The height at which the end of a rope of length $$l$$ should be tied so that a man pulling at the other end may have the greatest tendency to overturn the pillar, is A. $$\frac{3}{4}l$$ B. $$\frac{1}{2}l$$ C. $$\frac{l}{{\sqrt 2 }}$$ D. $$\frac{2}{{\sqrt 3 }}l$$

The correct answer is $\boxed{\frac{l}{{\sqrt 2 }}}$.

The tendency of the man to overturn the pillar is proportional to the torque he exerts. The torque is the product of the force he exerts and the distance from the point of application of the force to the pivot point. The force the man exerts is equal to his weight, which is $mg$, where $m$ is his mass and $g$ is the acceleration due to gravity. The distance from the point of application of the force to the pivot point is the length of the rope, $l$.

The torque is maximized when the force is applied at a right angle to the rope. This is the case when the rope is tied at a height of $\frac{l}{{\sqrt 2 }}$.

Option A is incorrect because it is not a right angle to the rope. Option B is incorrect because it is not the maximum torque. Option C is incorrect because it is not a right angle to the rope. Option D is incorrect because it is not the maximum torque.