If the centroid of a triangle with vertices $(4, p, -3)$,$(-1, -1, 2)$,and $(3, 5, -8)$ is given by the mid-point of $(1, 4, -2)$ and $(q, 2, -4)$,then $p^2 + q^2 =$

$A(2,3,-4), B(-3,3,-2), C(-1,4,2), D(3,5,1)$ are the vertices of a tetrahedron. If $G_1, G_2$ and $G_3$ are the centroids of the three faces having the vertex $D$ in common,then the centroid of the $\Delta G_1 G_2 G_3$ is

If $D(2, 1, 0)$,$E(2, 0, 0)$,and $F(0, 1, 0)$ are mid-points of the sides $BC$,$CA$,and $AB$ of $\triangle ABC$,respectively,then the centroid of $\triangle ABC$ is

If the centroid of $\Delta ABC$ is $(0,0,0)$,where $A(1,1,1), B(2,1,2), C(x, y, z)$,then $(x, y, z) = \ldots \ldots$

Match the following columns:

Column $I$	Column $II$
$(A)$ The centroid of the triangle formed by $(2, 3, -1)$,$(5, 6, 3)$,$(2, -3, 1)$ is	$(p)$ $(2, 2, 2)$
$(B)$ The circumcentre of the triangle formed by $(1, 2, 3)$,$(2, 3, 1)$,$(3, 1, 2)$ is	$(q)$ $(3, 1, 4)$
$(C)$ The orthocentre of the triangle formed by $(2, 1, 5)$,$(3, 2, 3)$,$(4, 0, 4)$ is	$(r)$ $(1, 1, 0)$
$(D)$ The incentre of the triangle formed by $(0, 0, 0)$,$(3, 0, 0)$,$(0, 4, 0)$ is	$(s)$ $(3, 2, 1)$

In $\triangle ABC$,if the midpoints of the sides $AB, BC$ and $CA$ are respectively $(l, 0, 0), (0, m, 0)$ and $(0, 0, n)$,then $\frac{AB^2+BC^2+CA^2}{l^2+m^2+n^2}=$