jee-main 2025 Q14

jee-main · India · session1_29jan_shift1 Matrices Determinant and Rank Computation
Let M and m respectively be the maximum and the minimum values of $$f(x) = \begin{vmatrix} 1+\sin^2 x & \cos^2 x & 4\sin 4x \\ \sin^2 x & 1+\cos^2 x & 4\sin 4x \\ \sin^2 x & \cos^2 x & 1+4\sin 4x \end{vmatrix}, \quad x \in \mathbf{R}.$$ Then $M^4 - m^4$ is equal to:
(1) 1280
(2) 1295
(3) 1215
(4) 1040
Let M and m respectively be the maximum and the minimum values of
$$f(x) = \begin{vmatrix} 1+\sin^2 x & \cos^2 x & 4\sin 4x \\ \sin^2 x & 1+\cos^2 x & 4\sin 4x \\ \sin^2 x & \cos^2 x & 1+4\sin 4x \end{vmatrix}, \quad x \in \mathbf{R}.$$
Then $M^4 - m^4$ is equal to:\\
(1) 1280\\
(2) 1295\\
(3) 1215\\
(4) 1040