Step 1: Basicity and Lanthanoid Contraction: - As we move across the lanthanide series, atomic size decreases due to lanthanoid contraction.
- \( La(OH)_3 \) has a larger ionic radius, making it more basic than \( Lu(OH)_3 \).
Step 2: Explanation: - Larger ionic size in \( La^{3+} \) leads to weaker bond strength in \( La(OH)_3 \), making hydroxide ions (\( OH^- \)) more available.
- \( Lu^{3+} \) has a smaller radius, leading to a stronger attraction between \( Lu^{3+} \) and \( OH^- \), reducing basicity.
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 $