Charges $$Q,$$ $$2Q$$ and $$4Q$$ are uniformly distributed in three dielectric solid spheres $$1,2$$ and $$3$$ of radii $$R/2,R$$ and $$2R$$ respectively, as shown in figure. If magnitude of the electric fields at point $$P$$ at a distance $$R$$ from the center of sphere $$1,2$$ and $$3$$ are $${E_1}$$, $${E_2}$$ and $${E_3}$$ respectively, then

Four charges Q₁, Q₂, Q₃ and Q₄ of same magnitude are fixed along the x axis at x = $$-$$2a, $$-$$a, +a and +2a, respectively. A positive charge q is placed on the positive y axis at a distance b > 0. Four options of the signs of these charges are given in List I. The direction of the forces on the charge q is given in List II. Match List I with List II and select the correct answer using the code given below the lists.

List I		List II
P.	Q$$_1$$, Q$$_2$$, Q$$_3$$, Q$$_4$$ all positive	1.	+x
Q.	Q$$_1$$, Q$$_2$$ positive; Q$$_3$$, Q$$_4$$ negative	2.	$$ - $$x
R.	Q$$_1$$, Q$$_4$$ positive; Q$$_2$$, Q$$_3$$ negative	3.	+y
S.	Q$$_1$$, Q$$_3$$ positive; Q$$_2$$, Q$$_4$$ negative	4.	$$ - $$y

Two non-conducting solid spheres of radii $$R$$ and $$2R,$$ having uniform volume charge densities $${\rho _1}$$ and $${\rho _2}$$ respectively, touch each other. The net electric field at a distance $$2$$ $$R$$ from the center of the smaller sphere, along the line joining the centers of the spheres, is zero. The ratio $${{{\rho _1}} \over {{\rho _2}}}$$ can be

Two large vertical and parallel metal plates having a separation of $$1$$ $$cm$$ are connected to a $$DC$$ voltage source of potential difference $$X$$. A proton is released at rest midway between the two plates. It is found to move at $${45^ \circ }$$ to the vertical JUST after release. Then $$X$$ is nearly