Let the slope of the curve y = cos^$$-$$1 (sin x) be tan$$\theta$$. Then, the value of $$\theta$$ in the interval (0, $$\pi$$) is

Which one of the following is correct in respect of the function $$f(x) = x\sin x + \cos x + {1 \over 2}{\cos ^2}x$$ ?

In which one of the following intervals is the function $$f(x) = {x^2} - 5x + 6$$ decreasing?

A flower-bed in the form of a sector has been fenced by a wire of 40 m length. If the flower-bed has the greatest possible area, then what is the radius of the sector?