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Question #40521

Difficulty: 8/10 | 🟢 Free

The Question

Find the complete solution set for $x$ satisfying the inequality: $\frac{\sin^{-1}(x) \cdot \left(3\cos^{-1}(x) - \pi\right)}{1 - 4x^2} \ge 0$

Options

A.
$\left[-1, -\frac{1}{2}\right) \cup \left[0, \frac{1}{2}\right) \cup \left(\frac{1}{2}, 1\right]$
B.
$\left(- \frac{1}{2}, 0\right] \cup \left(\frac{1}{2}, 1\right]$
C.
$\left[-1, -\frac{1}{2}\right) \cup [0, 1]$
D.
$\left(-\infty, -\frac{1}{2}\right) \cup [0, \infty)$

Check Your Answer

Correct Answer

Step-by-Step Solution

Explanation

How the Examiner Thinks

Specialist

Targeted practice for niche, high-difficulty concepts that frequently appear in JEE Advanced exams.

Concepts Behind This Question

Wavy Curve (Method of Intervals)|Algebraic-Trigonometric Graphical Mapping|Domain Restrictions

Why This Question Is Tricky

Common Mistakes

This question tests the intersection of the Wavy Curve method with inverse trigonometric domain restrictions.

The primary trap is twofold: first, students often forget to restrict the final solution to the principal domain $[-1, 1]$ of $\sin^{-1}(x)$ and $\cos^{-1}(x)$ , leading to unbounded intervals.

Second, they may cancel the common sign-equivalent factor $(1/2 - x)$ algebraically without explicitly excluding the critical point $x = 1/2$ from the final solution set, leading them to incorrectly choose an option that includes $1/2$ as a valid solution.

Quick Facts About This Question

Question Information

Subject	Mathematics
Chapter	Linear Inequalities - Class 11
Concept	Wavy Curve (Method of Intervals)
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free