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

Let $W$ denote the words in the English dictionary. Define the relation $R$ by

$R=\{(x, y) \in W \times W \mid$ the words $x$ and $y$ have at least one letter in common}. Then, $R$ is

A solid which is not transparent to visible light and whose conductivity increases with temperature is formed by

The circuit has two oppositively connected ideal diodes in parallel. What is the current following in the circuit?