1. Number of unpaired electrons:
- (A) $\mathrm{O}_{2}$: 2
- (B) $\mathrm{N}_{2}$: 0
- (C) $\mathrm{F}_{2}$: 0
- (D) $\mathrm{S}_{2}$: 2
- (E) $\mathrm{Cl}_{2}$: 0
2. Paramagnetic behavior: - Molecules with unpaired electrons exhibit paramagnetic behavior.
- Therefore, $\mathrm{O}_{2}$ and $\mathrm{S}_{2}$ are paramagnetic.
Therefore, the correct answer is (4) A & D only.
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: