Match the following complexes with their number of unpaired electrons:
List-I (Complex) | List-II (No. of unpaired electrons) | ||
---|---|---|---|
A) \([\mathrm{MnCl}_6]^{3-}\) | I) 5 | ||
B) \([\mathrm{FeF}_6]^{3-}\) | II) 2 | ||
C) \([\mathrm{Mn(CN)}_6]^{3-}\) | III) 0 | ||
D) \([\mathrm{Co(C}_2\mathrm{O}_4)_3]^{3-}\) | IV) 4 |
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 $