The value of the integral $$\int\limits_0^{2a} {[{{f\left( x \right)} \over {\left\{ {f\left( x \right) + f\left( {2a - x} \right)} \right\}}}]\,dx} $$ is equal to $$a$$.

Find the area of the region bounded by the curve $$C:y=$$
$$\tan x,$$ tangent drawn to $$C$$ at $$x = {\pi \over 4}$$ and the $$x$$-axis.

In the formula X = 3YZ², X and Z have dimensions of capacitance and magnetic induction respectively. The dimensions of Y in MKSQ system are _____________

A boat which has a speed of 5 km/hr in still water crosses a river of width 1 km along the shortest possible path in 15 minutes. The velocity of the river water in km/hr is