$A$ charged spherical shell of radius $R$ carries a total charge $Q$. Let $\Phi$ be the electric flux through a closed cylindrical surface of height $h$ and 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 statement$(s)$ 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 $\Phi = \frac{Q}{5\epsilon_0}$

• A
  $1, 2, 3, 4$
• B
  $1, 2, 4$
• C
  $1, 2$
• D
  $1, 3, 4$