What is called a Gaussian surface?

$A$ point charge $q$ is placed at the corner of a cube of side $a$ as shown in the figure. What is the electric flux through the face $ABCD$?

What kind of Gaussian surface is used to calculate the electric field due to the charge distribution?

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...

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):

The flat base of a hemisphere of radius $a$ with no charge inside it lies in a horizontal plane. $A$ uniform electric field $\vec{E}$ is applied at an angle $\frac{\pi}{4}$ with the vertical direction. The electric flux through the curved surface of the hemisphere is