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Let p, q, r be nonzero 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 10x + 100y + 1000z = 0 qr x + pr y + pq z = 0 List-I List-II (I) If r q = 10, then the system of linear equations has (P) x = 0, y = 9 10 , z = 9 1 − as a solution (II) If r p ≠ 100, then the system of linear equations has (Q) x = 9 10 , y = – 9 1 , z = 0 as a solution CAREER POINT Kota H.O. : Career Point Ltd., CP Tower, IPIA, Road No.1, Kota (Raj.), Ph: 080-47250011 www.careerpoint.ac.in 19 Paper-1 (III) If q p ≠ 10, then the system of linear equations has (R) infinitely many solutions (IV) If q p = 10, then the system of linear equations has (S) no solution (T) at least one solution The correct option is :

1. (I) → (T); (II) → (R); (III) → (S); (IV) → (T)
2. (I) → (Q); (II) → (S); (III) → (S); (IV) → (R)
3. (I) → (Q); (II) → (R); (III) → (P); (IV) → (R)
4. (I) → (T); (II) → (S); (III) → (P); (IV) → (T)

Correct answer: (I) → (Q); (II) → (S); (III) → (S); (IV) → (R)

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