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 c x + y + z = 1 10 x + 100 y + 1000 z = 0 { qr } x + { pr } 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=10/9, y=-1/9, z=0 as a solution III 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 [JEE Adv 2022 P1]

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Examsnet · Accepted Answer

Correct Answer is : (I)→(Q);(II)→(S);(III)→(S);(IV)→(R)(I) arrow (Q); (II) arrow (S); (III) arrow (S); (IV) arrow (R)(I)→(Q);(II)→(S);(III)→(S);(IV)→(R)

List-I	List-II
I	If $\frac{q}{r}=10$ , then the system of linear equations has	P	$x=0, y=\frac{10}{9}, z=-\frac{1}{9}$ as a solution
II	If $\frac{p}{r}\neq 100$ , then the system of linear equations has	Q	$x=\frac{10}{9}, y=-\frac{1}{9}, z=0$ as a solution
III	$\frac{p}{q}\neq 10$ , then the system of linear equations has	R	infinitely many solutions
IV	If $\frac{p}{q}=10$ , then the system of linear equations has	S	no solution
		T	at least one solution

JEE Advanced 2022 Paper 1