Electric flux and Gauss's law

A disk of radius $a/4$ having a uniformly distributed charge $6C$ is placed in the $x$-$y$ plane with its centre at $(-a/2,0,0)$. A rod of length $a$ carrying a uniformly distributed charge $8C$ is placed on the $x$-axis from $x=a/4$ to $x=5a/4$. Two point charges $-7C$ and $3C$ are placed at $(a/4,-a/4,0)$ and $(-3a/4,3a/4,0)$, respectively. Consider a cubical surface formed by six surfaces $x=\pm a/2$, $y=\pm a/2$, $z=\pm a/2$. The electric flux through this cubical surface is

A solid sphere of radius $R$ has a charge $Q$ distributed in its volume with a charge density $\rho=\kappa r^a$, where $\kappa$ and $a$ are constants and $r$ is the distance from its centre. If the electric field at $r=\dfrac R2$ is $\dfrac18$ times that at $r=R$, find the value of $a$.

The electric field at $r=R$ is

For $a=0$, the value of $d$ (maximum value of $\rho$ as shown in the figure) is

The electric field within the nucleus is generally observed to be linearly dependent on $r$. This implies

A long, hollow conducting cylinder is kept coaxially inside another long, hollow conducting cylinder of larger radius. Both the cylinders are initially electrically neutral.

A spherical portion has been removed from a solid sphere having a charge distributed uniformly in its volume as shown in the figure. The electric field inside the emptied space is