To determine the basic strength of the given molecules, we need to consider the electron-donating and electron-withdrawing effects of substituents on the phenyl group.
- (A): \(\text{C}_6\text{H}_4\text{NH}_2\text{O}\) (Hydroxyl group is an electron-donating group, which increases the basicity of the amine group.)
- (B): \(\text{C}_6\text{H}_4\text{NH}_2\text{MeO}\) (Methoxy group is a strong electron-donating group, which further increases the basicity of the amine group.)
- (C): \(\text{C}_6\text{H}_4\text{NH}_2\text{NO}_2\) (Nitro group is a strong electron-withdrawing group, which decreases the basicity of the amine group.)
- (D): \(\text{C}_6\text{H}_4\text{NH}_2\text{CH}_3\) (Methyl group is a weak electron-donating group, but its effect is weaker than the hydroxyl or methoxy group.) The order of basic strength is determined by the electron-donating ability of the substituent groups. Therefore, the order is: \[ \text{B}>\text{A}>\text{D}>\text{C} \] Thus, the correct order is \( B>A>C>D \), which corresponds to option (4).
If \[ f(x) = \int \frac{1}{x^{1/4} (1 + x^{1/4})} \, dx, \quad f(0) = -6 \], then f(1) is equal to:
The term independent of $ x $ in the expansion of $$ \left( \frac{x + 1}{x^{3/2} + 1 - \sqrt{x}} \cdot \frac{x + 1}{x - \sqrt{x}} \right)^{10} $$ for $ x>1 $ is: