What can be said about the electric charge if the electric flux associated with a closed loop (surface) is zero?

The electric field in a region is given by $\vec E = a\hat i + b\hat j$. Here $a$ and $b$ are constants. Find the net flux passing through a square area of side $l$ parallel to the $y-z$ plane.

If charge $q$ is placed on one of the vertex of a cube, then total electric flux passing through the cube is . . . . . . .

$C_1$ and $C_2$ are two hollow concentric cubes enclosing charges $2Q$ and $3Q$ respectively as shown in the figure. The ratio of electric flux passing through $C_1$ and $C_2$ is:

An infinitely long thin non-conducting wire is parallel to the $z$-axis and carries a uniform line charge density $\lambda$. It pierces a thin non-conducting spherical shell of radius $R$ in such a way that the arc $PQ$ subtends an angle $120^{\circ}$ at the centre $O$ of the spherical shell,as shown in the figure. The permittivity of free space is $\epsilon_0$. Which of the following statements is (are) true?
$(A)$ The electric flux through the shell is $\sqrt{3} R \lambda / \epsilon_0$
$(B)$ The $z$-component of the electric field is zero at all the points on the surface of the shell
$(C)$ The electric flux through the shell is $\sqrt{2} R \lambda / \epsilon_0$
$(D)$ The electric field is normal to the surface of the shell at all points

Consider an electric field $\vec{E} = E_0 \hat{i}$,where $E_0$ is a constant. The flux through the shaded area (as shown in the figure) due to this field is