An electrostatic field line leaves at an angle $\alpha$ from a point charge $q_{1}$ and connects with a point charge $-q_{2}$ at an angle $\beta$ ($q_{1}$ and $q_{2}$ are positive). See the figure below. If $q_{2} = \frac{3}{2} q_{1}$ and $\alpha = 30^{\circ}$,then:

The figure shows the electric field lines of three charges with charges $+1, +1$,and $-1$. The Gaussian surface in the figure is a sphere containing two of the charges. The total electric flux through the spherical Gaussian surface is

If the radius of the spherical Gaussian surface is increased, then the electric flux due to a point charge enclosed by the surface

Select the correct statement$(s)$:
$(1)$ The density of electric field lines is independent of the magnitude of the electric field vector $E$ at a given point.
$(2)$ The density of electric field lines is proportional to the magnitude of the electric field vector $E$ at a given point.
$(3)$ Electric field lines do not exist in reality. They are only a graphical representation of the electric field.
$(4)$ Electric field lines exist in reality.

$A$ 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?

$A$ point source of $3000 \ lumen$ is located at the centre of a cube of side length $2 \ m$. The flux through one side is......$lumen$.