$A$ particle of charge $+q$ and mass $m$ moving under the influence of a uniform electric field $E\hat i$ and a uniform magnetic field $B\hat k$ follows a trajectory from $P$ to $Q$ as shown in the figure. The velocities at $P$ and $Q$ are $v\hat i$ and $-2v\hat j$ respectively. Which of the following statement$(s)$ is/are correct?

$A$ charge $Q$ is uniformly distributed over the surface of a nonconducting disc of radius $R$. The disc rotates about an axis perpendicular to its plane and passing through its centre with an angular velocity $\omega$. As a result of this rotation,a magnetic field of induction $B$ is obtained at the centre of the disc. If we keep both the amount of charge placed on the disc and its angular velocity constant and vary the radius of the disc,then the variation of the magnetic induction at the centre of the disc will be represented by which of the following figures?

Six point charges,each of magnitude $q$,are arranged in different manners as shown in the image. In each case,a point $M$ and a line $PQ$ passing through $M$ are shown. Let $E$ be the electric field and $V$ be the electric potential at $M$ (potential at infinity is zero) due to the given charge distribution when it is at rest. Now,the whole system is set into rotation with a constant angular velocity about the line $PQ$. Let $B$ be the magnetic field at $M$ and $\mu$ be the magnetic moment of the system in this condition. Assume each rotating charge to be equivalent to a steady current. Match the conditions in Column $I$ with the configurations in Column $II$.

Column $I$	Column $II$
$(A)$ $E=0$	$(p)$ Charges at corners of a regular hexagon. $M$ is the centre. $PQ$ is perpendicular to the plane.
$(B)$ $V \neq 0$	$(q)$ Charges on a line perpendicular to $PQ$ at equal intervals. $M$ is the mid-point.
$(C)$ $B=0$	$(r)$ Charges on two coplanar concentric rings. $M$ is the common centre. $PQ$ is perpendicular to the plane.
$(D)$ $\mu \neq 0$	$(s)$ Charges at corners and mid-points of a rectangle. $M$ is the centre. $PQ$ is parallel to the longer sides.
	$(t)$ Charges on two coplanar,identical rings. $M$ is the mid-point between centres. $PQ$ is perpendicular to the line joining centres.

$A$ proton moving with a constant velocity passes through a region of space without any change in its velocity. If $\vec{E}$ and $\vec{B}$ represent the electric and magnetic fields respectively,then the region of space may have :
$(A)$ $E=0, B=0$
$(B)$ $E=0, B \neq 0$
$(C)$ $E \neq 0, B=0$
$(D)$ $E \neq 0, B \neq 0$
Choose the most appropriate answer from the options given below :

Two straight long conductors $AOB$ and $COD$ are perpendicular to each other and carry currents $i_1$ and $i_2$. The magnitude of the magnetic induction at a point $P$ at a distance $a$ from the point $O$ in a direction perpendicular to the plane $ACBD$ is

$A$ particle of specific charge $(q/m)$ is projected from the origin of coordinates with initial velocity $(u\hat{i} - v\hat{j})$. Uniform electric and magnetic fields exist in the region along the $+y$ direction,of magnitude $E$ and $B$ respectively. The particle will definitely return to the origin once if: