Evaluate the following : $$\,\,\int\limits_0^{\pi /2} {{{x\sin x\cos x} \over {{{\cos }^4}x + {{\sin }^4}x}}} dx$$

Sketch the region bounded by the curves $$y = \sqrt {5 - {x^2}} $$ and $$y = \left| {x - 1} \right|$$ and find its area.

Plank' constant has dimension __________.

Two identical trains are moving on rails along the equator on the earth in opposite directions with the same speed. They will exert the same pressure on the rails.