If the mean of p, q, r is M and pq + qr + rp = 0, then the mean of $p^2, q^2,r^2$ is

$3M^2$

(p+q+r)/3 =M

p+q+r = 3M

and, pq + qr + rp = 0

We know (a+b+c)² = a²+b²+c² + 2(ab+bc+ca)

(p+q+r)² = p²+q²+r² + 2(pq + qr + rp) = p²+q²+r² (Since pq + qr + rp = 0)

Thus p²+q²+r² = (p+q+r)² = 9M²

Mean of p²+q²+r² = 9M²/3 = 3M²

The correct answer is option (2) : $3M^2$