Jee Advanced
Matrices And Determinants
JEE Advanced 2022 Paper 1 Online
Let \(p, q, r\) be nonzero real numbers that are, respectively, the \(10^{\text {th }}, 100^{\text {th }}\) and \(1000^{\text {th }}\) terms of a harmonic progression. Consider the system of linear equations
$$$ \begin{gathered} x+y+z=1 \\ 10 x+100 y+1000 z=0 \\ q r x+p r y+p q z=0 \end{gathered} $$$
.tg {border-collapse:collapse;border-spacing:0;}
.tg td{border-color:black;border-style:solid;border-width:1px;font-family:Arial, sans-serif;font-size:14px;
overflow:hidden;padding:10px 5px;word-break:normal;}
.tg th{border-color:black;border-style:solid;border-width:1px;font-family:Arial, sans-serif;font-size:14px;
font-weight:normal;overflow:hidden;padding:10px 5px;word-break:normal;}
.tg .tg-7btt{border-color:inherit;font-weight:bold;text-align:center;vertical-align:top}
.tg .tg-0pky{border-color:inherit;text-align:left;vertical-align:top}
| List-I | List-II |
|---|---|
| (I) If \(\frac{q}{r}=10\), then the system of linear equations has | (P) \(x=0, \quad y=\frac{10}{9}, z=-\frac{1}{9}\) 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) If \(\frac{p}{q} \neq 10\), 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 |
The correct option is: