What is the position of tetrahedral voids in FCC lattice?

The correct option is C

√3a/4 distance from corners

As we saw in the derivation of distance between 2 tetrahedral voids, each tetrahedral void is located at a distance of $\sqrt{\frac{3a}{4}}$ from the corners of the unit cell or cube. By knowledge of symmetry, we know that each tetrahedral void is symmetrically placed in the unit cell.

So, we can say that the center of each tetrahedron is at a distance of $\sqrt{\frac{3a}{4}}$ from the corners of the unit cell.

In the figure above, we can clearly see the yellow dot which is the centre of the tetrahedron.