Number of stereoisomers possible for the complexes, $\left[\mathrm{CrCl}_{3}(\mathrm{py})_{3}\right]$ and $\left[\mathrm{CrCl}_{2}(\mathrm{ox})_{2}\right]^{3-}$ are respectively} (py = pyridine, ox = oxalate)
1. $\left[\mathrm{CrCl}_{3}(\mathrm{py})_{3}\right]$: - Facial and meridional isomers are possible. - Total stereoisomers = 2.
2. $\left[\mathrm{CrCl}_{2}(\mathrm{ox})_{2}\right]^{3-}$:
- Geometrical isomers: cis and trans.
- Optical isomers for cis: 2.
- Optical isomers for trans: 1.
- Total stereoisomers = 3.
Therefore, the correct answer is (3) 2 & 3.
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: