To solve the given problem, we need to analyze the two statements provided with respect to the chemical reactivity of the compounds with p-toluenesulfonyl chloride and the solubility of the resultant products in aqueous NaOH.
Statement I claims that: "All the following compounds react with p-toluenesulfonyl chloride."
The compounds listed are: \(C_6H_5NH_2\) (aniline), \((C_6H_5)_2NH\) (diphenylamine), and \((C_6H_5)_3N\) (triphenylamine).
Explanation:
Therefore, Statement I is false because triphenylamine does not react with p-toluenesulfonyl chloride.
Statement II claims that: "Their products in the above reaction are soluble in aqueous NaOH."
Explanation:
Thus, Statement II is false because the products are not soluble in aqueous NaOH.
The correct answer is: "Both Statement I and Statement II is false".
The reaction with p-toluenesulfonyl chloride (TsCl) is known as the Hinsberg test, which is specific for 1$^\circ$ amines.
Only 1$^\circ$ amines (C$_6$H$_5$NH$_2$) react with TsCl to form sulfonamides that are soluble in aqueous NaOH.
2$^\circ$ amines ((C$_6$H$_5$)$_2$NH) react with TsCl to form sulfonamides that are insoluble in NaOH.
3$^\circ$ amines ((C$_6$H$_5$)$_3$N) do not react with TsCl at all.
Thus:
Statement I: False. Not all the given compounds react with TsCl.
Statement II: False. Only the sulfonamide formed by 1$^\circ$ amines is soluble in NaOH.


Let \( \alpha = \dfrac{-1 + i\sqrt{3}}{2} \) and \( \beta = \dfrac{-1 - i\sqrt{3}}{2} \), where \( i = \sqrt{-1} \). If
\[ (7 - 7\alpha + 9\beta)^{20} + (9 + 7\alpha - 7\beta)^{20} + (-7 + 9\alpha + 7\beta)^{20} + (14 + 7\alpha + 7\beta)^{20} = m^{10}, \] then the value of \( m \) is ___________.