The decreasing values of bond angles from NH₃ (106^o) to SbH₃ (91^o ) down group-15 of the periodic table is due to

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