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Asked in JEE Main 27th June 2nd Shift 2022 · Electric flux through a surface
Place the charge at the centre of the flat circular face, with the curved cap closing the surface above it.
The charge sits exactly on the boundary, so only half of its total flux q/(ε₀) heads into the hemispherical region.
That half must leave through the curved cap, giving Φ_curved=q/(2ε₀), which is the value the official key prints.
Note a subtlety worth telling students: on the flat face itself ⃗E lies in the plane of the face, so ⃗E· d⃗A=0 everywhere on it and the flux through the flat surface alone is strictly zero. The intended reading of the question is the flux through the closed hemisphere, i.e. q/(2ε₀).
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