Sodium phenoxide when heated with $$C{O_2}$$ under pressure at $${125^ \circ }C$$ yields a product which on acetylation products $$C.$$



The major product $$C$$ would be

Let $$f_k\left( x \right) = {1 \over k}\left( {{{\sin }^k}x + {{\cos }^k}x} \right)$$ where $$x \in R$$ and $$k \ge \,1.$$
Then $${f_4}\left( x \right) - {f_6}\left( x \right)\,\,$$ equals :

If z is a complex number such that $$\,\left| z \right| \ge 2\,$$, then the minimum value of $$\,\,\left| {z + {1 \over 2}} \right|$$ :

If $$a \in R$$ and the equation $$ - 3{\left( {x - \left[ x \right]} \right)^2} + 2\left( {x - \left[ x \right]} \right) + {a^2} = 0$$ (where [$$x$$] denotes the greater integer $$ \le x$$) has no integral solution, then all possible values of a lie in the interval :