JEE Advanced 2022 Mathematics question

Let be nonzero real numbers that are, respectively, the , and terms of a harmonic progression. Consider the system of linear equations

x + y + z = 1

10x + 100y + 1000z = 0

qr x + pr y + pq z = 0.

List-I (I) If , then the system of linear equations has (II) If , then the system of linear equations has (III) If , then the system of linear equations has (IV) If , then the system of linear equations has List-II (P) as a solution (Q) 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)Correct
• (C)(I) → (Q); (II) → (R); (III) → (P); (IV) → (R)
• (D)(I) → (T); (II) → (S); (III) → (P); (IV) → (T)