A charged particle goes undeflected in a region of space containing an electric field $\overrightarrow{E}$ and a magnetic field of induction $\overrightarrow{B}$. Both the fields are non-zero and uniform. Which of the following is possible?

Lorentz force acting on a charged particle when it is moving in a combined electric and magnetic field is 

$\overrightarrow{F}=q\overrightarrow{E}+q\left(\overrightarrow{v}\times \overrightarrow{B}\right)$

So according to this if deflection of  the particle is zero then if E, V and B are parallel it will have no deflection but motion will be either accelerated or retarded.

if E is perpendicular to B i.e assume X and Y axis respectively and v is along E x B  i.e. along Z axis 

then qE  along X and q(VxB) will be along  -ve X could cancel each other.