JEE Mains · Maths · STD 12 - 3 and 4 . metrices and determinant
If \([x]\) denotes the greatest integer \( \leq x\), then the system of linear equations
\([sin \,\theta ] x + [-cos\,\theta ] y = 0\) \([cot \,\theta ] x + y = 0\)
- A have infinitely many solutions if \(\theta \in \left( {\frac{\pi }{2},\frac{{2\pi }}{3}} \right)\) and and has a unique solution if \(\theta \in \left( {\pi ,\frac{{7\pi }}{6}} \right)\)
- B have infinitely many solutions if \(\theta \in \left( {\frac{\pi }{2},\frac{{2\pi }}{3}} \right) \cup \left( {\pi ,\frac{{7\pi }}{6}} \right)\)
- C has a unique solution if \(\theta \in \left( {\frac{\pi }{2},\frac{{2\pi }}{3}} \right)\) and and have infinitely many solutions if \(\theta \in \left( {\pi ,\frac{{7\pi }}{6}} \right)\)
- D has a unique solution if \(\theta \in \left( {\frac{\pi }{2},\frac{{2\pi }}{3}} \right) \cup \left( {\pi ,\frac{{7\pi }}{6}} \right)\)
Answer & Solution
Correct Answer
(A) have infinitely many solutions if \(\theta \in \left( {\frac{\pi }{2},\frac{{2\pi }}{3}} \right)\) and and has a unique solution if \(\theta \in \left( {\pi ,\frac{{7\pi }}{6}} \right)\)
Step-by-step Solution
Detailed explanation
\(\left[ {\sin \theta } \right]x + \left[ { - \cos \theta } \right]y = 0\,\,\,\,\,\,\,.......\left( 1 \right)\) \(\left[ {\cot \theta } \right]x + y = 0\,\,\,\,\,\,\,......\left( 2 \right)\) Case \(I\) Whene \(\theta \in \left( {\frac{\pi }{2},\frac{{2\pi }}{3}} \right)\)…
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