The \( t_{2g}^3 e_g^1 \) configuration is typical for a weak field ligand. In such cases, the electrons tend to occupy the higher energy \( e_g \) orbitals, as opposed to pairing up in the lower energy \( t_{2g} \) orbitals. This leads to a low spin complex.
Final Answer: Weak field ligand, low spin complex.
A hydrocarbon which does not belong to the same homologous series of carbon compounds is
Let $ P_n = \alpha^n + \beta^n $, $ n \in \mathbb{N} $. If $ P_{10} = 123,\ P_9 = 76,\ P_8 = 47 $ and $ P_1 = 1 $, then the quadratic equation having roots $ \alpha $ and $ \frac{1}{\beta} $ is: