$A$ charge $q$ is placed at the centre of the open end of a cylindrical vessel. The flux of the electric field through the surface of the vessel is:

$A$ 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?

An infinite,uniformly charged sheet with surface charge density $\sigma$ cuts through a spherical Gaussian surface of radius $R$ at a distance $x$ from its center,as shown in the figure. The electric flux $\Phi$ through the Gaussian surface is

The figure shows the electric field lines for a system of two charges. Choose the correct option regarding the electric field intensity at points $A$,$B$,and $C$.

Consider a cube of side length '$a$' centered at the origin. It is enclosed by three fixed point charges: $(-q)$ at $(0, -a/4, 0)$,$(+3q)$ at $(0, 0, 0)$,and $(-q)$ at $(0, a/4, 0)$. Choose the correct option.

Two point charges $8 \mu \text{C}$ and $-2 \mu \text{C}$ are located at $x = 2 \text{ cm}$ and $x = 4 \text{ cm}$, respectively on the $x$-axis. The ratio of electric flux due to these charges through two spheres of radii $3 \text{ cm}$ and $5 \text{ cm}$ with their centers at the origin is . . . . . . .