Suppose a population A has 100 observations 101, 102,........, 200, and another population B has 100 observations 151, 152,......., 250. If V_A and V_B represent the variances of the two populations, respectively, then $${{{V_A}} \over {{V_B}}}$$ is

If $$0 < x < \pi $$ and $$\cos x + \sin x = {1 \over 2},$$ then $$\tan x$$ is :

The value of $$\int\limits_1^a {\left[ x \right]} f'\left( x \right)dx,a > 1$$ where $${\left[ x \right]}$$ denotes the greatest integer not exceeding $$x$$ is

The set of points where $$f\left( x \right) = {x \over {1 + \left| x \right|}}$$ is differentiable is