If the function $f$ defined on $\left( {\frac{\pi }{6},\frac{\pi }{3}} \right)$ by $f\,(x)\, = \,\left\{ {\begin{array}{*{20}{c}}
{\frac{{\sqrt 2 \,\cos \,x - \,1}}{{\cot \,x\, - \,1}}\,,\,x\, \ne \,\frac{\pi }{4}}\\
{k,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,x\, = \frac{\pi }{4}}
\end{array}} \right.$ is continuous, then $k$ is equal to
→Let A = {2, 3, 4, 5, ..., 17, 18}. Let $'\simeq'$ be the equivalence relation on A × A, cartesian product of A with itself, defined by $(\text{a, b})\simeq(\text{c, d)}$ if ad = bc. Then, the number of ordered pairs of the equivalence class of (3, 2) is:
→