WBJEE · Maths · Area Under Curves
If the point \((2 \cos \theta, 2 \sin \theta)\) for \(0 \in(0,2 \pi)\) lies in the region between the lines \(x+y=2\) and \(x-y=2\) containing the origin, then \(\theta\) lies in
- A \(\left(\theta, \frac{\pi}{2}\right) \cup\left(\frac{3 \pi}{2}, 2 \pi\right)\)
- B \([0, n]\)
- C \(\left(\frac{\pi}{2} \cdot \frac{3 \pi}{2}\right)\)
- D \(\left[\frac{\pi}{4}, \frac{\pi}{2}\right]\)
Answer & Solution
Correct Answer
(C) \(\left(\frac{\pi}{2} \cdot \frac{3 \pi}{2}\right)\)
Step-by-step Solution
Detailed explanation
Given that \((2 \cos \theta, 2 \sin \theta)\) will lie on the circle \(x^{2}+y^{2}=4\) (from the given figure). Since, point lies on the region containing origin. So, point will be on the shaded region. \(\therefore\) \(\theta \in\left(\frac{\pi}{2}, \frac{3 \pi}{2}\right)\)
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