jee-main 2024 Q70

jee-main · India · session1_30jan_shift1 3x3 Matrices Direct Determinant Computation
$f ( x ) = \left| \begin{array} { c c c } 2 \cos ^ { 4 } x & 2 \sin ^ { 4 } x & 3 + \sin ^ { 2 } 2 x \\ 3 + 2 \cos ^ { 4 } x & 2 \sin ^ { 4 } x & \sin ^ { 2 } 2 x \\ 2 \cos ^ { 4 } x & 3 + 2 \sin ^ { 4 } x & \sin ^ { 2 } 2 x \end{array} \right|$ then $\frac { 1 } { 5 } f ^ { \prime } ( 0 )$ is equal to:
(1) 0
(2) 1
(3) 2
(4) 6
$f ( x ) = \left| \begin{array} { c c c } 2 \cos ^ { 4 } x & 2 \sin ^ { 4 } x & 3 + \sin ^ { 2 } 2 x \\ 3 + 2 \cos ^ { 4 } x & 2 \sin ^ { 4 } x & \sin ^ { 2 } 2 x \\ 2 \cos ^ { 4 } x & 3 + 2 \sin ^ { 4 } x & \sin ^ { 2 } 2 x \end{array} \right|$ then $\frac { 1 } { 5 } f ^ { \prime } ( 0 )$ is equal to:\\
(1) 0\\
(2) 1\\
(3) 2\\
(4) 6