A charge 'q' is placed at one corner of a cube as shown in the figure. The flux of electrostatic field  through the shaded area is: 

Concept: 

Flux due to one charge = q/ ϵ_o     -----(1)

We need 8 cubes to cover that charge placed at the corner (4 cubes upward and 4 downwards)

Flux due to charge placed at one corner of cube = q/ 8ϵo       -----(2)

Flux through the inner surface of cube = 0 (only outer surfaces will contribute to flux)

Calculations:

Given:  

Here, total flux through cube = q/ 8ϵo (From equation (2))

Three surfaces of the cube contribute to flux, flux through one surface = (q/ 8ϵo) × 1/3 = q/ 24ϵ_o

Here flux is calculated by 2 surfaces whose half surface is covered so that we can calculate it as = (ϕ₁ + ϕ₂)/ 2 

Total flux through covered area = 1/2 × ( q/ 24ϵo + q/ 24ϵo) = q/ 24ϵo

Hence, Option 4) is correct.