- Statement I: The radius of isoelectronic species increases as the nuclear charge decreases. So, the correct order is \( {Mg}^{2+}<{Na}^+<{F}^-<{O}^{2-} \), which is correct.
- Statement II: The magnitude of electron gain enthalpy of halogens increases as the size of the atom increases. The correct order should be \( {Cl}>{Br}>{I}>{F} \), not \( {Cl}>{F}>{Br}>{I} \). Therefore, this statement is incorrect. Thus, the correct answer is that Statement I is correct but Statement II is incorrect.
Let one focus of the hyperbola $ \frac{x^2}{a^2} - \frac{y^2}{b^2} = 1 $ be at $ (\sqrt{10}, 0) $, and the corresponding directrix be $ x = \frac{\sqrt{10}}{2} $. If $ e $ and $ l $ are the eccentricity and the latus rectum respectively, then $ 9(e^2 + l) $ is equal to:
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: