Tangent is drawn to ellipse
$${{{x^2}} \over {27}} + {y^2} = 1\,\,\,at\,\left( {3\sqrt 3 \cos \theta ,\sin \theta } \right)\left( {where\,\,\theta \in \left( {0,\pi /2} \right)} \right)$$.

Then the value of $$\theta $$ such that sum of intercepts on axes made by this tangent is minimum, is

In $$\left[ {0,1} \right]$$ Languages Mean Value theorem is NOT applicable to

If the angles of a triangle are in the ratio $$4:1:1$$, then the ratio of the longest side to the perimeter is

The focal chord to $${y^2} = 16x$$ is tangent to $${\left( {x - 6} \right)^2} + {y^2} = 2,$$ then the possible values of the slope of the chord, are