If $$y(t)$$ is a solution of $$\left( {1 + t} \right){{dy} \over {dt}} - ty = 1$$ and $$y\left( 0 \right) = - 1,$$ then $$y(1)$$ is equal to

If $$l\left( {m,n} \right) = \int\limits_0^1 {{t^m}{{\left( {1 + t} \right)}^n}dt,} $$ then the expression for $$l(m, n)$$ in terms of $$l(m+n, n-1)$$ is

If $$\,\left| z \right| = 1$$ and $$\omega = {{z - 1} \over {z + 1}}$$ (where $$z \ne - 1$$), then $${\mathop{\rm Re}\nolimits} \left( \omega \right)$$ is

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