Six identical particles each of mass m are arranged at the corners of a regular hexagon of side length a. If the mass of one of the particle is doubled, the shift in the centre of mass is

Center of mass of six equal masses is at the center of hexagon.

We can assume a single particle of mass 6m at center and another particle of mass m placed at a distance of 'a' from the center of hexagon.

$COM=\frac{6 m\times 0+m\times a}{6 m+m}=\frac{a}{7}$