(i) Ethanol is heated with sodium bromide and conc. \( H_2SO_4 \):
(ii) Toluene reacts with \( Cl_2 \) gas in the presence of Fe powder in the dark:
(iii) Benzene diazonium chloride reacts with water:
(iv) 2-Bromopentane is heated with alcoholic \( KOH \):
(i) Ethanol is heated with sodium bromide and conc. \( H_2SO_4 \): \[ C_2H_5OH + NaBr + H_2SO_4 \rightarrow C_2H_5Br + NaHSO_4 + H_2O. \]
(ii) Toluene reacts with \( Cl_2 \) gas in the presence of Fe powder in the dark:
\[ C_6H_5CH_3 + Cl_2 \xrightarrow{Fe} C_6H_4ClCH_3 + HCl. \]
(iii) Benzene diazonium chloride reacts with water:
\[ C_6H_5N_2^+Cl^- + H_2O \xrightarrow{\Delta} C_6H_5OH + N_2 + HCl. \]
(iv) 2-Bromopentane is heated with alcoholic \( KOH \):
\[ CH_3CH(Br)CH_2CH_2CH_3 \xrightarrow{alc.\,KOH} CH_3CH=CHCH_2CH_3 + HBr. \]
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 $