jee-main 2025 Q10

jee-main · India · session1_23jan_shift2 Matrices Linear System and Inverse Existence
The system of equations $$x + y + z = 6$$ $$x + 2 y + 5 z = 9$$ $$x + 5 y + \lambda z = \mu$$ has no solution if
(1) $\lambda = 15 , \mu \neq 17$
(2) $\lambda \neq 17 , \mu \neq 18$
(3) $\lambda = 17 , \mu \neq 18$
(4) $\lambda = 17 , \mu = 18$
The system of equations
$$x + y + z = 6$$
$$x + 2 y + 5 z = 9$$
$$x + 5 y + \lambda z = \mu$$
has no solution if\\
(1) $\lambda = 15 , \mu \neq 17$\\
(2) $\lambda \neq 17 , \mu \neq 18$\\
(3) $\lambda = 17 , \mu \neq 18$\\
(4) $\lambda = 17 , \mu = 18$