence of the field and explain how the particle describes this path.

As we know the force on a charged particle in a magnetic field is given by

Where q = charge of the particle ,

          v = velocity of particle and B is the magnetic field in that region.

The force exerted on a charged particle in a magnetic field only exist if the velocity of the particle is perpendicular to the direction of the magnetic field as the equation  suggest. 
If velocity has a component along B, this component remains unchanged as the motion along the magnetic field will not be affected by the magnetic field. The motion in a plane perpendicular to B is as before a circular one, thereby producing a helical motion

Thus the described path will be helical as shown in the figure and the velocity's parallel component will make the particle move along the direction of the field.