The length of the chord of the parabola x² $$=$$ 4y having equation x – $$\sqrt 2 y + 4\sqrt 2 = 0$$  is -

The curve amongst the family of curves represented by the differential equation, (x² – y²)dx + 2xy dy = 0 which passes through (1, 1) is :

The positive value of $$\lambda $$ for which the co-efficient of x² in the expression x² $${\left( {\sqrt x + {\lambda \over {{x^2}}}} \right)^{10}}$$ is 720, is -

The value of $$\lambda $$ such that sum of the squares of the roots of the quadratic equation, x² + (3 – $$\lambda $$)x + 2 = $$\lambda $$ has the least value is -