A rectangle R with end points of one of its sides as (1, 2) and (3, 6) is inscribed in a circle. If the equation of a diameter of the circle is 2x $$-$$ y + 4 = 0, then the area of R is ____________.

A projectile is launched at an angle '$$\alpha$$' with the horizontal with a velocity 20 ms^$$-$$1. After 10 s, its inclination with horizontal is '$$\beta$$'. The value of tan$$\beta$$ will be : (g = 10 ms^$$-$$2).

A girl standing on road holds her umbrella at 45$$^\circ$$ with the vertical to keep the rain away. If she starts running without umbrella with a speed of 15$$\sqrt2$$ kmh^$$-$$1, the rain drops hit her head vertically. The speed of rain drops with respect to the moving girl is :

A silver wire has a mass (0.6 $$\pm$$ 0.006) g, radius (0.5 $$\pm$$ 0.005) mm and length (4 $$\pm$$ 0.04) cm. The maximum percentage error in the measurement of its density will be :