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Jee Main 2025Hard JEE math MCQ

Let \( M \) and \( m \) respectively be the maximum and the minimum values of \[ f(x) = \begin{bmatrix} 1 + \sin^2 x \cos^2 x 4\sin 4x \\ \sin^2 x 1 + \cos^2 x 4\sin 4x \\ \sin^2 x \cos^2 x 1 + 4\sin 4x \end{bmatrix}, x \in \mathbb{R} \] Then \( M^4 - m^4 \) is equal to:
  1. A. \quad 1280 \\
  2. B. \quad 1295 \\
  3. C. \quad 1215 \\
  4. D. \quad 1040 \\

Solution

The correct option is **A**. (A. \quad 1280 \\)

MATH

hardPYQ Reworded
Question
Read carefully, then pick the best option.
Let M M and m m respectively be the maximum and the minimum values of f(x)=[1+sin2xcos2x4sin4xsin2x1+cos2x4sin4xsin2xcos2x1+4sin4x],xR f(x) = \begin{bmatrix} 1 + \sin^2 x \cos^2 x 4\sin 4x \\ \sin^2 x 1 + \cos^2 x 4\sin 4x \\ \sin^2 x \cos^2 x 1 + 4\sin 4x \end{bmatrix}, x \in \mathbb{R} Then M4m4 M^4 - m^4 is equal to:
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