1

IIT-JEE 1983

Fill in the Blanks
The function $$y = 2{x^2} - In\,\left| x \right|$$ is monotonically increasing for values of $$x\left( {x \ne 0} \right)$$ satisfying the inequalities ......... and monotonically decreasing for values of $$x$$ satisfying the inequalities ............

Answer

$$x \in \left( { - {1 \over 2},{\mkern 1mu} 0} \right) \cup \left( {{1 \over 2},{\mkern 1mu} \alpha } \right);{\mkern 1mu} {\mkern 1mu} \left( { - \alpha ,{\mkern 1mu} - {1 \over 2}} \right) \cup \left( {0,{\mkern 1mu} {1 \over 2}} \right)$$
2

IIT-JEE 1983

Fill in the Blanks
The larger of $$\cos \left( {In\,\,\theta } \right)$$ and $$In $$ $$\left( {\cos \,\,\theta } \right)$$ If $${e^{ - \pi /2}} < \theta < {\pi \over 2}$$ is ..................

Answer

$$\cos \left( {In\,\,\theta } \right)$$

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