




Step 1: Analyzing the given reaction.
The given reaction involves the reduction of a molecule containing a carbonyl group (C=O) and an amide group (-NH\(_2\)) using lithium aluminum hydride (LiAlH\(_4\)), followed by hydrolysis with H\(_3\)O\(^+\).
1. Step 1: Reduction with LiAlH\(_4\)
Lithium aluminum hydride (LiAlH\(_4\)) is a strong reducing agent. When it reacts with a carbonyl compound (such as a ketone or aldehyde), it reduces the carbonyl group to a primary or secondary alcohol. \item In this case, the carbonyl group (C=O) of the given compound will be reduced to a hydroxyl group (-OH), resulting in an intermediate amide being reduced to a primary amine group (-NH\(_2\)). The structure of the intermediate product will be: \[ \text{H}_2\text{NC} - \text{CH}_2 - \text{CH}_2\text{OH} \] where the ketone group is reduced to an alcohol group.
2. Step 2: Hydrolysis with H\(_3\)O\(^+\)
After reduction, the product is treated with an acidic solution (H\(_3\)O\(^+\)), which will hydrolyze the intermediate and result in a final product where the amide group has been converted to an amine group (-NH\(_2\)) attached to a hydroxyl group (-OH). This confirms the product as: \[ \text{H}_2\text{N} - \text{CH}_2\text{OH} \] This is the final product, and it is a primary amine with a hydroxyl group attached to the adjacent carbon. Thus, the product 'X' is \( \text{H}_2\text{N} - \text{CH}_2\text{OH} \).
The colour of the solution observed after about 1 hour of placing iron nails in copper sulphate solution is:
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 ___________.