List-I Tetrahedral Complex | List-II Electronic configuration |
---|---|
(A) TiCl4 | (I) e2, t20 |
(B) [FeO4]2- | (II) e4, t23 |
(C) [FeCl4]- | (III) e0, t22 |
(D) [CoCl4]2- | (IV) e2, t23 |
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: