jee-main 2023 Q78

jee-main · India · session1_25jan_shift2 Composite & Inverse Functions Find or Apply an Inverse Function Formula
If the function $f ( x ) = \left\{ \begin{array} { c l } ( 1 + | \cos x | ) \frac { \lambda } { | \cos x | } , & 0 < x < \frac { \pi } { 2 } \\ \mu , & x = \frac { \pi } { 2 } \\ e ^ { \frac { \cot 6 x } { \cot 4 x } } , & \frac { \pi } { 2 } < x < \pi \end{array} \right.$ is continuous at $x = \frac { \pi } { 2 }$, then $9 \lambda + 6 \log _ { e } \mu + \mu ^ { 6 } - e ^ { 6 \lambda }$ is equal to
(1) 11
(2) 8
(3) $2 e ^ { 4 } + 8$
(4) 10
If the function $f ( x ) = \left\{ \begin{array} { c l } ( 1 + | \cos x | ) \frac { \lambda } { | \cos x | } , & 0 < x < \frac { \pi } { 2 } \\ \mu , & x = \frac { \pi } { 2 } \\ e ^ { \frac { \cot 6 x } { \cot 4 x } } , & \frac { \pi } { 2 } < x < \pi \end{array} \right.$ is continuous at $x = \frac { \pi } { 2 }$, then $9 \lambda + 6 \log _ { e } \mu + \mu ^ { 6 } - e ^ { 6 \lambda }$ is equal to\\
(1) 11\\
(2) 8\\
(3) $2 e ^ { 4 } + 8$\\
(4) 10