**Solution:**

To find the condition for which the system of equations has no solution, let's solve the given system of equations:

Equation 1: px + qy = r
Equation 2: px + qp = s

To eliminate the variables, we can subtract Equation 1 from Equation 2:

(px + qp) - (px + qy) = s - r
qp - qy = s - r
q(p - y) = s - r

Now, we can see that for the system of equations to have a solution, the left side of the equation (q(p - y)) must be equal to the right side (s - r). Therefore, the condition for no solution is that the left side is not equal to the right side.

Let's denote the condition for no solution as C.

C: q(p - y) ≠ s - r

To further simplify this condition, we can divide both sides by q:

(p - y) ≠ (s - r) / q

Now, let's analyze the options:

a) ps = qr
If ps = qr, then (s - r) = 0, and the condition becomes:
(p - y) ≠ 0 / q
(p - y) ≠ 0

In this case, the condition is satisfied, and there is a solution.

b) ps ≠ qr
If ps ≠ qr, then (s - r) ≠ 0, and the condition becomes:
(p - y) ≠ (s - r) / q

In this case, the condition is satisfied, and there is no solution.

c) pq = rs
If pq = rs, then (s - r) = 0, and the condition becomes:
(p - y) ≠ 0 / q
(p - y) ≠ 0

In this case, the condition is satisfied, and there is a solution.

d) None of these
Since option b) satisfies the condition for no solution, the correct answer is option d) None of these.

Therefore, the condition for which the system of equations px + qy = r and px + qp = s has no solution is none of the given options.