A charged shell of radius R carries a total charge Q. Given ϕ as the flux of electric field through a closed cylindrical surface of height h, radius r and with its center same as that of the shell. Here, center of the cylinder is a point on the axis of the cylinder which is equidistant from its top and bottom surfaces. Which of the following options is/are correct?[∈0 is the permittivity of free space]

Option-1: If h=8R5  and r=3R5 , the cylindrical surface just fits into the sphere. If h<8R5 , the cylindrical surface will be well inside the sphere.  ϕ=qin∈0=0∈0=0  (1) is correct Option -2: If h>2R and r>R the sphere will be well inside the cylinder.∴ϕ=Q∈0   (2) is correct Option -3:      qin=QAB2=Q21−cosθ×2=Q1−45=Q5 ∴ϕ=qin∈0=Q5∈0  (3) is correct Option -4:   qin=Q21−cos53º×2=2Q5    ⇒ϕ=2Q/5ϵ0   (4) is wrong