A body is at rest at $$x=0.$$ At $$t=0,$$ it starts moving in the positive $$x$$-direction with a constant acceleration. At the same instant another body passes through $$x=0$$ moving in the positive $$x$$ direction with a constant speed. The position of the first body is given by $${x_1}\left( t \right)$$ after time $$'t';$$ and that of the second body by $${x_2}\left( t \right)$$ after the same time interval. Which of the following graphs correctly describes $$\left( {{x_1} - {x_2}} \right)$$ as a function of time $$'t'$$ ?

Consider a block of conducting material of resistivity $$'\rho '$$ shown in the figure. Current $$'I'$$ enters at $$'A'$$ and leaves from $$'D'$$. We apply superposition principle to find voltage $$'\Delta V'$$ developed between $$'B'$$ and $$'C'$$. The calculation is done in the following steps:
(i) Take current $$'I'$$ entering from $$'A'$$ and assume it to spread over a hemispherical surface in the block.
(ii) Calculate field $$E(r)$$ at distance $$'r'$$ from A by using Ohm's law $$E = \rho j,$$ where $$j$$ is the current per unit area at $$'r'$$.
(iii) From the $$'r'$$ dependence of $$E(r)$$, obtain the potential $$V(r)$$ at $$r$$.
(iv) Repeat (i), (ii) and (iii) for current $$'I'$$ leaving $$'D'$$ and superpose results for $$'A'$$ and $$'D'.$$

For current entering at $$A,$$ the electric field at a distance $$'r'$$ from $$A$$ is

This question contains Statement - $$1$$ and Statement - $$2$$. of the four choices given after the statements, choose the one that best describes the two statements.

Statement - $$1$$:

For a mass $$M$$ kept at the center of a cube of side $$'a'$$, the flux of gravitational field passing through its sides $$4\,\pi \,GM.$$

Statement - 2:

If the direction of a field due to a point source is radial and its dependence on the distance $$'r'$$ from the source is given as $${1 \over {{r^2}}},$$ its flux through a closed surface depends only on the strength of the source enclosed by the surface and not on the size or shape of the surface.

Shown in the figure below is a meter-bridge set up with null deflection in the galvanometer.

The value of the unknown resister $$R$$ is