Q72. Let the sum of the maximum and the minimum values of the function $f ( x ) = \frac { 2 x ^ { 2 } - 3 x + 8 } { 2 x ^ { 2 } + 3 x + 8 }$ be $\frac { \mathrm { m } } { \mathrm { n } }$, where $\operatorname { gcd } ( \mathrm { m } , \mathrm { n } ) = 1$. Then $\mathrm { m } + \mathrm { n }$ is equal to : (1) 195 (2) 201 (3) 217 (4) 182 Q73. Let $f : \mathbf { R } \rightarrow \mathbf { R }$ be a function given by $f ( x ) = \left\{ \begin{array} { l l } \frac { 1 - \cos 2 x } { x ^ { 2 } } , & x < 0 \\ \alpha , & x = 0 \\ \frac { \beta \sqrt { 1 - \cos x } } { x } , & x > 0 \end{array} \right.$, where $\alpha , \beta \in \mathbf { R }$. If $f$ is continuous at $x = 0$, then $\alpha ^ { 2 } + \beta ^ { 2 }$ is equal to : (1) 3 (2) 12 (3) 48 (4) 6
Q72. Let the sum of the maximum and the minimum values of the function $f ( x ) = \frac { 2 x ^ { 2 } - 3 x + 8 } { 2 x ^ { 2 } + 3 x + 8 }$ be $\frac { \mathrm { m } } { \mathrm { n } }$, where $\operatorname { gcd } ( \mathrm { m } , \mathrm { n } ) = 1$. Then $\mathrm { m } + \mathrm { n }$ is equal to :\\
(1) 195\\
(2) 201\\
(3) 217\\
(4) 182
Q73.\\
Let $f : \mathbf { R } \rightarrow \mathbf { R }$ be a function given by $f ( x ) = \left\{ \begin{array} { l l } \frac { 1 - \cos 2 x } { x ^ { 2 } } , & x < 0 \\ \alpha , & x = 0 \\ \frac { \beta \sqrt { 1 - \cos x } } { x } , & x > 0 \end{array} \right.$, where $\alpha , \beta \in \mathbf { R }$. If $f$ is continuous at $x = 0$, then $\alpha ^ { 2 } + \beta ^ { 2 }$ is equal to :\\
(1) 3\\
(2) 12\\
(3) 48\\
(4) 6