Problem
Let p, q, r be nonzero real numbers that are, respectively, the 10th, 100th and 1000th terms of a harmonic progression. Consider the system of linear equations:
x + y + z = 1
10x + 100y + 1000z = 0
qrz + rpq + pqz = 0
Match the following.
| List-1 | List-2 |
| (I) If q/r = 10, then the system of linear equations has | (P) x = 0, y = 10/9, z = -1/9 as a solution |
| (II) If p/r ≠ 100, then the system of linear equations has | (Q) x = 10/9, y = -1/9, z = 0 as a solution |
| (III) If p/q ≠ 10, then the system of linear equations has | (R) infinitely many solutions |
| (IV) If p/q = 10, then the system of linear equations has | (S) no solution |
| (T) at least one solution |