$A$ hemisphere of radius $R$ is placed in a uniform electric field $E$ so that its axis is parallel to the field. Which of the following statement$(s)$ is/are true?

When does the electric flux associated with a closed surface become positive,zero,or negative?

Which of the field patterns given below is valid for an electric field as well as for a magnetic field?

The electric field in a region is given by $\overrightarrow{E} = (\frac{3}{5} E_{0} \hat{i} + \frac{4}{5} E_{0} \hat{j}) \, N/C$. The ratio of the flux of this field through a rectangular surface of area $0.2 \, m^{2}$ (parallel to the $y-z$ plane) to that through a surface of area $0.3 \, m^{2}$ (parallel to the $x-z$ plane) is $a : b$,where $a = \dots$ [Here $\hat{i}, \hat{j}$ and $\hat{k}$ are unit vectors along the $x, y$ and $z$-axes respectively].

Consider a cylinder of length $L$ and radius $R$ placed in a uniform electric field $E$ such that its axis is parallel to the electric field. The total electric flux associated with the cylinder is .......

An electric field $\overrightarrow{E} = (2x\hat{i}) \text{ NC}^{-1}$ exists in space. $A$ cube of side $2 \text{ m}$ is placed in the space as per the figure given below. The electric flux through the cube is .................. $\text{Nm}^2 \text{C}^{-1}$.