Plz help !!!a charged particle is fired at an angle(say x) to a uniform magnetic field directed along x-axis.During its motion along a helical path,the particle will

1.never move parallel to the x axis.

2.move parallel to the x-axis once during every rotation for all values of 'x'.

3.move parallel to the x-axis at least once during every rotation if 'x'=45 degrees.

4.never move perpendicular to x- direction.

one or more options may be correct.

Answer :
(a,d)
Solution :
When the particle moves in a helical path, the plane of the helical path will be slightly inclined with x-axis. Hence, options (a) and (d) are correct.

The component of velocityvalong the direction ofBisvcosθ.
Since the trajectory will be helical, the trajectory will never be perpendicular to the direction of magnetic fieldB, it's trajectory will be inclined at a small angle to the direction of the magnetic field.
It will also never move parallel tox−axis.