The correct statements about of the following reaction sequence is (are)

Cumene (C₉H₁₂) $$\mathrel{\mathop{\kern0pt\longrightarrow} \limits_{(ii)\,{H_3}{O^ + }}^{(i)\,{O_2}}} $$ P $$\mathrel{\mathop{\kern0pt\longrightarrow} \limits_{}^{CHC{l_3}/NaOH}} $$ Q (major) + R (minor)

Q $$\mathrel{\mathop{\kern0pt\longrightarrow} \limits_{PhC{H_2}Br}^{NaOH}} $$ S

Let $$S = \left\{ {x \in \left( { - \pi ,\pi } \right):x \ne 0, \pm {\pi \over 2}} \right\}.$$ The sum of all distinct solutions of the equation $$\sqrt 3 \,\sec x + \cos ec\,x + 2\left( {\tan x - \cot x} \right) = 0$$ in the set S is equal to

Let $$ - {\pi \over 6} < \theta < - {\pi \over {12}}.$$ Suppose $${\alpha _1}$$ and $${\beta_1}$$ are the roots of the equation $${x^2} - 2x\sec \theta + 1 = 0$$ and $${\alpha _2}$$ and $${\beta _2}$$ are the roots of the equation $${x^2} + 2x\,\tan \theta - 1 = 0.$$ $$If\,{\alpha _1} > {\beta _1}$$ and $${\alpha _2} > {\beta _2},$$ then $${\alpha _1} + {\beta _2}$$ equals

A debate club consists of 6 girls and 4 boys. A team of 4 members is to be select from this club including the selection of a captain (from among these 4 members ) for the team. If the team has to include at most one boy, then the number of ways of selecting the team is