Let M and m respectively be the maximum and the minimum values of 1 + sin ² x cos ² x 4 sin 4x 1 + sin ² x cos ² x 4 sin 4x sin ² x cos ² x 1 + 4 sin 4x, x R. Then M⁴ - m⁴ is equal to:

Matrices and Determinants: JEE Main 2025 Mathematics question

JEE Main 2025 · January, Unspecified (session-level dataset) · Q114

JEE Main 2025January, Unspecified (session-level dataset)MathematicsMediumMatrices and Determinants245× since 2002

Let

M

and

m

respectively be the maximum and the minimum values of

\begin{vmatrix} 1 + \sin^2 x & \cos^2 x & 4 \sin 4x \\ 1 + \sin^2 x & \cos^2 x & 4 \sin 4x \\ \sin^2 x & \cos^2 x & 1 + 4 \sin 4x \end{vmatrix}, x \in \mathbf{R}

. Then

M^4 - m^4

is equal to:

JEE Main 2025 Matrices and Determinants Question with Solution (January Unspecified (session-level dataset), Q114) | JEE Arc

JEE Main 2025 · January, Unspecified (session-level dataset) · Q114

JEE Main 2025January, Unspecified (session-level dataset)MathematicsMediumMatrices and Determinants245× since 2002

Let

M

and

m

respectively be the maximum and the minimum values of

\begin{vmatrix} 1 + \sin^2 x & \cos^2 x & 4 \sin 4x \\ 1 + \sin^2 x & \cos^2 x & 4 \sin 4x \\ \sin^2 x & \cos^2 x & 1 + 4 \sin 4x \end{vmatrix}, x \in \mathbf{R}

. Then

M^4 - m^4

is equal to: