In the figure, the inner (shaded) region $A$ represents a sphere of radius $r_A=1$, within which the electrostatic charge density varies with the radial distance $r$ from the center as ${\rho }_A=kr$, where $k$ is positive. In the spherical shell $B$ of outer radius $r_B$, the electrostatic charge density varies as ${\rho }_B=\frac{2k}{r}$. Assume that dimensions are taken care of. All physical quantities are in their SI units.

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Which of the following statement(s) is/(are) correct?

Consider a region in free space bounded by the surfaces of an imaginary cube having sides of length $a$ as shown in the figure. A charge $+Q$ is placed at the centre $O$ of the cube. $P$ is such a point outside the cube that the line $OP$perpendicularly intersects the surface $ABCD$ at $R$ and also $OR=RP=a/2$. A charge $+Q$ is placed at point $P$ also. What is the total electric flux through the five faces of the cube other than $ABCD?$

Given below are two statements
Statement $\mathrm{I}$ : An electric dipole is placed at the centre of a hollow sphere. The flux of electric field through the sphere is zero, but the electric field is not zero anywhere in the sphere.

Statement $\mathrm{II}$ : If $R$ is the radius of a solid metallic sphere and $Q$ be the total charge on it. The electric field at any point on the spherical surface of radius $r\left(<R\right)$ is zero but the electric flux passing through this closed spherical surface of radius $r$ is not

In the light of the above statements, choose the correct answer from the options given below:

What is the electric flux for Gaussian surface A that encloses the charged particles in free space? [Given: $\left.q_1=-14 \mathrm{nC},q_2=78.85 \mathrm{nC},q_3=-56 \mathrm{nC}\right]$

Arrangement of charges are shown in the figure. Flux linked with the closed surface $P$ and $Q$ respectively are ________ and ________ .

Let the electrostatic field, $E$ at distance, $r$ from a point charge, $q$ not be an inverse square but instead an inverse cubic, e.g. $E=k\frac{q}{r^3}\hat{r}$, here $k$ is a constant. Consider the following two statements: (I) Flux through a spherical surface enclosing the charge is, $\varphi =\frac{q_{\mathrm{enclosed}}}{{\epsilon }_0}$. (II) A charge placed inside a uniformly charged shell will experience a force. Which of the above statements are valid?