If equation of a sphere is 2(x² + y² + z²) – 4x – 8y + 12z – 7 = 0 and one extremity of its diameter is (2, –1, 1), then the other extremity of diameter of the sphere will be

(0, 5, 7)

The centre of the sphere is (1, 2, –3) so if other extremity of diameter is (x₁, y₁, z₁), then

$\frac{x_1+2}{2}=1, \frac{y_1-1}{2}=2, \frac{z_1+1}{2}=-3$

∴ Required point is (0, 5, 7).

Hence (3) is the correct answer.