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Jee Main 2025 — Hard 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

hard • PYQ 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+sin⁡2xcos⁡2x4sin⁡4xsin⁡2x1+cos⁡2x4sin⁡4xsin⁡2xcos⁡2x1+4sin⁡4x],x∈R 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 M4−m4 M^4 - m^4 is equal to:
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