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Question #41250

Difficulty: 8/10 | 🟢 Free

The Question

Let $A(\theta) = \begin{pmatrix} 1+\sin^2\theta & \cos^2\theta & \sin 2\theta \\ \sin^2\theta & 1+\cos^2\theta & \sin 2\theta \\ \sin^2\theta & \cos^2\theta & 1+\sin 2\theta \end{pmatrix}$ and $f(\theta) = |\text{adj}(2 A(\theta))|$ . The maximum value of $f(\theta)$ for $\theta \in \mathbb{R}$ is

Options

A.
36
B.
72
C.
144
D.
576

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

Determinant Scaling Property|Adjoint-Determinant Relation|Parametric form pitfalls

Why This Question Is Tricky

Common Mistakes

This question tests the student's ability to correctly combine the determinant scaling property and the adjoint-determinant relation.

The core trap lies in evaluating $|\text{adj}(kA)|$ .

Students frequently commit the 'Index Fallacy' by assuming $|\text{adj}(kA)| = k^{n-1}|A|^{n-1}$ or $k^n|A|^{n-1}$ , rather than the correct $k^{n(n-1)}|A|^{n-1}$ .

By embedding this in a parametric matrix, the student is forced to first correctly evaluate and maximize the variable determinant $|A(\theta)|$ , ensuring they cannot simply guess the scaling factor without completing the multi-step algebraic process.

Quick Facts About This Question

Question Information

Subject	Mathematics
Chapter	Determinants - Class 12
Concept	Determinant Scaling Property
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free