If $${\log _5}{{(a + b)} \over 3} = {{{{\log }_5}a + {{\log }_5}b} \over 2}$$, then $${{{a^4} + {b^4}} \over {{a^2}{b^2}}}$$ is equal to

The number of distinct solutions of the equation $${5 \over 4}{\cos ^2}2x + {\cos ^4}x + {\sin ^4}x + {\cos ^6}x = 2$$ in the interval [0, 2$$\pi$$] is

If the tangent at a point $$\left( {4\cos \phi ,{{16} \over {\sqrt {11} }}\sin \phi } \right)$$ to the ellipse $$16{x^2} + 11{y^2} = 256$$ is also a tangent to $${x^2} + {y^2} - 2x = 15$$, then $$\phi$$ equsls

The distance of point of intersection of the tangents to the parabola x = 4y $$-$$ y² drawn at the points where it is meet by Y-axis, from its focus is