Let $p , q , r$ be nonzero real numbers that are, respectively, the $10 ^ { \text {th } } , 100 ^ { \text {th } }$ and $1000 ^ { \text {th } }$ terms of a harmonic progression. Consider the system of linear equations

$$\begin{gathered}
x + y + z = 1 \\
10 x + 100 y + 1000 z = 0 \\
q r x + p r y + p q z = 0
\end{gathered}$$

\textbf{List-I}\\
(I) If $\frac { q } { r } = 10$, then the system of linear equations has\\
(II) If $\frac { p } { r } \neq 100$, then the system of linear equations has\\
(III) If $\frac { p } { q } \neq 10$, then the system of linear equations has\\
(IV) If $\frac { p } { q } = 10$, then the system of linear equations has

\textbf{List-II}\\
(P) $x = 0 , \quad y = \frac { 10 } { 9 } , z = - \frac { 1 } { 9 }$ as a solution\\
(Q) $x = \frac { 10 } { 9 } , \quad y = - \frac { 1 } { 9 } , z = 0$ as a solution\\
(R) infinitely many solutions\\
(S) no solution\\
(T) at least one solution

The correct option is:\\
(A) (I) → (T); (II) → (R); (III) → (S); (IV) → (T)\\
(B) (I) → (Q); (II) → (S); (III) → (S); (IV) → (R)\\
(C) (I) → (Q); (II) → (R); (III) → (P); (IV) → (R)\\
(D) (I) → (T); (II) → (S); (III) → (P); (IV) → (T)