JEE Advance - Mathematics (2006 - No. 11)
Let $$\theta \in \left( {0,{\pi \over 4}} \right)$$ and $${t_1} = {\left( {\tan \theta } \right)^{\tan \theta }},\,\,\,\,{t_2} = \,\,{\left( {\tan \theta } \right)^{\cot \theta }}$$, $${t_3}\, = \,\,{\left( {\cot \theta } \right)^{\tan \theta }}$$ and $${t_4}\, = \,\,{\left( {\cot \theta } \right)^{\cot \theta }},$$then
$${t_1} > {t_2} > {t_3} > {t_4}$$
$${t_4} > {t_3} > {t_1} > {t_2}$$
$${t_3} > {t_1} > {t_2} > {t_4}$$
$${t_2} > {t_3} > {t_1} > {t_4}$$