Lorentz Force Questions

An electron (mass $9\times 10^{-31}\text{kg}$ and charge $1.6\times 10^{-19}\text{C}$) moving with speed $c/100$ ($c$ = speed of light) is injected into a magnetic field $\vec{B}$ of magnitude $9\times 10^{-4}\text{T}$ perpendicular to its direction of motion. We wish to apply a uniform electric field $\vec{E}$ together with the magnetic field so that the electron does not deflect from its path. Then (speed of light $c=3\times 10^8{\text{ms}}^{-1}$):

A beam of electrons passes un-deflected through mutually perpendicular electric and magnetic fields. If the electric field is switched off, and the same magnetic field is maintained, the electrons move:

A particle of mass $m$, charge $Q$ and kinetic energy $T$ enters a transverse uniform magnetic field of induction $\vec{B}$. After $3$ seconds the kinetic energy of the particle will be:

The magnetic force acting on a charged particle of charge $-2\mu \text{C}$ in a magnetic field of $2\text{T}$ acting in $y$ direction, when the particle velocity is $(2\hat{i}+3\hat{j})\times 10^6{\text{ms}}^{-1}$, is:

A proton released from rest starts with acceleration $a_0$ towards west. When projected towards north with speed $v_0$, it moves with initial acceleration $3a_0$ towards west. The electric and magnetic fields in the room are: