Two identical positive charges are fixed on the $y$-axis, at equal distances from the origin $O$. $A$ particle with a negative charge starts on the $x$-axis at a large distance from $O$, moves along the $+x$-axis, passes through $O$, and moves far away from $O$. Its acceleration $a$ is taken as positive in the positive $x$-direction. The particle's acceleration $a$ is plotted against its $x$-coordinate. Which of the following best represents the plot?

Column $II$ corresponds to the graph of magnitude of electric field versus distance from the centre of the charge distribution in Column $I$. Match the items in Column $I$ with the corresponding graphs in Column $II$.

Column-$I$	Column-$II$
$(A)$ Ring along its axis	$(P)$ Graph with a peak at a distance $r > 0$
$(B)$ Uniformly charged solid sphere	$(Q)$ Graph increasing linearly for $r < R$ and decreasing as $1/r^2$ for $r > R$
$(C)$ Uniformly charged spherical shell	$(R)$ Graph with zero field for $r < R$ and decreasing as $1/r^2$ for $r > R$
$(D)$ Combination of charge $+Q$ and $-Q$ at the perpendicular bisector	$(S)$ Graph with a maximum at the center and decreasing as $r$ increases

Two small spheres each carrying a charge $q$ are placed $r$ metre apart. If one of the spheres is taken around the other one in a circular path of radius $r$,the work done will be equal to

Two electric charges $+2 \mu C$ and $-4 \mu C$ are separated by a distance $3 \ m$ in air. At a point $P$ located on the line joining the two charges and in between them, the electric potential is zero. Then the electric field at point $P$ (in $NC^{-1}$) is (in $,000$)

$A$ Van de Graaff generator produces:

Which of the following statement$(s)$ is/are correct?
$(A)$ If the electric field due to a point charge varies as $r^{-2.5}$ instead of $r^{-2}$,then the Gauss law will still be valid.
$(B)$ The Gauss law can be used to calculate the field distribution around an electric dipole.
$(C)$ If the electric field between two point charges is zero somewhere,then the sign of the two charges is the same.
$(D)$ The work done by the external force in moving a unit positive charge from point $A$ at potential $V_A$ to point $B$ at potential $V_B$ is $(V_B - V_A)$.