Mathematics · 2021
JEE Main · 24 February 2021, Shift 2 · Q72
For the system of linear equations: x-2 y=1, x-y+k z=-2, k y+4 z=6, k ∈ R, consider the following statements: (A) The system has unique solution if k…
For the system of linear equations :
$$x-$\displaystyle 2$ y=$\displaystyle 1$, x-y+k z=-$\displaystyle 2$, k y+$\displaystyle 4$ z=$\displaystyle 6$, k \in \mathbf{R},
$$consider the following statements :
(A)
The system has unique solution if $\displaystyle k \neq 2, k \neq-2$.
(B)
The system has unique solution if $\displaystyle k=-2$.
(C)
The system has unique solution if $\displaystyle k=2$.
(D)
The system has no-solution if $\displaystyle k=2$.
(E)
The system has infinite number of solutions if $\displaystyle k \neq-2$.
Which of the following statements are correct ?
Official answer
(1)
(A) and (D) only
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JEE Main 2021 Mathematics question, with the answer from NTA’s final answer key. Where our answers come from.