If a point charge is placed at the centre of the cube, then flux linked to the surface shaded in figure.
Answer & explanation
Correct answer: option 4
The correct answer is Option (2) → $\frac{Q}{6ε_0}$
$\text{Total flux by Gauss's law: } \Phi_{total} = \frac{Q}{\varepsilon_0}$
Since charge $Q$ is at the center of the cube, the flux is equally shared among the 6 faces.
Flux through one face:
$\;\;\; \Phi_{face} = \frac{Q}{6\varepsilon_0}$
In the figure, 3 faces are shaded. So flux through shaded region:
$\;\;\; \Phi_{shaded} = 3 \times \frac{Q}{6\varepsilon_0} = \frac{Q}{2\varepsilon_0}$