Let p, q, r be nonzero real numbers that are, respectively, the 10^{t h}, 100^{\text{th }} and 1000^{\text{th }} terms of a harmonic progression. Consider the system of linear equations {c} x+y+z=1 10 x+100 y+1000 z=0 \text{ qr } x+\text{ 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\neq100 , then the system of linear equations has Q x=10/9,y=-1/9,z=0 as a solution III p/q\neq10 , 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]

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

( {\I}) \to( {\T}) ;( {\II}) \to( {\R}) ;( {\III}) \to( {\S}) ;( {\IV}) \to( {\T})

( {\I}) \to( {\Q}) ;( {\II}) \to( {\S}) ;( {\III}) \to( {\S}) ;( {\IV}) \to( {\R})

( {\I}) \to( {\Q}) ;( {\II}) \to( {\R}) ;( {\III}) \to( {\P}) ;( {\IV}) \to( {\R})

( {\I}) \to( {\T}) ;( {\II}) \to( {\S}) ;( {\III}) \to( {\P}) ;( {\IV}) \to( {\T})

Matrices and Determinants

Section: Mathematics

Question : 12 of 56

Marks: +1, -0

Let p,q,r be nonzero real numbers that are, respectively, the 10th,100‌th ‌ and 1000‌th ‌ terms of a harmonic progression. Consider the system of linear equations
cx+y+z=1
10x+100y+1000z=0
‌ qr ‌x+‌ pr ‌y+pqz=0.

List-I

List-II

=10 , then the system of linear equations has

x=0,y=

,z=−

as a solution

≠100 , then the system of linear equations has

,y=−

,z=0 as a solution

III

≠10 , then the system of linear equations has

infinitely many solutions

=10 , then the system of linear equations has

no solution

at least one solution

[JEE Adv 2022 P1]

(I)→(T);(II)→(R);(III)→(S);(IV)→(T)
(I)→(Q);(II)→(S);(III)→(S);(IV)→(R)
(I)→(Q);(II)→(R);(III)→(P);(IV)→(R)
(I)→(T);(II)→(S);(III)→(P);(IV)→(T)

Validate

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