JEE Main 2019 — Math solution

JEE Main2019Math

If [x] denotes the greatest integer $\leq$ x, then the system of linear equations [sin $θ$ ]x + [– cos $θ$ ]y = 0 [cot $θ$ ]x + y = 0

A
Has a unique solution if $θ \in (\frac{π}{2}, \frac{2 π}{3})$ and have infinitely many solutions if $θ \in (π, \frac{7 π}{6})$
B
Has a unique solution if $θ \in (\frac{π}{2}, \frac{2 π}{3}) \cup (π, \frac{7 π}{6})$ .
C
Have infinitely many solutions if $θ \in (\frac{π}{2}, \frac{2 π}{3})$ and has a unique solution if $θ \in (π, \frac{7 π}{6})$
D
Have infinitely many solutions if \theta \in \left( { \dfrac{\pi }{2}, \dfrac{{2\pi }}{3}} \right)\,\,\, \cup \left( {\pi , \dfrac{{7\pi }}{6}} \right)\.

Solution

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