In a region of space,the electric field is given by $\vec E = 8\hat i + 4\hat j + 3\hat k$. The electric flux through a surface of area $100 \text{ units}$ in the $x-y$ plane is...

Which of the following is a correct statement?

$A$ large charged plane having surface charge density $4.9 \times 10^{-6} \text{ C m}^{-2}$ lies in the $x-y$ plane. $A$ circular plane of radius $1 \text{ cm}$ is lying completely in the region where $x, y$ and $z$ coordinates are all positive. When the plane's normal makes an angle $60^{\circ}$ with the $z$-axis,the electric flux through the circular plane is (Given: $\frac{1}{4 \pi \varepsilon_0} = 9 \times 10^9 \text{ N m}^2 \text{ C}^{-2}$)

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., $E = k \cdot \frac{q}{r^3} \hat{r}$, where $k$ is a constant.
Consider the following two statements:
$(I)$ Flux through a spherical surface enclosing the charge is $\phi = q_{\text{enclosed}} / \varepsilon_0$.
$(II)$ $A$ charge placed inside a uniformly charged shell will experience a force.
Which of the above statements are valid?

Four closed surfaces $S_1, S_2, S_3$ and $S_4$ together with charges $+q, -q$ and $-2q$ are shown. Through which one of the surfaces is the net flux zero?

$A$ sphere of radius $R$ and charge $Q$ is placed inside a concentric imaginary sphere of radius $2R$. The flux associated with the imaginary sphere is