Let the foot of perpendicular from a point P(1, 2, $$-$$1) to the straight line $$L:{x \over 1} = {y \over 0} = {z \over { - 1}}$$ be N. Let a line be drawn from P parallel to the plane x + y + 2z = 0 which meets L at point Q. If $$\alpha$$ is the acute angle between the lines PN and PQ, then cos$$\alpha$$ is equal to ________________.

Let y = y(x) be solution of the following differential equation $${e^y}{{dy} \over {dx}} - 2{e^y}\sin x + \sin x{\cos ^2}x = 0,y\left( {{\pi \over 2}} \right) = 0$$ If $$y(0) = {\log _e}(\alpha + \beta {e^{ - 2}})$$, then $$4(\alpha + \beta )$$ is equal to ______________.

If the value of

$${\left( {1 + {2 \over 3} + {6 \over {{3^2}}} + {{10} \over {{3^3}}} + ....upto\,\infty } \right)^{{{\log }_{(0.25)}}\left( {{1 \over 3} + {1 \over {{3^2}}} + {1 \over {{3^3}}} + ....upto\,\infty } \right)}}$$

is $$l$$, then $$l$$² is equal to _______________.

Consider the following frequency distribution :

Class :	10-20	20-30	30-40	40-50	50-60
Frequency :	$$\alpha $$	110	54	30	$$\beta $$

If the sum of all frequencies is 584 and median is 45, then | $$\alpha$$ $$-$$ $$\beta$$ | is equal to _______________.