jee-main 2024 Q71

jee-main · India · session1_30jan_shift1 3x3 Matrices Linear System with Parameter — Infinite Solutions
Consider the system of linear equation $x + y + z = 4 \mu , x + 2 y + 2 \lambda z = 10 \mu , x + 3 y + 4 \lambda ^ { 2 } z = \mu ^ { 2 } + 15$, where $\lambda , \mu \in \mathrm { R }$. Which one of the following statements is NOT correct?
(1) The system has unique solution if $\lambda \neq \frac { 1 } { 2 }$ and $\mu \neq 1$
(2) The system is inconsistent if $\lambda = \frac { 1 } { 2 }$ and $\mu \neq 1, 15$
(3) The system has infinite number of solutions if $\lambda = \frac { 1 } { 2 }$ and $\mu = 15$
(4) The system is consistent if $\lambda \neq \frac { 1 } { 2 }$
Consider the system of linear equation $x + y + z = 4 \mu , x + 2 y + 2 \lambda z = 10 \mu , x + 3 y + 4 \lambda ^ { 2 } z = \mu ^ { 2 } + 15$, where $\lambda , \mu \in \mathrm { R }$. Which one of the following statements is NOT correct?\\
(1) The system has unique solution if $\lambda \neq \frac { 1 } { 2 }$ and $\mu \neq 1$\\
(2) The system is inconsistent if $\lambda = \frac { 1 } { 2 }$ and $\mu \neq 1, 15$\\
(3) The system has infinite number of solutions if $\lambda = \frac { 1 } { 2 }$ and $\mu = 15$\\
(4) The system is consistent if $\lambda \neq \frac { 1 } { 2 }$