Solution:
(i) Preparation of ethanol from fermentation of sugar
C₆H₁₂O₆ ⟶ (Yeast) 2C₂H₅OH + 2CO₂
(ii) Reimer-Tiemann Reaction
C₆H₅OH + CHCl₃ + NaOH ⟶ o-Hydroxybenzaldehyde + p-Hydroxybenzaldehyde
(iii) Williamson’s Synthesis
R-O⁻ + R'-X ⟶ R-O-R' + X⁻
OR
(i) Preparation of alcohols from Grignard’s reagent:
Primary Alcohol:
R-MgX + HCHO ⟶ (H₂O) R-CH₂OH + Mg(OH)X
Secondary Alcohol:
R-MgX + CH₃CHO ⟶ (H₂O) R-CHOH-CH₃ + Mg(OH)X
Tertiary Alcohol:
R-MgX + R'CO-R'' ⟶ (H₂O) R-C(OH)-R'R'' + Mg(OH)X
Write the product obtained when D-glucose reacts with \( H_2N - OH \).
Find the values of \( x, y, z \) if the matrix \( A \) satisfies the equation \( A^T A = I \), where
\[ A = \begin{bmatrix} 0 & 2y & z \\ x & y & -z \\ x & -y & z \end{bmatrix} \]
(b) Order of the differential equation: $ 5x^3 \frac{d^3y}{dx^3} - 3\left(\frac{dy}{dx}\right)^2 + \left(\frac{d^2y}{dx^2}\right)^4 + y = 0 $