The locus of the mid-points of the perpendiculars drawn from points on the line, x = 2y to the line x = y is :

If the function ƒ defined on $$\left( { - {1 \over 3},{1 \over 3}} \right)$$ by

f(x) = $$\left\{ {\matrix{ {{1 \over x}{{\log }_e}\left( {{{1 + 3x} \over {1 - 2x}}} \right),} & {when\,x \ne 0} \cr {k,} & {when\,x = 0} \cr } } \right.$$

is continuous, then k is equal to_______.

If the mean and variance of eight numbers 3, 7, 9, 12, 13, 20, x and y be 10 and 25 respectively, then x.y is equal to _______.

If the system of linear equations,
x + y + z = 6
x + 2y + 3z = 10
3x + 2y + $$\lambda $$z = $$\mu $$
has more than two solutions, then $$\mu $$ - $$\lambda $$² is equal to ______.