Mathematics · 2019
JEE Main · 12 April 2019, Shift 2 · Q65
If [x] denotes the greatest integer ≤ x, then the system of linear equations [ sin θ] x+[- cos θ] y=0; [ cot θ] x+y=0
If $\displaystyle [x]$ denotes the greatest integer $\displaystyle \leq x$, then the system of linear equations
$$\begin{aligned}
& {[\sin \theta] x+[-\cos \theta] y=0} \\
& {[\cot \theta] x+y=0}
\end{aligned}
$$
Official answer
(4)
have infinitely many solutions if $\displaystyle \theta \in\left(\frac{\pi}{2}, \frac{2 \pi}{3}\right)$ and has a unique solution if $\displaystyle \theta \in\left(\pi, \frac{7 \pi}{6}\right)$.
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JEE Main 2019 Mathematics question, with the answer from NTA’s final answer key. Where our answers come from.