$A$ metallic sphere of radius $R$ carrying a charge $q$ is kept at a certain distance from another metallic sphere of radius $R/4$ carrying a charge $Q$. What is the electric flux at any point inside the metallic sphere of radius $R$ due to the sphere of radius $R/4$?

Five point charges $\frac{1}{\pi}, \frac{2}{\pi}, \frac{3}{\pi}, \frac{4}{\pi}$ and $\frac{-5}{\pi} \ nC$ are located inside a pyramid. The total electric flux through the surface of the pyramid is

$A$ point charge '$Q$' is placed at a point inside a hollow conducting sphere. Which of the following electric field patterns is correct?

$A$ charged shell of radius $R$ carries a total charge $Q$. Let $\Phi$ be the flux of the electric field through a closed cylindrical surface of height $h$,radius $r$,with its center coinciding with that of the shell. The center of the cylinder is a point on the axis of the cylinder equidistant from its top and bottom surfaces. Which of the following option$(s)$ is/are correct? [$\epsilon_0$ is the permittivity of free space]
$(1)$ If $h > 2R$ and $r > R$,then $\Phi = \frac{Q}{\epsilon_0}$
$(2)$ If $h < \frac{8R}{5}$ and $r = \frac{3R}{5}$,then $\Phi = 0$
$(3)$ If $h > 2R$ and $r = \frac{4R}{5}$,then $\Phi = \frac{2Q}{5\epsilon_0}$
$(4)$ If $h > 2R$ and $r = \frac{3R}{5}$,then $\Phi = \frac{Q}{5\epsilon_0}$

Three positive charges of equal value $q$ are placed at the vertices of an equilateral triangle. The resulting lines of force should be sketched as in:

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