The spin-only magnetic moment (\(\mu\)) value (B.M.) of the compound with the strongest oxidising power among \(Mn_2O_3\), \(TiO\), and \(VO\) is ……. B.M. (Nearest integer).
The magnetic moment (\(\mu\)) is given by: \[ \mu = \sqrt{n(n+2)} { B.M.} \] where \( n \) is the number of unpaired electrons.
- \( Mn_2O_3 \): Mn oxidation state is \( +3 \) (\(d^4\)), unpaired electrons = 4.
- \( TiO \): Ti oxidation state is \( +2 \) (\(d^2\)), unpaired electrons = 2.
- \( VO \): V oxidation state is \( +2 \) (\(d^3\)), unpaired electrons = 3.
Since \( Mn_2O_3 \) has the highest oxidation state and strongest oxidising power, we calculate: \[ \mu = \sqrt{4(4+2)} = \sqrt{24} \approx 4.9 \] Rounding to the nearest integer, the answer is 4 B.M.
The sum of the spin-only magnetic moment values (in B.M.) of $[\text{Mn}(\text{Br})_6]^{3-}$ and $[\text{Mn}(\text{CN})_6]^{3-}$ is ____.
Match List-I with List-II and select the correct option.
Which one of the following graphs accurately represents the plot of partial pressure of CS₂ vs its mole fraction in a mixture of acetone and CS₂ at constant temperature?

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 ___________.