Let p , q , r be non-zero real numbers that are, respectively, the 10 th , 100 th and 1000 th terms of a harmonic progression. Consider the system of linear equations x + y + z = 1 10 x + 100 y + 1000 z = 0 q r x + p r y + p q z = 0 List- I List- II 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 =

Step-by-step solution

Given, x + y + z = 1             ⋯ 1 10 x + 100 y + 1000 z = 0             ⋯ 2 q r x + p r y + p q z = 0               ⋯ 3 Now equation 3 can be re-written as x p + y q + z r = 0         ∵   p , q , r ≠ 0 Now given p ,   q   &   r  are 10 t h , 100 t h  & 1000 t h  term of an h.p , So, let p = 1 a + 9