The function $$f(x) = \sec \left[ {\log \left( {x + \sqrt {1 + {x^2}} } \right)} \right]$$ is

On the set $\mathbb{R}$ of real numbers the relation $\rho$, defined by $\mathrm{x} \rho \mathrm{y}(\mathrm{x}, \mathrm{y} \in \mathbb{R})$ iff

Let $A_1, A_2, \ldots, A_6$ are six sets, each with four elements and $B_1, B_2, \ldots ., B_n$ are $n$ sets, each with two elements. Let $S=A_1 \cup A_2 \cup \ldots \cup A_6=B_1 \cup B_2 \cup \ldots \cup B_n$.

Given that each element of $S$ belongs to exactly four of the A's and to exactly three of the B's. Then $n$ is

The number of reflexive relations on a set $A$ of $n$ elements is equal to