Please anyone can explain me the cycloid path of a charged particle in mutually perpendicular electric and magnetic field..
I have a lot of confusion over it...

I'm confused about what you are asking here...

In an electric field, a charged particle would make a parabolic path, along the field lines.

In a magnetic field, a charged particle would make a circular path perpendicular to the field lines.

In a cross field (electric and magnetic field mutually at right angles), if the force due to either fields cancel out the other, the particle will pass through the field undeviated. If one force exceeds the other, then the particle will move according to the overriding force (ie. Circular if it's magnetic force and parabolic if it's electric force.)