Gauss's law should be invalid if

An infinitely long wire has a uniform linear charge density $\lambda = 2 \ nC/m$. The net flux through a Gaussian cube of side length $a = \sqrt{3} \ cm$, if the wire passes through any two corners of the cube that are maximally displaced from each other, would be $x \ Nm^2 C^{-1}$, where $x$ is: [Neglect any edge effects and use $\frac{1}{4 \pi \varepsilon_0} = 9 \times 10^9 \ SI$ units] (in $\pi$)

Consider a uniform electric field $\vec{E} = 3 \times 10^3 \hat{k} \text{ N C}^{-1}$. The electric flux of this field through a square of $20 \text{ cm}$ on a side whose plane is parallel to the $yz$-plane is $....... \text{ N m}^2 \text{ C}^{-1}$.

$A$ charge is uniformly distributed on the surface of a spherical rubber balloon. As it is blown up,the total electric flux coming out of the surface

Two co-axial conducting cylinders of same length $\ell$ with radii $\sqrt{2} R$ and $2 R$ are kept,as shown in Fig. $1$. The charge on the inner cylinder is $Q$ and the outer cylinder is grounded. The annular region between the cylinders is filled with a material of dielectric constant $\kappa=5$. Consider an imaginary plane of the same length $\ell$ at a distance $R$ from the common axis of the cylinders. This plane is parallel to the axis of the cylinders. The cross-sectional view of this arrangement is shown in Fig. $2$. Ignoring edge effects,the flux of the electric field through the plane is ($\epsilon_0$ is the permittivity of free space):

$A$ wire has a charge of $Q \text{ coulomb}$ per $cm$. What is the total electric flux passing through the cylinder of length $1 \ m$?